ECON 301 Midterm Flashcards

1
Q

Risk Premium + How to Calculate

A

Risk Premium: max amount of money a risk-averse person would pay to avoid taking a risk and get certain expected value of uncertain wealth

  1. Exact Method: E(U(W))=U(E(W)-F)
    Approximate Method - Coefficients of Risk-Aversion rA(W)=-U”(W)U’(W) Arrow-Prate coefficient of absolute risk aversion at wealth, summary and measure of degree of risk=aversion, changes with wealth, F=rA(EW)Var(W)2
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2
Q

Certainty Equivalent + How to Calculate

A

Certainty Equivalent CE=E(W)-F or CE=U-1(E(U(W)))level of income/wealth, expected utility of random wealth, best lottery/random wealth with highest expected utility

point at which the individual is indifferent between the risky option and receiving a certain, fixed amount

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3
Q

When is Risk-Premium Negative + Pareto Improvement of Efficiency

A
  • Risk-Loving implies negative risk-premium : they need to be compensated to avoid uncertainty
  • Pareto Improvement of Efficiency: risk loving/neutral give insurance to risk averse in exchange for a fee
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4
Q

Risk-Attitudes v. Actuarially Fair Condition Table

A

See doc

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5
Q

How is Demand of Insurance (x) Calculated

A

Maximize GU(WG-px)+BU(WB-px+x)
First Order Set to 0: GU’(WG-px)(-p)+BU’(WB-px+x)(1-p)=0
Confirm Concave Maximum (not minimum): GU”(WG-px)p2+BU”(WB-px+x)(1-p)2<0
BU’(WB-px+x)(1-p)=GU’(WG-px)(p)
U’(WB-px+x)U’(WG-px)=G(p)B(1-p)
Condition C: U’(WB-px+x)U’(WG-px)=1-BB(p)(1-p) Optimal x depends on probability of accidents B and price of insurance p
Ex. U(W)=log(W),U’(W)=1x, U”(W)=-1W2<0, WG-pxWB-px+x=p1-p1-BB

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6
Q

Insurance

A

Replaces an uncertain wealth with a more certain one, allows consumer to reduce/eliminate risk

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7
Q

Risk Averse + Preference + Marginal Utility of Wealth + Proof

A

Risk-Aversion: EU(W) <U(EW) prefers expected value of income guaranteed rather than random income/lottery
* Decreasing Marginal Utility of Wealth U’‘(W)<0 concavity of utility of wealth U(W): values of an additional dollar is smaller the more money you have, not willing to risk getting another dollar when you can lose a dollar with equal probability that has higher marginal utility
* Utility Functions: U(W)=log(W), U(W)=W=W1/2, U(W)=aW-bW2
Proof of Risk-Aversion + Loving: Fundamental Theorem of Calculus

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8
Q

Risk Neutral + Preference + Marginal Utility of Wealth + Proof

A

EU(W)=U(EW)
Constant Marginal Utility of Wealth U’‘(W)=0, U(W)=a+bW,b>0 linearity of utility of wealth: values of an additional dollar is same the more money you have, indifferent b/w random income and expected value of income, risk of getting another dollar when you can only lose a dollar with equal probability that has same marginal utility
Proof of Risk-Neutrality: EU(W)=i=1niU(Wi)=i=1ni(a+bW)=i=1nia+i=1nibWi=a+bi=1niWi=a+bEW=U(EW)

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9
Q

Risk-Loving + Preference + Marginal Utility of Wealth + Proof

A

Risk-Loving: EU(W)>U(EW)
Increasing Marginal Utility of Wealth U’‘(W)>0 convex utility of wealth U(W): prefers random income rather than guaranteed expected value, value of an additional dollar is larger the more money you have, willing to risk getting another dollar when you can only lose a dollar with equal probability that has lower marginal utility
Utility Functions: U(W)=W>1,U(W)=aeaW

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10
Q

Expected Utility v. Utility of Expected Wealth

A
  • Face uncertainty of receiving the random income → Expected Utility EU(W)=i=1niU(Wi), considers probability and utility, how people psychologically value uncertain outcomes
  • Face certainty of receiving the expected income→ Utility of Expected WealthU(EW)=i=1nU(i=1niWi), considers expected wealth and utility, ignores probability distribution and effects of risk perception, just utility of average wealth
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11
Q

Utility of Wealth v. Expected Utility Function

A
  • Utility of Wealth Function U(W)=U(I)=v(p1,…,pn,I)=u(x1(p1,…,pn,I),…,xn(p1,…,pn,I)): measures utility of money, indirect utility function with fixed prices and varying W, omitting prices from indirect utility function
  • Expected Utility Function EU(W)=i=1niU(Wi):
  • Conclusion: EU(W1)>EU(W2) this individual will prefer random income W1
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12
Q

How to evaluate utility under uncertainty?

A

U(W)
E(W)

E(U(W))=EU(W)
U(E(W))=U(EW)

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13
Q

Elasticity + Importance + Equation

A

Elasticity: % change in 1 variable resulting form a 1% increase in another variable
Importance: allows percentage comparison of quantity responsiveness to price, predicts effects of Demand and Supply shifts, price controls & taxation
Equation: ep=%Q%P=QQPP=QPPQ
* Elasticity of Demand use demand function → always negative
* Elasticity of supply use supply function → always positive

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14
Q

Infinitely Elastic Demand

A
  • HORIZONTAL: at any P* a tiny change in price leads to huge change in quantity demanded dQdP=-infinity
    Consumers will buy as much of the good at P* but any higher=0 demand, any lower=infinity demand
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15
Q

Zero Elasticity

A
  • VERTICAL: quantity demanded is the same at any price dQdP=0
    Consumers absolutely need to purchase Q*, would not buy any larger or smaller quantity (ex.Meds, bread in poor countries)
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16
Q

Elastic Demand

A

e(-infinity,-1):
Total expenditure decreases when price goes upd(expenditure)d(price)=Q(e+1)<0

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17
Q

Unit Elastic

A

e(-1): when price changes, total expenditure on good doesn’t change
d(expenditure)d(price)=Q(e+1)=0
Function: QD=aP e=QPPQ=PaPeaePe-1=1

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18
Q

Isoelastic Demand

A

Isoelastic Demand: elasticity is constant along the demand curve/hyperbola
Function: QD=aPe

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19
Q

Inelastic Demand/Supply

A

Inelastic Demand/Supply e(0,-1): demand is relatively unresponsive to price changes
When price goes up total expenditure on the good increases (same quantity demanded x higher price=higher total expenditure) d(expenditure)d(price)=Q(e+1)>0

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20
Q

Effects of Price Changes on Expenditure Depending on Elasticity of Demand Table

A

See doc

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21
Q

Cross-Price Elasticities

A

Cross-Price Elasticities ebDa=dQDa/dPb Pb/QDa: % change in QD in one good resulting from 1% incr. In price of another good

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22
Q

Income Elasticity of Demand

A

Income Elasticity of Demand eID=dQDdIIQD: % change in quantity demanded resulting from 1% increase in income

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23
Q

Price Elasticity of Linear Demand

A

Price Elasticity of Linear Demand: ep=QDPPQD=-bPa-bP<0, (QD=a-bP dQDdQS) always positive
Elasticity Large (absolute value) ← P Large & Quantity Small
Elasticity Small (absolute value) ← P small & Quantity Large

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24
Q

Elasticity & Effects of Demand Shifts

A
  • Elastic Supply (flat): large change in Q & small change in P
  • Inelastic Supply (steep): small change in Q & large change in P
  • Elastic Demand (flat): large change in Q & small change in P
  • Inelastic Demand (steep): small change in Q & large change in P
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25
Knowing elasticities gives same info as Demand & Supply Curves
See doc
26
Individual Demand + Function + Curve + Derivation
Individual Demand: relation b/w quantity demanded and its determinants (preferences, prices & income) indicating how much an individual consumer will purchase * **Derivation**: obtained by solving consumer utility maximization problem subject budget constraint * Individual Demand **Function**: x*(p1,p2,...,pn,I)=D(p1,p2,...,pn,I) * Individual Demand **Curve**: relation b/w quantity and price of demanded good for fixed levels of prices and income x*(p1,p2,...,pn)=D(p1,p2,...,pn)
27
Income Consumption v. Engel Curves + Graph
* Income Consumption Curve: changes in individual demand as income changes * Engel Curves: relation b/w income & demand for the good, upward slope (normal good), downward slope (inferior good)
28
Market Demand Curve
Market Demand Curve: sum of all the individual demand curves in the market, relating quantity that all consumers buy in mkt to price of that good (add horizontally) Shifts: changes in number of consumers leaving/entering market and factors that influence the demand of many consumers
29
Consumer Surplus
**Consumer Surplus** (per unit at a point on line or full): measures consumer benefit of consuming a good in units of money, answers the question how well does the economy work, how much consumer benefit produced? * **Calculation**: difference b/w willingness to pay and price/actual amount paid, area under demand curve above price line
30
Constraint Maximization Problem + Process
**Constraint Maximization Problem:** max u(x1,...,xn) such that I=p1x1+...+pnxn, where xi is quantity of good & pi is price of good & I is consumer’s income 1. Form Lagrangian Function L=u(x1,...,xn)+(I-p1x1-...-pnxn), where is Lagrange multiplier on budget constraint 1. First-Order Conditions for xi, Lxi=ui'-pi=0 1. Set Equal Marginal Principle ==u1'p1=u2'p2 or Set MRS equal Price Ratio u1'u2'=p1p2 isolate for x1 (If it cannot hold it is a corner solution, the item that gives more quantity for same income will be spent to the max 1pi units) 1. Sub xi into budget constraint I=p1x1+...+pnxn isolate for x2 gives both demand functions 1. If pi given sub in & solve for optimal bundle quantities
31
Constraint Minimization Problem + Process
Find I' when prices change to (p1',...p'n) to be at same utility level/indifference curve as with I & (p1,..,pn) Compute level of utility attained at old I & (p1,..,pn)=u= standard Consumer Max Problem max u(x1,...,xn) subject to p1x1+..+xnpnI to create demand functions x1*(p,...,p,I),...,,xn*(p,...,p,I) Sub Demand Functions into utility function to create an Indirect Utility Function: shows highest level of utility obtained under any I & (p1,..,pn), decision-making under uncertainty u(x1*(p,...,p,I),...,xn*(p,...,p,I))=v(p1,...,pn,I) Minimal Income min p1'x1+...+pn'xn needed to achieve old level of utility uu(x1,...,xn) under new prices (p1',...,p2') 2 Methods Lagrangian Method: L=p1'x1+...+pn'xn+(u-u(x1,...,xn)) Compute Expenditure Function E(p1',...,p2',u)=p1'x1h,...,pn'xnh: minimum income needed to achieve given utility level u under prices (p1',...,p2') Need to Raise Individual Income by: E(p1',...,p2',u)-I so individual has enough money to attain the previous utility level u Solution Quantities are called Hicksian/Compensated Demands: (x1h(p1',...,pn',u),...,xnh(p1',...,pn',u)) Duality Method: utility maximization + expenditure minimization Set Equation u=v(p1,...,pn,I) & isolate for I creating expenditure function E(p1,...,pn,u)=I
32
Revealed Preferences Approach + Draw Graph
* observing consumer choices under different budget constraints we can infer which baskets are prefered * Due to Law of Diminishing Marginal Rate of Substitution all consumers have convex indifference curve
33
Main Principle of theory Of Consumer Behavior:
Main Principle of theory Of Consumer Behavior: consumers choose combo of goods that will maximize utility (preferences) given the limited budget (income & prices) available to them.
34
Main Principles of Econ Behavior
Rationality: each does what is best (varies) for themselves Self-Interest: each maximizes its objective HH max utilities (benefits) Firms max profits
35
Market + Scope + Importance
* Market: collection of buyers and sellers who, through their actual or potential interactions, determine the price of a product or set of products, and quantities transacted * Scope/Boundaries: geographical and in terms of range of products produced/sold within it, if a product is interchangeable with another they are in the same market * Ex. Sweeteners (is a market) v. Corn Syrup (not a market) * Ex. Blood Pressure Drugs (is a market) v. Drugs (not a market) * Importance of Understanding Definition: (i) firms must understand who it actual+potential competitors are for various products that it sells or might sell in the future, (ii) public policy decisions (mergers or concentrations of mkt) *
36
What Shifts Demand Curve?
* Income: Normal Goods: as income incr. demand incr. at same price (luxuries), Inferior Goods: as income incr. demand decr. at same price (fast food) * Price of Other Goods: Complements: goods consumed together, price and demand shifts opposed (ex. Incr. price → decr. demand), Substitutes: two goods interchangeably in consumption, price and demand shifts same (ex. Incr. price → incr. demand)
37
What Shifts Supply Curve?
* Production/input costs (wages, interest rates, raw materials, energy, technology): decr. Input costs → produce more for same P/sell same Q for lower P * Price of jointly produced goods → symbiotic, without a competition for inputs (ex.Beef & hides (ex.price incr. → supply incr.) shift in same direction * Article Reading Natural Gas & Oil * Price of a good that is produced from the same inputs → competition (ex.price incr. → supply decr.) shift in opposing directions * Military v. civilian aircraft
38
Market Mechanism
Moving to Equilibrium: In a free competitive mkt P & Q change until the mkt clears, starts where there is a shortage or surplus * **Equilibrium**: Q0 mkt clears at price P0 so quantity supplied equates to quantity demanded, no change * Surplus: P1 too high → S>D → will start to discount to sell supply → P will fall until equilibrium * Shortage: P1 too low → D>S → will start to increase price to lower demand → P will rise until equilibrium * Assumptions: * At any given price a given quantity will be produced & sold * Competitive Mkt: both sellers & buyers have little mkt power, ability to individually affect mkt price, or else P & Q can be fixed or changed at will for monopolist’s interest
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3 Assumptions of Consumer Preferences
* Complete: able to rank all basket of goods which is better or worse * Transitive: must be logically sound/rational, A>B>C * Monotonicity or Non-Satiation Consumers: always prefer more of any good to less, cuz free disposal * “Bads”: more of it is bad, pollution * “Goods”: more of it is good, pollution reduction
40
Rule for Optimal Point
MRS doesnt equal PF/PC so individuals can reallocate income to increase utility MRS>PFPC decr. Clothing, incr. Food consumption until they equal MRS
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Corner Solution
**Corner Solution**: consumer optimally spends all income on one good and none on another, highest indifference curve consumer can attain, typically MRSPFPC * Price change can cause corner solution to change corners or change into interior solution even with same preferences/indifference curves
42
Interior Solution + Equal Marginal Principle
**Interior Solution** - Best/Optimal consumption bundle has highest utility (highest indifference curve) that is on the budget line (affordable), when indifference curve is tangent to budget line=slopes are equal (or corner solution if linear utility function), any point higher will be above the budget line, Absolute Value of Slope of Indifference Curve MRS=-dCdF=MUFMUC=PFPC equals Absolute Value of Slope Budget Line 1. Located on budget line: consumer spends all income b/c more is better 2. Gives most preferred combo of G+S: highest attainable indifference Curve among all points on the budget lines **Equal Marginal Principle**: MUFPF=MUCPC utility is maxed when budget is allocated so that marginal utility per dollar of expenditure is the same for each good, no incentive to change behavior (equilibrium), utility of last cent spent on food equals utility of last cent spent on clothing
43
Logical Mathematical Proof by Contradiction (Null-Hypothesis/Assume not true): try to prove that not on equal marginal principle gives greater utility
See doc
44
Non Linear Budget Constraint
See doc
45
Budget Constraint + Derivation + Changes
Budget Line: depicts all combos of goods for which total money spent equals total income - Rearrange equation: C=IPC-PFPCF or F=IPF-PCPFC - Slope (Price Ratio) -PFPC=dCdF or -PCPF=dFdC units of one good traded off for increase of 1 unit of the other good, rate at which the two goods can be substituted without changing the amount of money spent, ratio of prices of 2 goods with a minus sign - Intercept (Units if all Income spent on 1 good) IPC or IPF, simplest way to draw is identifying these, maximum units 1. Income: parallel shift outward/inward from original line, intercepts move by same amount cuz more/less goods can be bought 2. Price: intercept of good with price change moves accordingly IPC or IPF If ratio of prices change unevenly it will change slope of budget line If ratio of prices stays the same, but incr/decr. It will shift outward/inward
46
Marginal Utility of a Good v. Law of Diminishing Marginal Rate of Substitution
**Marginal Utility of a Good Partial Derivative of Utility Function** In Terms of Good of Interest - MU=u(x1,...,xn)x: additional satisfaction obtained from consuming 1 additional unit of good, changes with the amount of good available, non-satiation axiom implies it is positive sloping **Law of Diminishing Marginal Rate of Substitution** (Decreasing Convex): more X, the more X willing to give away for the other good, slope of indifference curves decreases the more of a single good it has. Can’t be convex
47
Diminishing Marginal Returns Principle
Diminishing Marginal Returns Principle - Concavity of MRS: slope/utility of a good decreases as the more given Upward Slopes UX>0: the more of a good the more utility, marginal utility is positive Concave U2X2<0: as consumption of a good incr. it’s marginal utility decr. due to satiation a good is worth more when we’ve consumed less of it worth less when consumed lots, slope increases decreasingly As X incr. & Y decr.=MUX decr. as MUY incr. so MRS=-dYdX=MUXMUY
48
Marginal Rate of Substitution
Marginal Rate of Substitution Slope of Indifference Curve=MRS=-dYdX|U=U=UXUY=MUXMUY depends on Marginal utility of Each Good = Ratio of Marginal Utility: how a person trades one good for another remaining at the same utility level/indifference curve, amount of one good given up to obtain 1 extra unit of another good
49
# Mar Indifference Curves
Graphical Representation using Indifference Map to describe preferences/ranking of individuals, can differ b/w people Indifference Curves: represent all combinations of mkt baskets that one is indifferent b/w, equally satisfied with any basket on the same indifference curve Most Preferred - Above curve>curve>below curve - Least Preferred Along curve are equally preferred Downward Slope=follows Non-satiation axiom Upward Slope violates Insatiation=more is better Northeast more preferred as more of every good Indifference curves cannot cross to satisfy transitive and non-satiation Prove things by contradiction, assumptions are disproved Derive Indifference Curve using Utility Function: set U=#1,#2..., isolate for C or F, graph each new function Every bundle (x1,...,xn) that has same utility u(x1,...,xn)=u forms a indifference curve, along curve equally preferred
50
Utility Function
Utility Function u(X,Y) = Preference Ordering of Bundles: describes which has bigger utility/preference, magnitude and unit meaningless can’t say it is twice as high, all relative, Ordinal: the only thing of significance is its order, intervals are meaningless Utility Function Theorem: if individual preferences satisfy completeness, transitivity & continuity properties there exists a utility function Still is a utility function even after applying the same increasing function f to all, making it increasing as it still shows rank preference v=f(u()) as equality b/w functions are still same EX. U(F,C)=F+2C mkt basket with 8 food, 3 clothes utility is 14=8+2(3) Set of different indifference curves U3>U2>U1
51
Firm's Supply Function/Decision Summary
Choose quantity q such that rules 1-3 are satisfied: (1) marginal cost is equal to price: MC(q) = P (2) marginal cost is increasing: MC’(q)>0 (this is why we say that supply curve is marginal cost curve) (3) Price P must be above shut down price, for the firm to produce a positive quantity. If P is below the shut-down price, the firm should not produce and set q=0. Long run shut-down price is the minimum of ATC. Short run shut-down price is the minimum of AVC (In the short run the firm ignores the fixed cost).
52
Firm's Optimal Decision is Determined by 2 Things
1. **Profit maximization**: What output determined by production function, input prices, output prices, How much, How to produce, What prices, How to compete 3. **Production technology**: transforms inputs into outputs described by production function q=F(i1,...,in) indicates maximum quantity of output that can be attained using a quantity of inputs in most efficient manner - Common Inputs: K=capital, L=labor, M=land, A=technology - Capital: machinery, tools, equipment, gadgets, materials, buildings - Several Inputs: based on marginal & average benefits & costs of production, decided how much and how to produce, what inputs - Graph: C & D are efficient representing max level of output that can be produced by using given amounts of labor under a given production function. A & B are inefficient involve waste of resources
53
Marginal v. Average Product of an Input + Equation + Relation Graph/Explanation
1. **Marginal Product:** change in output resulting from a unit change in input keeping all other inputs unchanged, benefit of an input, partial derivative of production function with respect to j’th input MPj=dq/dIj=F'j, MPj>0 if free disposal: you can discard unproductive inputs 2. **Average Product of an Input**: how much output produced per particular unit of input APj=q/Ij=F(I1,I2,...,In)Ij **Relation:** - When MP>AP, AP is increasing: adding students who are older than average will lift average up - When MP
54
Short Run v. Long Run
* **Short Run**: certain inputs remain fixed, such as capital, equipment, buildings, land * **Long Run**: all inputs are variable so different combos of inputs deliver same desired output creating trade-offs/substitution b/w inputs to produce optimal input choice
55
How to Determine Optimal Input Choice
Optimally what combo of inputs to produce a certain output, guiding principle minimal cost for given output
56
Isoquants + MRTS + 3 Types
**Isoquants** (indifference curves): shows all possible combinations of inputs that yield the same output, properties: Downward slope=MP positive, Farther from origin=higher levels of positive output, Isoquants do no cross **Marginal Rate of Technical Substitution** (MRTS=MRS): slope of isoquant, rate at which one input can be substituted for other keeping the level of output the same -dK/dL=MPL/MPK always positive although actual slope is negative, Moving Along a Isoquant: dQ0=MPL*dL+MPK*dK=0 1. **Perfect Substitutes** F(K,L)=aK+bL: constant marginal products of the inputs (MPK=a,MPL=b), MRTS is constant at all points MPLMPK=-dKdL=ba 1. **Perfect Complements** F(K,L)=min{Ka,Lb}: no substitution, inputs must be used in fixed proportions 1. **Cobb Douglas** F(K,L)=KaLb: hyperbola isoquant, different combinations can produce outputs flexibly
57
Law of Diminishing Marginal Returns + Graph of Total Output
**Law of Diminishing Marginal Returns**: use of an input increases with other inputs fixed, the marginal product of this input tends to decrease F"K<0, not negative, total output can still be increasing * **Assumptions**: quality of input, tech, and other inputs constant/fixed * **Exception**: increase input from -, small levels, MP may increase initially, a lot of capital compared to labor initially MPL is large and increasing at first as workers begin to specialize, when labor input large there may be too many compared to capital so MPL decreases * **As Labor Increases**: labor less productive, capital more protective, less capital to keep output constant, isoquant becomes flatter, diminishing MRTS, initially adding workers makes better use of existing capital, after appoint more labor is counterproductive from overcrowding, workers having nothing to do, prevent other workers from being productive
58
Why Didn't Malthus Food Crisis Happen?
* Agriculture Output Production Function Q=F(L,M) didn’t take into account changes in technology & capital stock * **Technology**: upward shift of production function, more output produced with same inputs, labor productivity increases * **Labor Productivity**: link to standard of living, consumption per capita can only increase if it increases, depends on 1)Growth in stock of capital/total amount of capital available for production, 2)Tech change/development allow factors of production to be used more efficiently * **Canadian Slow**: stock of capital growing more slowly, depletion of NR, regulations
59
How do firms decided whether or not to increase output?
Returns to scale, rate output increases as inputs are increased proportionately 1. Change input mix or increase quantity of input 1. Change scale of production by increasing all inputs in same proportion 1. Build new factory: duplicating existing production **Testing Process:**compare outputs when inputs are doubled F(tI1,...,tIn) v. doubled initial input output 2q * Decreasing Returns to Scale (F(tI1,...,tIn)<2q): decreasing efficiency with large size, coordination problems, relatively larger plants eventually reach this * Constant Returns to Scale (F(tI1,...,tIn)=2q): size doesn’t affect productivity, usually for relatively small plants * Increasing Returns to Scale (F(tI1,...,tIn)>2q): output more than doubles when inputs are doubled, larger output associated with lower cost, one firm is more efficient than many, relatively larger plants * **Perfect Substitutes** (CRTS): F(tK,tL)=a(tK)+b(tL)=tF(K,L) * **Perfect Complements** (CRTS): F(tK,tL)=min{tK/a,tL/b}=tmin{K/a,L/b}=tF(K,L) * **Cobb Douglas**: F(tK,tL)=(tK)a(tL)b=taKatbLb=ta+bKaLb=ta+bF(K,L), +=1 CRTS, +>1 IRTS, +<1 DRTS
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Optimal Output Choice
**Graphically:** Isoquant curve q=F(K,L), inputs on axes, Tangency Condition b/w isoquant & isocost line is optimal condition , Isocost Line wL+rK=H: describing cost level, cost of all combos of inputs with slope -w/r **Mathematically** 1. Compute 1st order conditions for each variable input: Lij=pj-F(ij,...,in)ij=0 1. Rearrange pj=F(ij,...,in)ij=MPjMP1p1=MPnpn 1. Optimality Condition MPKpL=pKpL: marginal product of an input divided by its price must be same across all inputs 1. Note: MRTS=Price Ratio 1. Isolate one input, so all other inputs are in terms of one ij(i1) 1. Substitute ij(i1) into Production Function & Solve for i1*(q): q=F(i1,i2(i1),...,in(i1))i1*(q) 1. Substitute i1*(q) into ij(i1) to get optimal quantity of each other output: i2*(q),...,in*(q) 1. Obtain Cost Function: C(q)=i=1i=npjij*+FC determined by production function 1. Solve mini=1i=npjij+FC=C(q) to find optimal output q **Goal**: maximize profits, minimize cost, maximize revenue **Profits**: Revenue-Cost=poF(i1,...,in)-(j=1j=npjij+FC) **Revenue**: poq=poF(i1,...,in) **Cost**: j=1j=npjij+FC=VC+FC
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Variable v. Fixed Costs
**Variable Costs** j=1j=npjij: used in various amounts depending on desired output **Fixed Costs FC**: needed in fixed amounts to start production, doesn’t depend on output and can’t be adjusted immediately, distinction/bw types important when decided shut-down production **Sunk Costs**: cannot be recouped if stopped (licenses, machinery, roads) **Non-Sunk** (Salvageable) Costs: can be recouped or partially when discontinued production (land, buildings)
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Derive Cost Function & Marginal Cost Function Given Production Function q=K^(1/2)L^(1/2)
C(q)=2qsqrt(wr) MC(q,w,r)=2sqr(wr)
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Returns to Scale of Cost Curves
Returns to Scale imply 1)U-shaped marginal cost curve, 2)U-shaped AVC & ATC, 3)MC crosses AVC and ATC at their minima * **CRTS** Production Function means Total Cost Function is linear TC(q)=cq+FC, c=constant marginal cost=MC(q)=AVC(q), marginal cost and average variable cost are constant and don’t depend on quantity * At Low Quantities: **IRTS** Production Function, output increases from low levels, workers can better specialize to a greater extent, scale provides flexibility, managers can organize production more effectively. When MCATC/AVC, ATC is increasing, Total Cost Function is convex, marginal cost is increasing, greater than ATC/AVC which are increasing
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Formula Total Cost Variable Cost Marginal Cost Average Cost Average Variable Cost Average Fixed Cost
Total Cost C(q)=j=1j=npjij+FC Variable Cost VC(q)=j=1j=npjij Marginal Cost MC(q)=dC(q)dq Average Cost ATC(q)=C(q)q=VC(q)q+FCq=AVC(q)+AFC(q) Average Variable Cost AVC(q)=VC(q)q Average Fixed Cost AFC(q)=FCq
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Produce or Sell?
option with lowest opportunity cost should confirm the decision **Opportunity Costs of Inputs**: value a input in its best alternative use, value forgone by using the input in your production, present=forward looking considering what is the best use of input with current prices to make optimal decisions today **OC of Inputs Firm Owns** rK=rental rateunits of capital: value they can be gotten by selling/leasing resources in mkt which is foregone if firm uses input in its production (ex. Capital, time Hw=hourswage) * **Accounting Costs**: record what had been spent, not used for economics
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Case 1: 1,000 tons of steel purchased 1 yr ago for $250 per ton, current price $500, what price of steel should the firm use when making decisions? Use steel for production, or sell steel? Case 2: Equipment could be sold $1000 today, able to sell for $200 next year. What is the cost of the restaurant to use equipment for 1 more year? Case 3: Baker’s Pie Shop is for sale at $25,000. Suppose that Jones is currently earning $35,000 annually as a baker while Smith earns $45,000. Who has a higher cost of owning and operating the pie shop? Case 4: A construction firm receives contract for $12,000 to install AC ducts. Operating expenses (including labor) are estimated at $8,000 and all necessary materials are already held in inventory. Materials (sheet metal) originally cost $5,000 but the current market value is $3,000. Accept the job or not? And why?
1. Should steel at this price when evaluating current project 2. 800 3. Jones: higher cost of owning and operating pie shop, as they would lose less from selling, they would lose less salary, lower Opportunity Cost=$25,000-$35,000=-$10,000 4. Take the job since opportunity cost is less.
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Supply Decisions 3 Rules
Supply Decision: output q to produce at a given market price in order to maximize profits Profit=pq-C(q) Optimal q: 1. **Rule 1** p=MC(q): choose q such that p=MC(q)=dProfitdq price equals marginal profit, maximize profits by taking first derivative of profits with respect to q, set to 0 1. **Rule 2** MC'(q)>0: q at which MC(q) is increasing, b/c if it is decreasing at q then increasing output the firm increases its profits, such q is not optimal (ex. q2 over q1, b/w them costs less to produce/lower MC than P/P>MC that firm sells) 1. **Rule 3** P above Shut-Down Price: produce positive quantity only if profits are positive, firm should shut-down=stop product if its profits are negative
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Short Run - To Produce or not + Graph
Pshort-run shut-down=minAVC(q): continue operating as long as they can cover variable costs, even if they’re not covering fixed costs, producer surplus should be positive for a firm to produce/not shut-down in short run Short-Run Profits (FC not included sunk): Producer Surplus=pq-VC(q), negative when PminAVC(q) firm should produce in short run
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Long Run - To Produce or not + Graph
Plong-run shut-down=minATC(q), if total revenues can’t eventually cover both fixed and variable costs, drivers will exit the industry, profits should be positive for firm to produce, price higher than short run Long Run Profits LR=pq-TC(q)=pq-VC(q)-FC * If Plong-run shut-downminATC(q) firm should produce a positive quantity in long-run
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Draw Cost Curves + Identify -/+ Profit Area + Supply Curve + Shutdown Point
Producer Surplus at q*: area of a rectangle with length equal to q* and height equal to difference b/w price (p) & average variable cost (AVC) at q*, equivalently it is the area b/w the price line & marginal cost curve * Revenue Area: 0PBq* * AVC Area: 0DCq*
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Factors that Shift Cost Curves
1. Changes in **Prices of Inputs**: higher prices shifts up cost curves, causing supply to be smaller at each price & shut-down price goes up 1. Changes in **Taxes**: adding per unit tax on each unit of output increases cost at each q, all curves shift up, lower supply at all prices, shut-down price increases 1. Change in **Technology**: increase in productivity/production function, produce more output from the same inputs, Marginal & Average Total Cost curves shift down, long run shut-down price decreases
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Given C(q)=2q+3q2+27, FC=27, find VC, MC, ATC, AVC, SR & LR Shutdown Price
C(q)=2q+3q2+27, FC=27 VC(q)=2q+3q2 MC(q)=2+6q ATC(q)=2+3q+27q AVC(q)=2+3q, minAVC(0)=2=MC(0) PSR=2 PLR=5
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SR v. LR Mkt Supply Function
**SR Mkt Supply Function**: shows amount of output that all existing firms in mkt will supply at a given price (summing marginal cost curves), is the sum of supply functions of all existing individual firms in the mkt **LR Mkt Supply**: each point on curve each firm makes 0 profit=minATC(q), shows supply from firms when none want to exit and non want to enter in long-run, can alter every aspect of production, needs to renew its fixed costs hence are free to stay or exit mkt, entry incr. Mkt supply in LR, exit reduces mkt supply in the LR most important factor to determining LR competitive mkt supply * Exit: as long as profits are negative * Enter: as long as profits are positive, it does better in this mkt than in any other mkt * 0 Profit: sufficient to stay in, even a small positive profit * Economic Profits: revenue-costs, costs include direct, indirect and opportunity costs * Shape: determined by extent to which changes in industry output affect prices of inputs with 3 types
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3 Mkt Supply Function Shapes + Draw Cost+Supply Curve
1. **Constant Cost Industry** (horizontal LR supply curve at p=minATC): cost functions don’t change, # of firms change, input prices don’t change, ATC remains same at each quantity 1. **Increasing Cost Industry**: input prices rise as more firms enter as they incr/ demand for inputs, competition drives their prices higher, upward left shift of marginal cost curve MC/AVC/ATC of each firm, higher price required for more firms to enter & incr supply in mkt creating incr+upward sloping curve, upward sloping, since input costs incr. Firms won’t enter infinitely until output price incr. To compensate 1. **Decreasing Cost Industry**: costs go down as more firms enter, incr. Firms allows firms to take advantage of larger size of mkt to get inputs cheaper ATC/MC/minATC (ex.Incr productivity, network industries), input production industry has increasing returns to scale, firms are willing to supply a higher quantity at lower price, downward sloping, if firm can sell a higher quantity they are willing to accept a lower price
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Competitive Short Run Equilibrium Properties + Components
1. Demand=Supply 1. Profit maximizing quantities supplied by all firms P=MC(q), PAVC optimal supply 1. Each consumer able to purchase utility maximizing bundle, no shortages * **Consumer Surplus**: net benefit of consumer, willingness to pay reflected by demand curve minus prices paid for good, area b/w demand curve & mkt price * **Producer Surplus**: total benefit to producers, producer revenue minus variable costs, are b/w supply curve and mkt price * **First Welfare Theorem of Economics**: Efficiency/Maximum Welfare/Surplus: area b/w demand & supply curves, total welfare/surplus=consumer + producer, maximizes/produces largest possible surplus given at competitive equilibrium * **Deadweight Losses/Efficiency Losses**: mainly caused by gov regulations and interference in economy, estimate of efficiency cost of policy
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Government Regulations
**Government Regulations:** benefit for some econ actors, generate deadweight loss, gov needs to balance benefits (political considerations) and costs (deadweight) * Price Ceiling: price below equilibrium price * Price Floor (Minimum Wage): * Price Support via government purchases: prices set above equilibrium maintained by gov purchases of excess supply to restrict or incentivize production, overall worse for society, selling internationally hurts producers in those countries, simply give money to farmers * Production Quotas: restriction on supply less than equilibrium Q causes price to increase * Subsidy to Producers * Subsidy to Consumers * Taxes: per unit or per $, on consumption or production: both CS & PS loss, transfer of surplus to gov, total loss of surplus is called burden of tax split b/w P & C dependent on relative elasticities of demand and supply, not how tax is collected * International Trade: Quotas and Tariffs ``voluntary’’ restraints on trade: keep domestic price above world price levels to protect domestic producers, higher profits, cost to consumers high, free trade=lower world price incentive for domestic C to purchase import goods (import=Qs-Qd) * Tariff: tax on imported good, T on each unit of output, new price is P*=T+PW higher than world * Import Quota: limit on Q of good that can be imported
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Price Support + Impact on C & P + DW + Graph
Price Support via government purchases: prices set above equilibrium maintained by gov purchases of excess supply to restrict or incentivize production, overall worse for society, selling internationally hurts producers in those countries, simply give money to farmers * C: Q demanded falls due to higher P, loss of CS A+B * P: incr Q produced to sell at high price, PS gain A+B+D * Gov Cost: buying surplus E, if destroyed is maximal welfare loss, tax is indirect cost on consumers * DW: Change CS + Change PS - Gov Cost
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Production Quotas + Impact on C & P + DW + Graph
Production Quotas: restriction on supply less than equilibrium Q causes price to increase DW: B+C Surplus Transfer from C to P: A Change CS: A-B Change PS: A-C
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Price Ceiling + Impact on C & P + DW + Graph
Price Ceiling: price below equilibrium price DW: B+C Surplus Transferred from P to C: A Change in CS: A-B Change in PS: C-A
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Subsidy to Consumers + Impact on C & P + DW + Graph
**Subsidy to Consumers**: payment reducing buyer’s price below seller’s price analyzed like a tax/negative tax, quantity increases, higher Ps>Pb payed, effect depends on elasticity of curves * CS + PS: increase,The benefit of the subsidy accrues mostly to buyers if -ED /ES is small, The benefit of the subsidy accrues mostly to sellers if -Ed /ES is large * Government Expenditure * DWL
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Taxes + Conditions + Determinants + % of Tax Percentage
**Taxes**: per unit or per $, on consumption or production: both CS & PS loss, transfer of surplus to gov, total loss of surplus is called burden of tax split b/w P & C dependent on relative elasticities of demand and supply, not how tax is collected Equilibrium Conditions QS=QD: 1) Difference b/w consumer payed PB and what sellers receive Ps is the tax T=PB-PS 2) Quantity sold & buyers price PB must be on demand curve, buyers only concerned with what they must pay 3) Quantity sold and sellers price PS must be on supply curve, sellers only concerned with what they receive More Inelasticity (steeper)=More of Burden: more sensitive to price change, D=C, S=P Percentage of Tax Burden Ratio: EsEs-Ed=Consumer tax burden,EdEs-Ed=Supplier tax burden
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Import Quota + Impact on C & P + DW + Graph
**Import Quota**: limit on Q of good that can be imported Foreign P Profit/Quota Holders: D CS Loss: A+B+C+D Domestic PS Gain: A DW: B+C Case of Foreign P/Quota Holder Domestic Surplus Loss=B+C+D Case of domestic quota holder/home gov Surplus Loss= B+C
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Tariff + Impact on C & P + DW + Graph
Tariff: extra fee paid at border for importing goods, tax on imported good, T on each unit of output, new price is P*=T+PW higher than world Domestic Supply incr, Demand decor, imports (width of D=Qs-Qd) shrink PS domestic incr.: A CS domestic loss: A+B+C+D DW: B+C Gov Revenue: D=tariff*imports Free Trade Surplus Loss: B+C, higher costs whole society pays+Qd by domestic falls
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3 Main Mkt Structures
3 Main Mkt Structures: more competition/firms better for consumers & overall efficiency 1. **Competitive Mkt** (P=MC): many small firms each price takers who have no effect on total mkt quantity or p, equilibrium efficient (no DWL without gov reg), lowest p, highest welfare for consumers. Demand is perfectly elastic, can sell q only at mkt p 1. **Oligopoly**: few large firms have effect on total Q/P, limited competition, equilibrium p higher & q lower than competitive mkts, loss of efficiency exists (DWL) 1. **Monopoly** (Worst for Consumers P>MC, MR=MC): price setter, one firm supplies whole mkt, no competition, owns the demand, chose any point on demand curve, equilibrium p higher, Q lower than both CM & O, there is DWL loss of efficiency. Price larger than MC by amount that depends inversely on elasticity of demand
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Source of Monopoly Power + Reducing Power
* **Barriers to Entry**: contrast to free entry, higher fixed costs, exclusive access to inputs, intellectual property rights, government restrictions, etc. * **Reducing Power Through Price Regulations**: can eliminate DWL, contrasting in CM, will produce Q/P same as CM efficient, * Pitfalls are if not properly set can lead to DWL, lower=shortage, higher=surplus * Below P4 avg cost of monopoly losses may lead to shut down in long run * **Natural Monopoly**: IRTS at all q, MC & ATC decr at all quantities, optimal to have single firm to produce all output rather than several, tricky to set P regulation as setting at competitive P incurs loss for monopoly cannot cover ATC * **Price Regulation Steps**: 1)Setting low P around Pc, 2)Subsidizing monopoly fixed cost to prevent losses (ex.Public utilities), By restricting price to be below the monopolist’s profit-maximizing price, the government can change the shape of the firm’s marginal revenue curve. When a price ceiling is imposed, MR is equal to the price ceiling for all quantities less than or equal to the quantity demanded at the price ceiling. For example, in the diagram the price ceiling is set at P, which is below the profit-maximizing price P*. The MR curve becomes the line PA and then jumps down to B and follows the original MR curve beyond that point. The optimal output for the monopolist is then Q, which is greater than the profit-maximizing output. If the government wants to maximize output, it should set a price ceiling at the point where the demand curve and the marginal cost curve intersect, point C in the diagram. Then, when the firm produces where MR = MC, it will be producing the output level at which P = MC, where P is the price ceiling. In this way, the government can induce the monopolist to produce the competitive level of output. If the price ceiling is set below this point, the monopolist will decrease output below the competitive level.
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Monopoly Profit + MR + AR
Chooses either P or Q, not both, we will focus on Q: higher Q means lower P & vice versa **Total Revenue** TR(q)=P(Q)Q requires Q=QD(p) P=P(Q) inverse demand function (isolate price from demand function) **Marginal Revenue** MR=P(q)+qdP(q)dq: Change in Revenue from Unit Change in Output to find optimal monopoly q & p, differentiate profits for profit-maximization, less than price since P’(Q) is downward sloping demand * P(q) producing one more unit brings P(Q) in revenue * dP(q)dq negative: extra unit produced results in price drop, reduces revenue from all units sold **Average Revenue** TR(q)q=P(q): avg P per unit sold which is demand curve where P(q)>MR(q)
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Monopoly Output Decision + Graph
* Profits Maximized at Output Level (q) where MR=MC or MR-MC=0 ddq=dTR(q)dq-dC(q)dq=0 * **Output Decision**: set MR=MC as at low output (q) MR>MC so by incr/ q, profits incr., while at high output MR
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Monopoly Supply Decision Example Given TR(q)=P(q)q=40q-q2 and Cost=C(q)=50+q2
Inverse Demand=P(q)=40-q TR(q)=P(q)q=40q-q2 MR(q)=40-2q Cost=C(q)=50+q2 MC(q)=2q AC(q)=50q+q MC=MR Supply Quantity2q=40-2qq=10 Price of Supply P(10)=40-10=30
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Monopoly Power Measurement
**Lerner Index of Monopoly Power** P-MC/P relative markup P (selling p expressed as percentage of cost) over marginal cost as % of P, expresses optimal monopoly p directly as markup over marginal cost: optimal P is such that markup is equal the inverse of the elasticity of demand * Higher the more monopoly power * Elastic demand → Ed large negative -1Ed small→ monopoly power small, lower markup, closer to perfect competitive mkt (P=MC) * Inelastic demand (0>Ed>-1) → Ed small negative -1Ed large → monopoly power large, higher markup, farther from to perfect competitive mkt (P=MC) * Will never produce a quantity in the inelastic portion of demand curve as you can incr. Revenue/profits by decr. Quantity & incr. P b/c marginal revenue is negative dTR(q)dq=P(q)+q(dPdq)=P(q)(q+qPdPdq)=P(q)(1+1ED)<0
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Pricing Example: if Ed=-4, MC=9, optimal price for monopoly to set
p-MCp=-1Ed p-9p=14 p-9=p4 4p4-p4=9 3p4=9 p=493 p=12
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Monopoly Social Costs
* Loss in CS & PS, DWL, transfer of CS to monopoly due to high P * Social cost exceeds DWL * Wasteful Rent Seeking: spend money & resources to gain monopoly power (ex.lobbying, marketing, building excess capacity) * Lack of Variety: similar/identical products * Lack of Competition: slow to innovate, reduce cost or introduce new options/products
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Find SR & LR Supply Function given Q_D = 34 - 8P and C(q)=q^(2)/2+ q/2+1/32
SR: p>=1/2 S(p)=p-1/2, otherwise S(p)=0 LR: p=1/4 S(p)=3/4, otherwise S(p)=0
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if world price=1, demand=34-8p, supply=12p-6, tariff=0.5 find free trade v. tariff, CS, PS, DWL, gov revenue, equilibrium, import quantity
DWL=-2.5=change CS+PS+Gov Revenue Freetrade: CS=42.25, PS=1.5 Tariff: CS=30.25, PS=6
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New equillibrium P & Q & What price sellers get, if $1 tax imposed given Qd=10-P, Qs=P+4. Equally Shared?
Pb=3.5, Ps=2.5, Tax Burden equally shared
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Difference b/w Tax & Subsidy v. Quota & Tariff Process
Tax: Pb-Ps=1 Subsidy: Ps-Pb=1 Quota: find new P when Q=quota number, same graph Tariff: find new P=Pw+T, same graph
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Why is there a social cost to monopoly power? If the gains to producers from monopoly power could be redistributed to consumers, would the social cost of monopoly power be eliminated? Explain briefly
When the firm exploits its monopoly power by charging a price above marginal cost, consumers buy less at the higher price, and consumer surplus decreases. Some of the lost consumer surplus is not captured by the seller, however, because the quantity produced and consumed decreases at the higher price, and this is a deadweight loss to society. Therefore, if the gains to producers were redistributed to consumers, society would still suffer the deadweight loss
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What price ceiling would minimize the most monopoly social cost and maximize output
Transform MC=MR into MC=P, so set P=MC
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Monopoly Graph + Pricing + Quantity + CS/PS Surplus + DWL
1. Demand function inverse=Average Revenue. Convert TR by multiplying by 1 and find MR 2. Set MR=MC and Isolate for q 3. Sub in q to demand to inverse demand f(x)=price
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Other things equal, expected income can be used as a direct measure of wellbeing A) always. B) if and only if individuals are not risk loving. C) if and only if individuals are risk neutral. D) no matter what a person's preference to risk. E) if and only if individuals are risk averse.
C) if and only if individuals are risk neutral.
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Producer surplus in a perfectly competitive industry is: A) the difference between revenue and variable cost. B) the difference between revenue and fixed cost. C) the same thing as revenue. D) the difference between revenue and total cost. E) the difference between profit at the profit maximizing output and profit at the profit minimizing output
A) the difference between revenue and variable cost.
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Suppose your firm has a U-shaped average variable cost curve and operates in a perfectly competitive market. If you produce where the product price equals average variable cost (on the upward sloping portion of the AVC curve), then your output will: A) exceed the profit maximizing level of output. B) generate zero economic profits. C) equal the profit maximizing level of output. D) be smaller than the profit maximizing level of output.
A) exceed the profit maximizing level of output. since your not at minAVC but on upward sloping chunk.
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A monopolist faces the following demand curve and total cost for its product: Q =200- 2P, TC = 5Q. What level of output maximizes total revenue v. Profit? A) 90 B) 0 C) 100 D) 95 E) none of the above
TR C) Profit D)
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Yachts are produced by a perfectly competitive industry in Dystopia. Industry output (Q) is currently 30,000 yachts per year. The government, in an attempt to raise revenue, places a $20,000 tax on each yacht. Demand is highly, but not perfectly, elastic. (20) Refer to Scenario 8.2. The result of the tax in the long run will be that (A) Q falls from 30,000; P rises by less than $20,000. (B) Q stays at 30,000; P rises by less than $20,000. (C) Q stays at 30,000; P rises by $20,000. (D) Q falls from 30,000; P rises by $20,000. (E) Q falls from 30,000; P does not change
A) Not full tax burden borne on consumers to Pb less than $20,000, Q will fall below 30,000
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Analytical Problem II
See notebook