Midterm 1

Question 1

What is the utility function in consumer theory?

Answer 1

It assigns numerical values to bundles of goods based on consumer preferences.

Question 2

Example of a Cobb-Douglas utility function?

Answer 2

u(c, k) = c^(1/2) k^(1/2).

Question 3

What is an indifference curve?

Answer 3

A curve that shows combinations of goods providing the same utility level.

Question 4

Equation for an indifference curve?

Answer 4

U(x, y) = k

Where “U” represents the utility function, “x” and “y” are the quantities of two goods, and “k” is a constant value representing the specific level of utility on that indifference curve

Question 5

What is the budget constraint equation?

Answer 5

p_x * x + p_y * y = I

where p_X and p_Y are prices and I is income.

Question 6

Equation for the budget line?

Answer 6

Reorganize budget constraint:

y = (I/p_y) - (p_x/p_y)(x).

Question 7

Marginal Rate of Substitution Equation

Answer 7

MRS_ck = - MU_c / MU_k

Question 8

Equation for equalizing bang-for-buck (Optimal bundle)

Answer 8

MU of x / price of x = MU of y / price of y

Question 9

What is the demand function?

Answer 9

It determines optimal consumption choices given prices and income.

Question 10

Example of demand functions for Cobb-Douglas utility?

Answer 10

x* = I / (2p_x), y* = I / (2p_y).

Question 11

What is own-price elasticity?

Answer 11

Measures how demand responds to changes in its own price.

Question 12

Equation for own-price elasticity?

Answer 12

ε_x = (dx / dp_x) * (p_x / x)

denominator of second part is x’s equation unless given/found already

Question 13

What is cross-price elasticity?

Answer 13

Measures how the demand for one good changes in response to the price of another good.

Question 14

Equation for cross-price elasticity?

Answer 14

ε_xy = (dx / dp_y) * (p_y / x).

Question 15

What is income elasticity?

Answer 15

Measures response to income changes.

Question 16

Equation for income elasticity?

Answer 16

ε_I = (dx* / dI) * (I / x*).

make sure to use x* which is the value of x in the optimal bundle where I is maximized

Question 17

How are goods classified based on elasticities?

Answer 17

Elastic is < -1
Inelastic is > -1

Substitutes if cross-price elasticity is > 0 Complements if cross-price elasticity is < 0

Normal (ε_I > 0),
Inferior (ε_I < 0).
Luxury if Income elasticity > 1
Necessary if < 1 but > 0

Question 18

What is a production function?

Answer 18

A relationship between inputs (capital K and labor L) and output (Q).

Q = f(K, L)

Question 19

Example of Cobb-Douglas production function?

Answer 19

f(K, L) = K^a L^b.

Question 20

What are the types of returns to scale?

Answer 20

Constant: a + b = 1, Increasing: a + b > 1, Decreasing: a + b < 1.

Question 21

What is the marginal product of labor (MPL)?

Answer 21

The additional output produced by an extra unit of labor.

Question 22

Equation for Marginal Product of Labor?

Answer 22

MPL = ∂q/∂L = ∂f(K,L) / ∂L

Question 23

What is the marginal product of capital (MPK)?

Answer 23

The additional output produced by an extra unit of capital.

Question 24

Equation for MPK?

Answer 24

MPK = ∂Q/∂K = ∂f(L,K)/∂K

Question 25

Calculating diminishing marginal utility

Answer 25

Take derivative of MUx to find if good x has diminishing marginal utility

Question 26

What is the marginal rate of technical substitution (MRTS)?

Answer 26

The trade-off between inputs required to maintain output. Gives us the amount of ywe can give up for a unit increase in xand still be able to produce the same quantity.

Question 27

Equation for MRTS?

Answer 27

MRTS_xy = dy/dx = - (MPx / MPy)

Question 28

What is the cost minimization condition?

Answer 28

Firms choose inputs to minimize cost while maintaining output level.

Question 29

Equation for cost minimization? B4B of K and L

Answer 29

MPK / p_K = MPL / p_L.

Question 30

What is the aggregate demand function?

Answer 30

The sum of individual demand functions for a good in a market.

Question 31

Example of aggregate demand equation?

Answer 31

Q(p) = 500(5 - p) + 50(20 - p) + 5q_d(p).

Question 32

What is the income elasticity of demand?

Answer 32

Measures how demand for a good changes with income.

Question 33

What is the condition for an optimal bundle?

Answer 33

MU_x / p_x = MU_y / p_y.

Question 34

Tangency condition =

Answer 34

Equality of bang-for-bucks (B4Bs)

Question 35

Bang-for-Buck (B4B)

Answer 35

Bang-for-buck (B4B): benefit-cost ratio or net value of the marginal unit (i.e. the very last unit or an additional unit…)

Question 36

Inverse Demand

Answer 36

What is the maximum (per unit) price such that the consumer buys a given quantity? Derive by inverting the demand function, i.e. express 𝑝 as a function of 𝑥 using the original demand equation

Question 37

Consumer Surplus Equation

Answer 37

Consumer surplus of p* = ((p-hat - p*) * q(p*)) / 2 p-hat = choke price = price where zero demand p* = chosen price Must compute for different consumer groups separately. ALWAYS GRAPH

Question 38

Aggregate Demand

Answer 38

Sum of all consumer's demand across different price ranges. Total Demand.

Question 39

Long-run vs. short-run

Answer 39

Short-run: one input (capital or labor) is fixed and cannot be changed Long-run: all inputs can be changed

Question 40

Returns to scale: output change if all inputs increased proportionally by factor t

Answer 40

Constant Returns to Scale (CRTS) if f (mK, mL) = mf(K,L) Increasing Returns to Scale (IRTS) if f(mK, mL) > mf(K,L) Decreasing Returns to Scale (DRTS) if f(mK, mL) < mf(K,L)

Question 41

Average product of labor: ratio of output to the amount of labor

Answer 41

= q/L = f(K,L)/L

Question 42

Isoquant

Answer 42

An isoquant is a set of input bundles that produce the same quantity of output Example: the number of labor units 𝐿 required to produce 𝑞 units of output, given capital 𝐾:

Question 43

Bang for Buck Equation

Answer 43

B4B_x = MU_x / px B4B_y = MU_y / py Capital: B4Bk = MP_k / pk Labor: B4BL = MP_L / pL

Question 44

Prove that both x and y are strictly greater than zero in the optimal bundle.

Answer 44

To prove that x* or y* or both are greater than zero, analyze B4B and MU. If x* or y* in those equations sends them to infinity, then they cannot be zero because the consumer would be missing out on utility/bang-for-buck.

Question 45

MRS Example: Suppose you find that MRSxy = -1/4 at some bundle (x, y). Describe in words what this tells us about the consumer

Answer 45

the consumer is willing to give up 1 unit of 𝑥 to gain 4 units of 𝑦 while maintaining the same level of utility. This implies that the consumer values 𝑦 much more relative to 𝑥 at this point.

Question 46

Average Product of Capital (K)

Answer 46

= q/K = f(K,L)/K