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From Flashcardlet > BEPP 250 Unit 2 > Flashcards

BEPP 250 Unit 2 Flashcards

0
Q

Profit

A

Economic profit =revenue -opportunity cost
Not accounting profit (only explicit costs). This includes opportunity cost
Denoted by pi

Profit (q)= R(q)- C(q)
Profit, as a function of quantity, = revenue - costs

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1
Q

Supply decision based on

A
  1. Whether to produce
  2. How much to produce

Firm is assumed to maximize profit

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2
Q

Perfectly competitive market

A

A market where firms and consumers act as price takers (no market power)
This means firm is too small to directly influence market outcomes
Firm must take market price, p, as a given and fixed regardless of how much it sells.
Why?

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3
Q

Why must firms take market price, p, as given

A

If a firm sells above p, nobody will buy from the firm because other firms are selling at p
If they sell below p, too much demand for the small firm to fulfill.

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4
Q

Profit function broken down (price taker and generally)

A

Profit =R(q) - C(q)
Revenue = R(q)= pq
Cost =F +VC (q)
Where F is the fixed cost and VC(q) is the variable cost with q.

Optimal output, q*, solves the profit maximization problem:
Max (q>=0) R(q)- C(q) = pq - F - VC(q)

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5
Q

Profit max problem in general

A

Conditional on producing strictly positive amount, profits maximized when MP = 0
This is because slope of profit function = marginal profit
So if MR>MC, keep producing until they’re equal.

So, take derisive of profit function with respect to q
We get MR(q)= MC(q)
This works regardless of if price taker or not.

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6
Q

Profit max problem for price taker

A 
Since R(q) = pq and firm takes p as a given, MR(q)= d(R(q))/dq = p for a price taking firm. 
So, price takers choose quantity such that p =MC(q*)
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7
Q

How does change in fixed cost impact optimal quantity?

A

It won’t. No impact because cost of the marginal unit is what matters. Marginal cost ignores fixed cost.

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8
Q

Price taking firm profit Max example:
Market price p = 36
Cost: C(q) = 10+ 20q +1/3 q^2

A

Maximize profit —>
p = MC
36 = 20+ q squared
q* = 4

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9
Q

Why does marginal cost increase

A

More we use the input, less good it becomes, so it costs more.
Optimal point is when MR =MC

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10
Q

How to decide if firm should shutdown?

A

A firm should shutdown if the revenue can’t cover its relevant costs.
Relevant costs:
Only pay variable costs when q>0, so this is relevant when shutting down.
Fixed costs? Depends on if they can be recovered or not.
Costs that can’t be recovered are sunk costs, while those that can be are avoidable costs.
Only avoidable costs are relevant to the shutdown decision since shutting down doesn’t allow you to recover any sunk costs.

So, shutdown if revenue <= variable costs + avoidable fixed costs.

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11
Q

Average avoidable cost

A

Suppose w is the %of fixed costs that are sunk.
Avoidable costs = variable costs + avoidable fixed costs = VC(q) + (1-w)*F, as these are the relevant costs.

AAC (q) = avoidable costs / q =
VC(q)/q + (1-w)*F/q =
AVC (q) +(1-w)AFC(q)
Average variable cost + average fixed costs that are recoverable.

Choose to operate (not shut down) when
pq > avoidable costs —> for a price taker, when p>AAC(q),operate.

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12
Q

Why operate in low demand seasons?

A

Firm operates as long as p> AAC(q)
However, can still not make profits. This is because with large sink costs, it makes sense to operate, as AC(q)> p > AAC(q)

To have strictly positive profits, pq- VC(q) -F >0
So, p> AC(q).
But, with large sunk costs, AC(q) much bigger than AAC(q)
So can operate and lose money, but less money than if not operate.

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13
Q

Why is Ferari cheaper than new Camry?

A

Because most of the Ferari fixed costs are avoidable (recoverable)while they aren’t for the Camry even though it is a lower fixed cost.

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14
Q

Shutdown price

A

Shutdown price is lowest price a firm would operate.
Since firm operates as long as p>AAC(q),shutdown price, p barm will be the minimum of AAC(q).
P bar = AAC(q bar)

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15
Q 
Shutdown price example 
Say C(q) = 10+ q^2 and 60% of fixed cost is sunk, find shutdown price and quantity
A

First get avoidable costs(q) = 10(1-.6)+q^2 = 4 + q^2
AAC(q)—> divide by q = 4/q + q
Now need to find the minimum of this—> take the derivative wrt q
= -4/q^2 +1 and set equal to 0
So, q bar = 2

Now, p bar = AAC(q bar) = 4/2+2 = 4
So, shutdown price is 4. If p is bigger than 4, operate. Otherwise, shutdown.

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16
Q

Shutdown price steps

A
  1. Get avoidable costs and divide by q so we have AAC(q)
  2. Take derisive of AAC(q)wrt q. Then set this equal to 0 to find the minimum of AAC.
  3. P bar (shut down price) = AAC(q bar)
    Just plug q bar back into the AAC function to get the shutdown price, p bar.
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17
Q

Supply function steps

A

Step 1. Get shutdown price (see previous slide)
2. Find the q star that maximizes profits given firm operates.
To do this, remember we want MR(q) = MC(q)
So, for a price taker, since p = MR(q), we have q(p) as the solution to p= MC(q)
—> take derivative of C(q) and set this equal to p.
Then solve for q in terms of p.
q(p) = 0 for p < or = to p bar
= q(p) for p > p bar.

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18
Q

Supply function ex:

C(q) = 10+ q^2 and from before, p bar =4

A
  1. P bar = 4
  2. P = MC(q) = 2q
    So, q = p/2
    So, q(p) = 0 for p less than or equal to 4 and p/2 for p greater than 4
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19
Q

Two steps in market interactions

A

Aggregation and equilibrium

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20
Q

Aggregate (or market)demand

A

Suppose individual consumers demand for a good is qi(p)
If there are N individuals, then just sum up all these demands at price p
Sum up the demand of each individual consumer at each price p
Multiply N*indiviudal demand.
Or if different, add them up

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21
Q

Aggregate (or market)supply

A

Sum up the supply of each individual firm at each price p.

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22
Q

Agg supply example:
Say 100 drivers with same cost function, C(q) = 10+ .0089q^2
And 50% of fixed costs are sunk. Get agg supply function:

A
  1. Get individual shutdown price. Find min of AAC —> AAC= 5/q + .0089 q
    Deriv =-5/q^2 + .0089 = 0
    q bar = 23.7
    Now plug this into the AAC function, p bar = .42
  2. Get individual supply function—> profit max quantity
    p = MC = 2(.0089)q
    So, q =p/.0178
    So, q(p) = 0 for p less than or equal to .42 and p/.0178 for p> .42
  3. Aggregate supply function
    100identical firms, simply multiply by 100. Keep p bar the same
    0 for p less than or equal to .42 and 100p/.0178 for p bigger than .42
23
Q

Competitive equilibrium

A

To get market price and quantity, set aggregate demand = agg supply
Qd(p) = Qw(p)

24
Q

Excess demand

A

AD> AS
this means the price is too low, as the downward sloping demand curve has a higher Q than the upward sloping supply curve for the given p.
Upward pressure on prices results, discouraging consumers and attracting firms.
P up, D down, S up

25
Q

Excess supply

A

Now, price is too high. Consumers don’t demand as much as is being supplied. So downward pressure on prices, attracting consumers and discouraging firms.
D goes up, S down, p down

26
Q

Competitive eq for price taker example:
Say Qs(p) = 0 for p less than or equal to .42 and 100p/.0178for p >.42
Qd(p) = (30-p)(100)

A

Conjecture p is above .42, meaning we set Qs = Qd and Qs is
100p/ .0178 which equals Qd = 100(30-p)
Solve for p, and we get .525
This is above .42, so conjecture is correct. If it weren’t correct, then we would shut down, supply 0
So, p= .42 and plug into Qs or Qd to get Q = 2948

Industry Profits = pq - NC(q/N)
Note: each firm supply q/100, so do cost for each indiv and multiply by 100 to get total cost.

Industry Profit = .525(2948) - 100C(29.48)

To get per driver profit, divide this by N, 100in this ex.

27
Q

Market power

A

If I choose too big of a q, I may drop the market price too low
This means I can influence the market and the price can change based on how much I produce.

28
Q

Monopoly

A

Firm is the only seller of a product with no close substitutes.
Only alternative for consumers is not buying anything, no alternate product.
No cross price elasticity.
Effective control of market prices. Use the SSNIP test to measure market share, if above 70 percent, then monopoly.

29
Q

Key difference with market power

A

Now, when firm considers output, q, thinks about how it will affect price.
Price is a function of q now.
For a price taker p’(q)= 0, as price stayed the same regardless.
For market power firm, price can change, will decrease in q. Dp/dq is negative.

30
Q

Marginal revenue for market power

A

No longer just p
Remember revenue = p*q =p(q) * q as p is function of q
So, MR(q)= p(q) + p’(q) * q

p is the gain from selling marginal unit but the rest is the loss from reducing price for all other units sold.

31
Q

Ex of marginal revenue with market power

A

Say that you can sell 10 units at 2 dollars each but if sell one extra units, price is now only 1 dollar per unit.
Before, make 20 dollars, now make only 11.
Benefit is the extra dollar from the last unit, but lose money too.
So, beneficial to charge higher price to make more money.

32
Q

Profit maximization for monopoly

A

Profit max monopoly quantity solves:
MR(qM)= MC(qM)
So, p(qM) + p’(qM) * qM = MC(qM)

Since p’ is negative, price is bigger than MC, not equal anymore.

Firm with market power will produce less to keep prices high and max profit.

33
Q

Monopoly profit max steps

A
  1. Invert demand function to get inverse demand function. This means getting p =… in terms of q
    Then multiply this by Q to get R(Q) and take derivative of this to get MR(q)
    NOTE, if linear inverse demand—> p= a-bq, then MR = a - 2bq
  2. Equate MR and MC
    This will give you QM
  3. Plug in optimal quantity into inverse demand to get optimal price.
  4. Compute profits
    PM*QM - NC(qM) where qM = QM/N
34
Q

Linear inverse demand shortcut

A

If inverse demand is linear, p = a-bq
So, MR(q)= a-2bq
Double the slope
Only if linear!

35
Q

Monopoly profit max example

Aggregate demand, QD=100(30-p) and C(Q)= 100 (10 + .0089(Q/100)^2)

A
  1. p = 30 - Q/100
    Since linear, MR(Q) = 30 - Q/50
  2. Set this equal to MC—> MC(Q) = .0178 Q/100
    Solve for QM, we get 1487 miles
  3. Plug into inverse demand —> pM = 30-QM/50 = 15.13
  4. Profits. PMQM -100C(QM)
    15.13(1487) - 100C(qM) = 21,301
    Restrict output, charge higher price
36
Q

Monopoly vs competitive graph

A

Mon has higher p and lower q
Consumer surplus goes down, producer surplus up with monopoly. But overall social surplus down. Deadweight loss

P> MC for Mon
This means the willingness to pay for the marginal unit is bigger than the cost of the marginal unit, so there is lost value. We stop production even though people value the good more than it costs to produce. But not worth it to maximize profit because would need to have cheaper price. Whereas they are equal for competitive markets.

37
Q

How does US law view monopolies

A

Illegal to blantanly create a monopoly and abuse the power.

38
Q

Shutdown price for a firm with fixed costs all sunk

A

Minimizing AAC, when q bar = 0. So never shut down. P bar = 0

39
Q

Combining different supply functions into Qs
Say firm 1 operates for p bigger than 8 and firm 2 always operates.
q(p)is same for both, p/2

A

For p between 0 and 8, just firm 2. So, Qs =p/2

For p bigger than 8, both firms. So, add them up. It is p.

40
Q

Price discrimination

A

Charging different prices to different people

41
Q

First degree price discrimination

A

Firms with perfect knowledge of individual valuations charge personalized prices.
Perfect price discrimination
Maximize total welfare, but consumers get zero surplus. unrealistic as firm wont know everyone’s WTP.

42
Q

Second degree price discrimination

A 
Firms offer different product quality / quantity so that consumers self select from menu of products. 
They choose, ex. Business class vs economy. Business more expensive. 
Welfare implications unclear
43
Q

Third degree price discrimination

A

This is what we will focus on
Firm sets different prices for exactly the same product in different markets based on observable characteristics
Requires 1. The ability to determine which segment a consumer belongs to and 2. Ability to restrict resale.

Instead of knowing WTP, can only group people in market segment and have different price for each segment.
Based on where customer belongs, charge different price.

44
Q

Elasticity of demand

A

Consumers can be very price sensitive (stingy) or not very price sensitive.
Elasticity measures how much quantity demanded changes when price is changed by a certain amount.
E= (Dq/q) / (dp/p) = dq/dp * p/q
Note we will have q in terms of p because of the demand function
Also note that dq/dp is the deriv of q with respect to p. Will have only p’s in our answer

Look at absolute value of E. Higher abs value is the more elastic one, lower value market.
More elastic, lower price because they are more sensitive to change in price. Lower price means more price sensitive.
Less elastic, higher price, as less price sensitive and will buy anyway. Higher price, less price sensitive.

Lower prices to get more elastic buyer, but tradeoff because less margins on high value market. So, price discrimination.

45
Q

If no price discrimination, firm choices:

A

Sell to both markets

Or only sell to high value, less elastic, market.

46
Q

Multiple market strategy trade offs

A

Selling to both:
Good is that larger market since both markets
But, in order to get to the low value market (stingy, more elastic),need to lower the price below what would originally optimally charge high value market.

Selling to both is profitable if:
Difference in elasticities between markets isn’t too big. Low value market isn’t too low value relative to high value market
Or if low value market is much larger relative to high value market, so don’t want to lose out on a large number of buyers.

Lower price gets more buyers, tradeoff because less margins on high value market. Need to decide if it is worth it

47
Q

What happens when price discrimination (3rd degree) is allowed?

A

If before we sold to both markets, then price for high value consumers will go up and for low value consumers will go down.

If before only sold to high value consumers, high value consumers price unchanged and set monopoly price for low value and sell positive quantities.

Welfare implications:
1. Increases profits. However, no change if firm earns zero profits from low value market.

  1. If optimal for firm to exclude some markets when restricted to a single price, then allowing pd will increase consumer surplus.
    No change if firm Chargers low value consumers’ WTP.
48
Q

Monopoly with multiple markets steps

A
  1. Aggregate demand function
    2 profits under strategy of selling to both markets
    A. Inverse demand
    B. MR=MC
    C. Check p is in the right range so selling to both markets
    D. Profits.
  2. Profits under selling to high value only
    A. What is high value? Less elastic (abs value lower)
    B. Info demand
    C. Mr = Mc
    D. Check p is valid in range
    D. Profits
  3. Whichever is higher profit and get p and q in each case if can’t pd
  4. Now can pd. Get the new profits, cs, and total welfare with pd and compare.
49
Q 
Monopoly with Mult Markets Ex:
q1= 100-p
q2=50-p
C(q)=10
Step 1
A
  1. Aggregate demand.
    If p is bigger than 100, nether market demands, so Qd=0
    If p is between 50 and 100, then just market 1, so Qd = 100-p
    If p is less than 50, then both markets. So, add up. Qd = 150-2p
50
Q 
Monopoly with Mult Markets Ex:
q1= 100-p
q2=50-p
C(q)=10
Step 2
A

Profits under strategy of selling to both markets.
A. Inverse demand. Since both markets, Q = 150-2p so p = 75-q/2
B. MR = MC.
Remember, linear inverse demand, so MR =75-q
Mc = 0, so q = 75
C. Check p. P = 75-q/2 = 37.5
To sell to both markets, p less than 50. This is valid.
D. Profits.
PQ - total cost
37.5(75)-10 = 2802.5

51
Q 
Monopoly with Mult Markets Ex:
q1= 100-p
q2=50-p
C(q)=10
Step 3
A

Computer profits under just selling to high value market.
First need to see which is high value market. Take the absolute value of the elasticities
E1= dq/dp * p/q
= -1(p/(100-p)) and E2 = -1(p/(100-p))
Absolute value, market 1 is smaller, less elastic, so higher value. Change in price doesn’t influence quantity demanded as much.
A. Inverse demand. P = 100-q
B. MR=MC, 100-2q =0,q =50
C. Check P. P =100-q = 50. This is valid.
Note, if p had not been valid, then would just sell to both markets.
D. Profits. 50(50)-10=2490

52
Q 
Monopoly with Mult Markets Ex:
q1= 100-p
q2=50-p
C(q)=10
Step 4
A

We got the profits and found that we have a higher profit when selling to both markets.
So p =37.5 and plug into each demand function to get q1 = 62.5 and q2 = 12.5

53
Q 
Monopoly with Mult Markets Ex:
q1= 100-p
q2=50-p
C(q)=10
What if we can price discriminate?
A

We already got Prof without pd = 2802.5

Profits with pd:
1. Market 1 we already optimized in step 3 and got a revenue of 2500
2. Optimize market 2
A. Inverse demand, p = 50-q
B. Set mr = Mc, 50-2q = 0, q =25
C. Get p = 50-q=25
D. Revenue = pq = 25(25)=625
3. So profits = (625+2500)-10. Total revenue - cost

See next page for CS and total welfare

54
Q

Consumer surplus

A

Difference between willingness to pay and actual price up until quantity produced. Area under inverse demand curve.

p= a-bq1
Cs1 = (a-PM)(q1M)/2, área of the CS triangle.

Can calculate before and after price discriminating for each market based on the price being charged. Will be same price, p, if can’t pd.

If sell to both markets before, Consumer surplus for high value market down when can pd and will go up for low value
If sell to only high value market before, cs for high value will stay same. For low value will increase (from 0)

Will increase only if pricing not at exactly the WTP. If exactly WTP, then consumer surplus =0

55
Q

Total welfare

A

Profit plus consumer surplus.

We see that total welfare is lower with price discrimination when previously was optimal to sell to both markets.
But will increase if before optimal only sell to high value market.

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