Download Study Guide for Final Practice Problem Answers

Practice Problem Answers. Study hard and you will do well! See you Tuesday 5/5 at 3:15 pm.
1. If the marginal product of labor is currently 10, and the marginal rate of technical substitution is
currently 20, what does the marginal product of capital equal?
MRTS=MPL/MPK; 20=10/MPK; MPK =0.5
2. A firm has access to two production processes with the following marginal cost curves:
MC1=0.4Q and MC2= 2 + 0.2Q
If it wants to produce 8 units of output, how much should it produce with each process?
The firm minimizes costs when it distributes production across the two processes so that marginal
cost is the same in each. If Q1 denotes production in the first process and Q2 is production in the
second process, we have Q1 + Q2 = 8 and 0.4Q1 = 2 + 0.2Q2, which yields Q1=6, Q2=2. The
common value of marginal cost will be 2.4.
3. You have been hired by the IRS to audit a dead economist's consulting firm. He left his
records incomplete so that only a student trained in economics could fill in the blanks. . You
have been hired by the IRS to audit a dead economist's consulting firm. He left his records
incomplete so that only a student trained in economics could fill in the blanks.
Clients Total
Cost
0
1
2
3
4
5
6
7
100
175
240
330
450
600
800
1100
Total
Fixed
Cost
100
100
100
100
100
100
100
100
Total
Variable
Cost
0
75
140
230
350
500
700
1000
Average
Total
Cost
175
120
110
112.5
120
133.33
157.14
Average
Variable
Cost
75
70
83.33
87.5
100
116.67
142.86
Average
Fixed
Cost
100
50
33.33
25
20
16.67
14.29
Marginal
Cost
75
65
90
120
150
200
300
Does the consulting firm exhibit diminishing returns for any number of clients between 0 and
7?
The firm exhibits diminishing returns for any number of clients greater than two.
4. Doug wants to go into the donut business. For $500 per month he can rent a bakery complete
with all the equipment he needs to make a dozen different kinds of donuts (K=l). He must pay
unionized donut bakers a monthly salary of $400 each. He projects his production function to be Q
= 5KL (where Q is tons of donuts).
a. What is Doug's monthly total cost function, variable cost function, and marginal cost?
b. How many bakers will Doug hire to make 25 tons of donuts?
c. What will happen to Doug's total cost if his production function turns out to be Q=2KL?
a) K=1 L=Q/5
TC = 500 + 400(Q/5) = 500 + 80Q
VC = 80Q
The marginal cost is equal to the slope of the total cost curve which is MC = 80.
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b) L = Q/5 = 25/5 = 5
c) K = 1, L = Q/2, TC = 500 + (400/2)Q = 500 + 200Q
5. A firm’s production is given by Q = K1/3L2/3; the price of labor (w) equals $12 and the price of
capital (r) equals $16.
a.) What is the optimal amount of capital and labor needed to produce 2,000 units?
b.) What do their total costs equal?
a. The MRTS=(2K/L) = (w/r=12/16); L=2.67K or K=.375L. Plugging this back into the
production function one finds:
2000 = (.375K)1/3L2/3=.7214L
L*=2772; K*=1040
b. TC = 2772*$12 + 1040*16 = $49903 (rounded)
6. Suppose your firm uses labor and capital in the production of commodity X. You are currently
employing 15 workers and 30 units of capital. The total wage bill (L x w) is $800 per day, and the
total capital payments bill is $1200 per day (K x r).
a. Suppose that you know that the marginal physical products of labor and capital are 20 and 18
respectively. Is your firm currently minimizing long run costs? Explain.
b. Alternatively, assume that your firm is indeed minimizing long run costs. What is the long run
marginal cost of output if you are certain that the marginal product of capital, MPk, at the current
output rate is 10? Explain.
a. No. After you translate the total wage bills into prices per unit of input, the current mix of inputs
does not meet the cost-minimizing condition: ratio of marginal products must equal the ratio of
input prices, or marginal product per dollar must be equal across all inputs.
b. If you are currently minimizing costs, you are using inputs so that the marginal products per
dollar are equal across inputs. Thus, with the rental price equal to $40, and MPk=10,
MC=r/MPk=$4.00
7. Assume a firm has total revenue function given by TR = 80Q and a total cost function given by
TC = 200 + Q2. Solve for their profit maximizing quantity and price. What do their profits equal?
Profit maximizing Q is found by solving for:
MR = MC
80 = 2Q
Q* = 40
Profits = TR – TC = 80*40 – (200 + 402 ) = 3200 – 1800 = 1400
8. Suppose a representative firm in a perfectly competitive, constant cost industry has a cost
function TC = 4Q2 + 100Q + 100.
a. What is the long-run equilibrium price for this industry?
The minimum point on LAC is found either by graphing the LAC curve or by taking the first
derivative and setting it to zero.
dLAC/dQ = 4 - 100/Q2 = 0, which yields Q = 5.
In the long run P = LAC = 140
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b. If market demand is given by the function Q = 1000 – P, where P denotes price, what is the total
quantity produce sold in this market? If all firms produce the same quantity, what is the total
number of firms in this market?
If demand is Q=1000-P, then at P=140, we get Q=860. So in long run equilibrium, there will be
860/5 = 172 firms.
9. Use the following production/cost table to answer the following questions.
Labor
Output(Q)
Fixed Costs Variable Costs Total Costs Marginal Costs
0
0
400
0
400
1
10
400
50
450
50/10=$5
2
22
400
100
500
50/12=$4.17
3
30
400
150
550
50/8=$6.25
4
38
400
200
600
50/8=$6.25
5
40
400
250
650
50/2=$25
6
41
400
300
700
50/1=$50
a. Fill in the blanks in the table above.
b. If this firm sells all its output at a constant price of $25, what is the profit maximizing Q? P=MC
at Q=40.
c. What do their profits equal?
TR=P*Q – TC = $25*40 - $650 = $1,000 - $650 = $350
10. Use the following diagram representing a perfectly competitive firm to answer the following
questions
P
MC
ATC
AVC
20
d=MR
15
14
6
400
500
600
800
Q
a. What is the profit maximizing quantity? 600
b. What does profit equal at the profit maximizing Q? ($20 - $15)*600=3,000
c. What is the shutdown price? $6 (minimum of AVC)
d. At what price would profits equal zero? $14 (minimum of ATC)
e. If price changes from $20 to $14, what happens to this firm’s output? Output would decrease from
600 to 450.
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Cost
marginal
cost
$70.00
E
$60.00
D
$50.00
C
$40.00
B
$30.00
A
$20.00
$10.00
$0.00
0
45
55
65
75
85
Quantity
11. Refer to the graph above. If the market price increases from $50 per unit to $60 per unit, how
will a profit-maximizing perfectly competitive firm change their output?
They will increase production from 65 to 75.
12. Suppose a firm is earning negative profit, but is continuing to operate. What do we know must
be true of TC compared to TR, and VC compared to TR? What do we know must be true of ATC
compared to P, and AVC compared to P?
Because profit is negative, we know that TR<TC. Because they are still operating we know that
TR>VC.
Similarly, we know that AVC<P<ATC.
13. Suppose a barber shop has fixed cost equal to $1,000/month and total costs equal to
$5000/month. This shop will continue to operate in the short run as long its total revenue is greater
than $4,000 (their variable costs)?
14. Explain what Adam Smith was referring to when he used the analogy of an “invisible hand”
leading us and guiding the allocation of resources in society?
He was talking about how prices and profits provide a signal and incentive to producers. When
prices increase (ie. if demand increases), more profit can be made, so more of it will it be produced.
When prices decrease (ie. if demand decreases), less profit can be made, so less of it will be
produced.
15. Give the formulas for economic and accounting profit. Why must economic profits always be below
accounting profit?
Accounting profit = Total revenue – explicit costs
Economic profit = Total revenue – explicit costs – implicit costs
Economic profit must always be below (there was a typo on the original question) accounting profit
because it is equal to accounting profit – implicit costs, and implicit costs can never be negative.
16. If total revenue=$3,000, explicit costs=$2,000, and implicit costs=$1,200, what is this firms
economic and accounting profit?
Acct. profit=$1,000; Economic profit= -$200
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17. What does it mean when economic profits are negative for a firm (mathematically and intuitively)?
Mathematically it means that (explicit + implicit costs) > total revenue.
Intuitively it indicates that the firm would be able toearn more if they devoted their resources toward their
next best alternative.
18. A firm’s accounting profit is $20,000, economic profit is $5,000, and total revenue equals
$100,000. What do their explicit costs and what implicit costs equal?
It means their total revenue is $20,000 greater than their explicit costs, so their explicit costs equal
$80,000. Because economic profit equals accounting profit minus implicit costs, their implicit
costs must equal $15,000.
19. Draw the MR, MC, ATC curves for a perfectly competitive firm that is earning zero profit.
P
ATC
MC
d=MR
Q
20. Explain the sequence of events that will occur when firms are earning economic profits in a perfectly
competitive industry by filling in the blanks below:
1. Firms enter the industry; 2. Market supply shifts right;
3. Equilibrium price decreases. ; 4. Firms’ marginal revenue decreases;
5. Firms’ profits decrease to zero.
21. Suppose farmers suddenly can earn considerably more per acre from growing wheat than from
growing potatoes. What can we expect will happen in the long run as far as number of farmers in
each industry and the prices of each good?
Some farmers will switch from growing potatoes to growing wheat. This will cause the price of
wheat to fall and the price of potatoes to rise.
22. In a competitive industry consisting of 10,000 firms, the short-run marginal cost curve for each
firm is given by MC = 200 + 30Q, and supply for the industry is given by 200 + .003Q. The
demand curve faced by the industry is given as P = 400 - .002Q.
a. Calculate the equilibrium price and quantities for the industry and each firm.
Set demand equal to supply: 400 - .002Q = 200 + .003Q
200= .005Q: so Q = 200/.005 = 40,000 for the industry
Q for firm = 40,000/10,000 = 4
P = 200 + 30(4) = 320
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b. Find the producer and consumer surplus at the equilibrium price.
Producer surplus (PS): PS = 1/2(320 - 200)[40,000] = 2,400,000
Consumer surplus (CS): CS = 1/2(400 - 320)[40,000] = 1,600,000
23. Suppose you are a profit maximization consultant for firms (which means you’re a consultant).
Given the selected information, select one of the following recommendations for each firm and
briefly explain why that is your recommendation. The options are:
a. Remain at the current output level.
b. Increase output.
c. Decrease output.
d. Shut down.
e. Go back and recalculate your figures because the ones supplied are not correct.
Firm
1
P
$3.90
2
3
$35.90
MR
$3.00
TR
Q
2000
TC
MC
$7400 $2.90
ATC
$9.00 $44000 4000
$9.00
$11.90
$37.90
$37.90 $35.90
5000
AVC
b. MR>MC
$10.74
a. MR=MC
e. P<MR
24. A monopolist has a demand curve given by P = 100 - Q and a total cost curve given by
TC = 16 + Q2. Find the monopolist’s profit-maximizing quantity and price. How much economic
profit will the monopolist earn?
The profit maximizing level of output for a single-price monopolist occurs where MR = MC. The
linear demand curve P = 100 – Q has a marginal revenue of MR = 100 – 2Q. By equating marginal
revenue and marginal cost (100 – 2Q = 2Q) we get a quantity of 25. The price charged for this
quantity is read off the demand curve so P = 100 – Q = 100 – 25 = 75. OR
MC = 2Q = MR = 100 - 2Q;
100 - 2Q = 2Q, so Q* = 25, P* = 75.
TR = 1875; TC = 641
 = TR - TC = 1234
25. Now suppose the monopolist in question 24 has a total cost curve given by TC = 32 + Q2
(Fixed costs have doubled). Find the monopolist’s profit-maximizing quantity and price. How
much economic profit will the monopolist earn?
The monopolist’s price and quantity are unaffected by fixed costs. However, the monopolist earns
lower profits:
 = TR – TC = 75Q – (32 + Q2) = 1875 – 657 = 1218. The difference in profits equals the
increase in fixed costs.
26. Now suppose the monopolist in question 24 has a long-run marginal cost curve given by
MC = $20. What is the deadweight loss area associated with this monopolist?
The profit-maximizing level of output for a single-price monopolist occurs where MR = LMC, The linear
demand curve P = 100 – Q has associated marginal revenue of MR = 100 – 2Q. Setting marginal revenue
equal to marginal cost, LMC = 20, we have 100 – 2Q = 20, which solves for Q = 40. The price charged
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for this quantity is read off the demand curve: P = 100 – Q = 100 – 40 = 60. A perfectly competitive
industry would produce the quantity such that P = LMC = 20 so that Q = 100 – 20 = 80. The total surplus
generated by perfect competition would be TS = (1/2)80(100 – 20) = 3200. By comparison, the
monopoly generates producer surplus PSm = 40(60 – 20) = 1600 and consumer surplus CSm = (1/2)40(100
– 60) = 800 for a total surplus of TSm = 160 = 80 = 2400. The efficiency loss due to monopoly is the
amount by which total surplus under monopoly falls short of the total surplus under perfect competition.
(TS = 2400 – 3200 = 800) The efficiency loss is the triangular area between the demand curve and
marginal cost (supply) with base equal to quantity by which output under perfect competition exceeds
output under monopoly.
P
$80
$60
MC
$40
D
MR
120
Q
170
27. Suppose the firm above is able to price discriminate, charges a price of $80 for the first 120 units, and a
price of $60 for the next 50 units. Calculate the change in consumer and producer surplus and deadweight
loss as a result of this price discrimination (compared to if they were a single price monopolist).
Producers gain $1,000 in surplus ($60-$40)*(170-120), and consumers gain $500 in surplus
[½ ($80-60)*(170-120)].
Deadweight loss decreases by the total gains in surplus ($1,500)
28. Use the following diagram representing a monopoly to answer the following questions
P
MC
ATC
12
11
9
8
7
3
MR
2400
3000 3300
D
5000
Q
7
a.) What is the profit maximizing quantity of production?
Q=2400
b.) What is the profit maximizing price to charge?
P=12
c.) What do profits equal?
Profits=(P-ATC)*Q = ($12-$9)*2400 = $7200
d.) What could we expect price and quantity to be if this were a competitive industry?
P=9; Q=3300.
e.) What would the quantity sold be if this were a perfectly price discriminating monopolist?
Q=3300.
f.) What would the deadweight loss equal if this were a perfectly price discriminating monopolist?
There will be zero deadweight loss if it were a perfectly price discriminating monopolist.
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