Sample Short Answer/Problem Questions: Review Session #2 Question 1: Costs of Production



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Sample Short Answer/Problem Questions: Review Session #2
Question 1: Costs of Production
1a) A fast-food restaurant currently pays $5 per hour for servers and $50 per hour for rental machinery. The restaurant uses seven hours of server time per unit of machinery time. Determine whether the restaurant is minimizing its cost of production when the ratio of the marginal product of capital to the marginal product of labor is 12. If not, what adjustments are called for to improve the efficiency in resource use?
In equilibrium, r/w = MPK/MPL. I.e. if the firm is minimizing its costs of production, then the MRTS will equal a ratio of the prices of the inputs. The ratio of prices, r/w = 50/5 = 10, and the MRTS of capital for labor . Since these two ratios are not equal, the firm should change the mix of inputs. To increase efficiency in the use of inputs, the firm should use more capital and use less labor to make the ratios equal.
1b) Complete the following table. Explain the pattern observed when looking at AC and MC.



Q

TFC

TVC

TC

MC

AFC

AVC

ATC

0

50

0

50

-

-

-

-

1

50

10

60

10

50

10

60

2

50

25

75

15

25

12.5

37.5

3

50

50

100

25

16.7

16.7

33.4

4

50

100

150

50

12.5

25

37.5

5

50

175

225

75

10

35

45

6

50

300

350

125

8.3

50

58.3

MC is increasing from 1Q, implying diminishing marginal product of labor. AC start high (due to the presence of fixed costs). AC decline initially as FC get spread out over more output, but then start to increase with the increase in AVC.


1c) In the European Union, more than 400 firms produce shoes but only 1 produces aircraft. What might be one of the main explanations for the difference in the number of firms in the two industries?
(Production) Economies of scale: the bigger is minimum efficient scale relative to market size, the fewer the number of firms that can survive.
Question 2: Perfect Competition
2a) Conigan Box Company produces cardboard boxes that are sold in bundles containing a thousand boxes. The market is perfectly competitive, with boxes currently selling for $100 per thousand. Conigan’s total and marginal cost curves, where Q is measured in number of bundles per year, are:
TC = 3,000,000 + 0.001Q2

MC = 0.002Q



  1. Calculate Conigan’s profit maximizing quantity. Is the firm earning a profit?

Conigan should equate P to MC. Thus, 100 = 0.002Q so Q = 50,000. To determine profit: = TR – TC. TR = PQ = $100 * 50,000 = $5,000,000. TC = 3,000,000 + 0.001(50,000)2 = 3,000,000 + 2,500,000 = 5,500,000. Thus, = 5,000,000 - 5,500,000 = -500,000. Conigan is losing 500,000 per year.




  1. Analyze Conigan’s position in terms of the shutdown condition. Should Conigan operate or shut down in the short-run? And in the long-run?

To determine if the firm should operate or shutdown, we must compare P to AVC = . TVC = TC – TFC = 5,500,000 - 3,000,000 = 2,500,000. Thus, AVC = = $50. Since P = $100, the firm should operate in the short-run. In the long-run, Conigan should think about exiting the market.


2b) Complete the following table for a price taking competitive firm, where the market price is $40. Determine the profit maximizing level of output.


Q

FC

TC

AC

MC

TR

AR

MR

0

25

25

-

-

0

-

-

1

25

35

35

10

40

40

40

2

25

60

30

25

80

40

40

3

25

105

35

45

120

40

40

4

25

185

46.3

70

160

40

40

5

25

285

57

100

200

40

40

6

25

405

67.5

120

240

40

40



Question 3: Analysis of Perfect Competition
Use the diagram to answer the following questions:


  1. What is the equilibrium p* and q* in the camera market?

p* = $50 and q* = 500




  1. Suppose the government places a tax on camera manufacturers of $20 per camera. Show the effect of the tax in the diagram. What price will buyers pay, and what price will sellers receive? How many cameras will be sold?

Tax = $20. Pb = $60, Ps = $40. 400 cameras will be sold.






  1. Why does the imposition of a tax lead to a deadweight loss? Calculate the deadweight loss associated with the $20 tax.

The DWL is because the quantity sold is less than the social optimum (there is a consumption distortion due to a higher Pb and a production distortion due to the lower Ps). The DWL = ½ * 20 * 100 = $1000


3b) The utilities commission in a city is currently examining pay telephone service in the city. The commission has been asked to evaluate a proposal by a city council member to place a $0.10 price ceiling on local pay phone service. The staff economist at the utilities commission estimates the demand and supply curves for pay telephone service as follows, where P = price of a pay telephone call, and Q = number of pay telephone calls per month:
QD = 1600 - 2400P

QS = 200 + 3200P




  1. Determine the equilibrium price and quantity without the price ceiling.

1600 – 2400P = 200 + 3200P. P = $0.25 and Q = 1000




  1. Determine the quantity that will be available if the price ceiling is imposed.

The price ceiling is $0.10. QD = 1600-(0.1*2400) = 1360; QS = 200 + (0.1*3200) = 520. The shortage is 1360-520 = 840 calls per month.



Question 4: Monopoly
4a) Draw two diagrams – the first to represent an individual firm in a perfectly competitive market in long-run equilibrium, and the second to represent a monopolist. Explain why monopoly leads to a deadweight loss.
Perfect Competition: Slide 2, Chapter 10

Monopoly: Slide 7, Chapter 10

Monopoly leads to a deadweight loss because total output produced is less than the social optimum (under perfect competition).
4b) The profit-maximizing price charged for goods produced is $16. The intersection of the marginal revenue and marginal cost curves occurs where output is 10 units. Assume constant marginal and average cost at $8. Draw a diagram to depict the above. What profit does the monopolist earn? Calculate the deadweight loss (assuming the perfectly competitive firm would produce 20 units).
To draw the diagram, start with a demand curve. The marginal revenue curve lies below the demand curve and intersects with MC at q=10.
Profit = (p-ac)q = (16-8)10 = $80.

DWL = ½ (10*8) = $40.


4c) Define a natural monopoly, explaining what the size of the market has to do with whether an industry is a natural monopoly. Suppose that a natural monopolist were required by law to charge its average cost. Draw a diagram, label the price charged, and the deadweight loss to society relative to marginal cost pricing.
Natural monopoly: economies of scale are sufficiently large relative to market size that there is room for only one firm in the market that produces efficiently. In other words, AC are everywhere declining over the relevant range of output (so if we had many firms producing, then each firm would produce less, leading to AC increasing).
Monopoly: Slide 15, Chapter 10. Note, the DWL is equal to the ½ * (Pac- Pmc) * quantity reduction.


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