Economics 160



Economics 160

Study Questions

PRODUCTION AND COSTS

1. What is meant by the “short run”? What is a fixed input?

2. a. Fill in the table below.

Labor (L) Total Product (Q) Marginal Product (MP)

0 0 .

1 20 .

2 45 .

3 75 .

4 100 .

5 120 .

6 135 .

7 145 .

b. What is the law of diminishing marginal returns? According to the above table, does diminishing returns set in right away? Why might the marginal product initially rise?

c. Draw a graph of the total product curve (production function) and the marginal product curve.

3. a. Fill in the table below. Assume that P = $0.50.

Labor (L) Q MP P*MP

0 0 --- ---- .

1 100 .

2 190 .

3 270 .

4 340 .

5 400 .

6 450 .

7 490 .

If the price for a unit of labor (wage rate) is $25 per labor unit, then how many workers would a profit-maximizing firm hire? Suppose the government passes a minimum wage law (price floor) that requires that firms pay a wage rate of at least $35 per unit of labor.

How workers would a profit-maximizing firm hire now?

4. Define: long run, fixed costs, variable costs.

5a. What is marginal cost? ..average total cost?...average fixed cost?... average variable cost?

5b. Fill in the table below.

Q TFC TVC TC AFC AVC ATC MC .

0 0 ---- ---- ---- ---- .

1 $10 .

2 $30 $45 .

3 $40 .

4 $140 .

5 $50 .

6. On a graph, draw in the AVC, ATC, and MC curves. What are the relationships between these three curves?

7. Which of the following regions violates the relationship between marginals and averages?

Marginal variable,

Average variable marginal variable

1 2 3 4 5

Average variable

8. True or False. Explain.

a. “If marginal cost is below average total cost then average total cost must be falling”.

b. “If the marginal product of labor is falling, then total product must be falling.”

c. “In the long run, all costs are variable costs.”

9. Country A has marginal product of labor of 10 and wage rate of $20/L. Country B has

a marginal product of labor of 2 and a wage rate of $5/L. Which country has the lower marginal cost?

10. What is meant by “economies of scale”? …by “diseconomies of scale”?

11. The following table shows long-run total cost for different quantities.

Does this firm experience economics of scale, diseconomies of scale , or constant returns to scale?

Q LRTC .

0 0 .

1 $20 .

2 $36 .

3 $48 .

4 $56 .

ANSWERS

1. Short run: a period of time over which at least one input is fixed. A fixed input is an input whose quantity cannot be varied (over some non-trivial period of time).

2. a.

Labor (L) Total Product (Q) Marginal Product (MP)

0 0 ---- .

1 20 20 .

2 45 25 .

3 75 30 .

4 100 25 .

5 120 20 .

6 135 15 .

7 145 10 .

2b. Diminishing marginal returns: As a firm adds equal amounts of one input, holding other inputs and technology constant, then beyond some point output may rise but at slower and slower rate.

No, it does not set in right away—initially MP rises, but past 3 units of labor is starts to fall.

MP might initially rise due to gains from division of labor or specialization.

3. Assume that P = $0.50.

Labor (L) Q MP P*MP

0 0 --- ---- .

1 100 100 $50 .

2 190 90 $45 .

3 270 80 $40 .

4 340 70 $35 .

5 400 60 $30 .

6 450 50 $25 .

7 490 40 $20 .

P*MP = price of labor = $25 at a quantity of labor of 6. So the firm hires 6 workers.

At a wage rate of $35, the firm hires 4 workers.

4. Long run: All inputs are variable. Fixed costs: costs which do not vary as output varies. Variable costs: costs which do vary as output varies.

5. a. Marginal cost (MC) = (change in TC)/(change in Q).

Average total cost = TC/Q Average Fixed cost = FC/Q

Average variable cost = VC/Q.

5b.

Q TFC TVC TC AFC AVC ATC MC .

0 $60 0 $60 ---- ---- ---- ---- .

1 $60 $10 $70 $60 $10 $70 $10 .

2 $60 $30 $90 $30 $15 $45 $20 .

3 $60 $70 $130 $20 $23.33 $43.33 $40 .

4 $60 $140 $200 $15 $35 $50 $70 .

5 $60 $250 $310 $12 $50 $62 $110 .

6.

$/unit MC ATC

AVC

QAVCmin QATCmin Q

a. ATC and AVC converge as Q increases. To see this, notice that ATC=AVC+AFC, or rearranged AFC = ATC-AVC. In other words, AFC represents the vertical gap between

the ATC curve and AVC curve. Since AFC always falls as Q rises, then the gap between

ATC and AVC always gets smaller as Q increases—that is, these curves converge.

b. The minimum point of the ATC curve occurs at a larger quantity than the minimum point of the AVC (see above graph). To understand this, notice that in between

the quantities QAVCmin and QATCmin MC is above AVC (and so AVC must be rising). If AVC is rising then we are already past its minimum point. Yet MC is below ATC (and so ATC must be falling) and if ATC is still falling it has not yet reached its minimum point. c. If MC > ATC, then ATC must be rising.

If MC> AVC, then AVC must be rising.

If MCATC. Yet, this is best the firm can do. Profits are maximized at MR=MC, if the firm was to produce more or less than this quantity profit would fall.

6. Profit-maximizing Q = 50 units (where MR=MC).

Profit at this quantity = (P-ATC)(Q) = (10-13)(50) = -150.

If the firm shuts down its profits (losses) equal FC.

To find FC notice that, AFC= ATC-AVC. At Q=50, AFC= 13-8= $5.

FC = AFC*Q= (5)(50) = $250. Therefore, losses if shut down equal $250.

It is better to continue to operate since losses are smaller (150 vs. 250).

7. SR equilibrium condition: P=MC for each firm.

LR equilibrium condition: P=MC=ATC. (That P=ATC indicates that economic profits are zero).

8. Economic Profit= TR – total explicit costs-total implicit costs.

TR = $400,000/year. Total explicit costs = $200,000+$100,000= $300,000.

Total implicit costs = $50,000 (the forgone salary) + $200,000 (forgone interest income).

Economic profit = 400,000-300,000-250,000= -$150,000.

Accounting profit=400,000-300,000= +$100,000.

9.

$/unit FIRM P MARKET

SRSM(n-m firms)

SRSM(n firms)

MC=SRSf

ATC

ATCSR LRS

P1 MR1 P1

PSR MRSR PSR

D1

D2

qsr q1 q QLR QSR Q1 Q

Assume market demand declines.

SR effects: The decrease in demand causes price to fall to PSR. This leads profit-maximizing firms to reduce output to qsr. At this new quantity, PSR < ATCSR and so firms are incurring losses in the short run.

LR effects: The existence of losses causes some firms to exit the industry. As this happens, the supply curve shifts to left. This causes price to be bid up. This process continues until P again equals ATC (which occurs at the original price). At this point, profit is again zero, so exit stops and as exit stops the supply curve stops shifting back.

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