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Homework II Summer 2005

(10 points) Answer both of the following essay questions (write only on the paper provided): 1. Carefully define Total Product of Labor (TPL), Average Product of Labor (APL) and Marginal Product of Labor (MPL). Carefully draw each of these three short-run production curves. Why do these three curves look the way that they do? How are these three curves related? Briefly explain your answer.

1

2

Q

Total Product of Labor (TPL) equals the production function and shows total output (Q) in the shortrun given the variable input, holding capital constant. Average Product of Labor (APL) equals Q/L while Marginal Product of Labor (MPL) equals the extra output gained by hiring one more unit of labor.

_ Q = f(L, K)

The curves are to the right and look the way they do because of the law of diminishing returns. That says that MP may initially rise due to returns to specialization but must eventually fall due to congestion in the short-run.

Labour

APL = slope of line drawn from origin on TP diagram to TP at the given level of labor. Notice that the curves are related as shown in the graphs to the right: •

when MP > 0 then TP is increasing.

•

When MP < 0 then TP is decreasing.

•

When MP is at max then TP is at inflection point.

•

When MP = 0 then TP is at a max.

•

If AP=MP then AP at max.

•

If MP>AP then AP increasing

•

If MP < AP then AP decreasing

MPL, APL

MPL = slope of TP curve.

APL

MPL Labour Graph 4

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2. The Table below contains production information for a firm. Use your definitions of MPL and APL from question 1 above to fill in the blanks in the table below. Carefully define the following costs: Total Cost (TC), Total Variable Cost (TVC), Total Fixed Cost (TFC), Marginal Cost (MC), Average Total Cost (ATC), Average Variable Cost (AVC), and Average Fixed Cost (AFC). In addition to the information in the completed table and the definitions of the costs you gave above, what information must you know in order to be able to calculate the firm’s costs (all seven of those mentioned above)? Briefly explain your answer. Amount of Capital

Amount of Labor

Total Output

APL

MPL

2

0

0

--

--

2

2

150

75

75

2

4

400

100

125

2

6

600

100

100

2

8

760

95

80

2

10

860

86

50

2

12

900

75

20

•

TC = payment for all inputs, explicit and implicit or = TVC +TFC

•

TVC = payment for variable inputs or production costs that varies.

•

TFC = payment for fixed inputs or production costs that don’t vary.

•

MC = ∆TC/∆Q = ∆TVC/∆Q = the extra cost of producing one more unit of output.

•

ATC = TC/Q; AFC = TFC/Q; AVC = TVC/Q

•

In addition to the above material you simply need to know the wage rate (the cost of each unit of labor) and the interest rate (the cost of each unit of capital.) Suppose that w = $125 while r = $1000 – see if you can calculate these numbers.

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(16 points) Answer all of the following 16 multiple-choice questions. Make sure that your answers are coded in the answer sheet provided. 1.

Consider the following two statements: I. A firm can produce on or below its isocost curve but cannot produce above it. II. The slope of the isocost curve equals the marginal rate of technical substitution. A. both statements are true. B. both statements are false. C. I is true while II is false. D. I is false while II is true.

2.

The short run for a firm is a period: A. generally more than three years. B. sufficient to adopt new technology. C. during which at least one productive resource cannot be varied. D. during which all productive resources can be varied

3.

4.

5.

6.

7.

Suppose that in the short-run (Labor is the only variable input) when output equals 50, (1) the firm uses 5 workers and pays them a wage $40 and (2) total fixed costs equal $200. Then we know all of the following except: A. Total Variable Cost (TVC) = $200. B. Average Total Cost (ATC) = $8. C. Average Variable Cost (AVC) = $4. D. Average Fixed Cost (AFC) = $8. Use the following Table to answer question 8

Which of the following equations represents Total Fixed Cost (TFC)? A. AFC÷ Q. B. AFC * Q. C. AVC * Q. D. TVC + TC. When a firm faces decreasing returns to scale then as the firm doubles its use of all inputs then output will: A. More than double. B. Exactly double. C. Less than double. D. It is impossible to say what will happen to output. In producing a given output, a profit maximizing firm would choose inputs in the long-run so that: A. The revenue gained by producing that output is maximized. B. The cost of producing that output is minimized. C. The average productivity of each input is maximized. D. The marginal productivity of each input is maximized.

L

Q

TFC

TVC

6

84

2000

750

8

120

2000

1000

10

160

2000

1250

8.

Given the Table above, we know all of the following except: A. the wage rate = $125. B. the marginal cost when L = 8 is 6.94. C. the average variable cost when L = 8 is 8.33. D. the marginal physical product of L when L = 10 is 40.

9.

The Total Costs of Production include: A. both explicit and implicit costs. B. both average fixed costs and average variable costs. C. only explicit costs. D. only implicit costs. E. only average variable costs.

10. Consider the following two statements: I. An isoquant curve shows different combinations of labor and capital that will all produce the same output. II. The slope of the isoquant equals negative the ratio of the price of labor to the price of capital. A. both statements are true. B. both statements are false. C. I is true while II is false. D. I is false while II is true.

Short-run cost curves are U-shaped due to: A. increasing input prices. B. the returns to specialization of labor that occurs at low production levels and the congestion that occurs at high production levels. C. increasing marginal product of labor (MPL). D. decreasing MPL. E. the returns to specialization of labor that occurs at high production levels and the congestion that occurs at low production levels.

11. Long-run cost minimization occurs when the firm chooses its inputs such that: A. The firm is on its isocost curve. B. The firm is on its isoquant curve. C. The firm’s isocost curve is tanget to its isoquant curve. D. The firm’s isocost curve intersects its isoquant curve.

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12. Which of the following terms represents marginal cost? A. TC ÷ Q. B. ∆ (change in) Q ÷ ∆ TC. C. Wage ÷ Marginal Product of Labor. D. Wage ÷ Average Product of Labor. 13. When the Average Fixed Cost is declining then we know that: A. Marginal Cost (MC) is declining. B. MC is increasing. C. MC is above Average Total Cost (ATC). D. MC is below ATC. E. None of the above. 14. Consider the following two statements: I. The law of diminishing returns states that eventually, as the use of an input increases, ceteris paribus, that input’s marginal product must decrease. II. Productivity curves and cost curves are ultimately based upon the law of diminishing returns. A. both statements are true. B. both statements are false. C. I is true while II is false. D. I is false while II is true. 15. When the marginal product of labor is increasing: A. the total product of labor is increasing. B. marginal cost is decreasing. C. the average product of labor is increasing. D. average variable costs are decreasing. E. all of the above are correct. 16. Consider the following two statements: I. A perfectly competitive firm maximizes profit where marginal revenue (MR) equals marginal cost (MC) while a monopoly maximizes profit by producing where MR > MC. II. A perfectly competitive firm’s demand curve is perfectly elastic at the market price. A. both statements are true. B. both statements are false. C. I is true while II is false. D. I is false while II is true.

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