Exercise Set 12
COST FUNCTIONS

I. Objectives

• To sketch the Average Cost and Marginal Cost curves
• To explain why AC is U-shaped
• To determine where MC intersects the AC curve
• To understand the effect of an increase in fixed costs on the AC and MC curves
• To illustrate the relationship between average cost and returns to scale

II. Data

• The cost function for a firm is: C = aQ + bQ² + F, where Q is output, C is total cost, and a, b and F are constants.
• The corresponding marginal cost function is: MC = a + 2bQ
  [Technical note: The derivative of C with respect to Q yields MC.]
• Select values for a, b and F, and sketch the TC curve.
• On a separate graph, sketch the AC and MC curves. [Note: AC is cost per unit of output, i.e. AC = TC/Q.]
• Find the output at which MC and AC curves intersect. Call this Q₁.
• Obtain the minimum value of AC.
• Click on Gimme Costs or something! to confirm your results.

III. Questions

1. Select values for the parameters: a = ____, b = _____ , F = _____. Obtain, and sketch, the following functions:
   1. TFC = __________
   2. TVC = __________
   3. TC = __________
   4. AFC = __________
   5. AVC = __________
   6. AC = __________
   7. MC = __________
2. Find the lowest point on the average cost curve. [Hint: At this point, AC = MC.]
3. The average cost curve is [ linear / U-shaped ]. Explain why.
4. An increase in the fixed cost will cause the AC curve to shift [ down / up ] and the MC curve to [ shift up / shift down / remain unchanged ]. Explain.
5. Suppose a laptop manufacturer is able to negotiate lower prices for its components from its suppliers. This is likely to cause the laptop manufacturer's [ AFC / AC ] curve to shift [ up / down ]. Explain.
6. Consider the AC curve. The region where the slope is negative corresponds to [ Increasing Returns to Scale / Constant Returns to Scale / Decreasing Returns to Scale ]. Explain.
7. If production exhibits decreasing returns to scale, an increase in output will lead to [ higher / lower ] unit costs of production.
8. A manufacturer of HDTV sets currently produces 300 sets a year at a cost of $6000 each. If its production rises to 2000, the average cost will fall to $3500. The firm will enjoy [ economies / diseconomies ] of scale by sliding [ up / down ] along the [ negatively / positively ] sloped segment of its average cost curve.

IV. Additional Questions

1. A firm produces watches. Its fixed cost is $48; the variable costs are given in the table below:

   Output (no. of watches)	0	1	2	3	4	5	6	7	8
   Variable Cost ($)	0	20	30	36	40	48	60	80	112

   1. Construct a table showing the values of output and the following cost functions:
      1. Total fixed cost
      2. Total variable cost
      3. Total cost
      4. Average fixed cost
      5. Average variable cost
      6. Average cost
      7. Marginal cost
   2. Provide sketches of each of the cost curves.
      1. Draw TFC, TVC and TC in Fig. 1.
      2. Draw AFC, AVC and AC in Fig. 2.
      3. Draw AC and MC in Fig. 3.
2. Explain why the typical average cost curve is U-shaped, i.e. why does it initially decline with output, and then increase as output increases?
3. The change in total cost that is incurred by producing one more unit of output is defined as:
   
   (a) average cost.
   (b) fixed cost.
   (c) elasticity of production.
   (d) marginal cost.
   (e) none of the above.
4. Answer Questions 5-9 on the basis of the following cost data:

   Output	Total Cost
   0	$24
   1	33
   2	41
   3	48
   4	54
   5	61
   6	69

5. The total variable cost of producing five units:
   a. is $61.
   b. is $48.
   c. is $37.
   d. is $24.
   e. cannot be determined from the information given.
6. The average total cost of producing three units of output:
   a. is $14.
   b. is $12.
   c. is $13.50.
   d. is $16.
   e. cannot be determined from the information given.
7. The average fixed cost of producing three units of output:
   a. is $8.
   b. is $7.40.
   c. is $5.50.
   d. is $6.
   e. cannot be determined from the information given.
8. The marginal cost of producing the sixth unit of output:
   a. is $24.
   b. is $12.
   c. is $16.
   d. is $8.
   e. cannot be determined from the information given.
9. The minimum AVC occurs at the output level of:
   a. Q = 3.
   b. Q = 4.
   c. Q = 5.
   d. Q = 6.
   e. none of the above.
10. In the short-run the Sure-Screen T-Shirt Company is producing 500 units of output. Its average variable costs are $2.00 and its average fixed costs are $0.50. The firm's total costs:
    a. are $2.50.
    b. are $1,250.
    c. are $750.
    d. are $1,000.
    e. cannot be determined from the information given.
11. Suppose that, when producing 10 units of output, a firm's AVC is $22, its AFC is $5, and its MC is $30. On the basis of this information we can say that the:
    a. firm's ATC is $35.
    b. firm's ATC is $57.
    c. firm's total cost is $270.
    d. firm's total cost is $30.
    e. firm is producing in the range of increasing returns.
12. Answer Questions 13-19 on the basis of the following cost data:

    Output	AFC	AVC
    1	$50.00	$100.00
    2	25.00	80.00
    3	16.67	66.67
    4	12.50	65.00
    5	10.00	68.00
    6	8.37	73.33
    7	7.14	80.00
    8	6.25	87.50

13. The average cost of five units of output:
    a. is $69.
    b. is $78.
    c. is $3.
    d. cannot be determined from the information given.
    e. is none of the above.
14. The total cost of four units of output is:
    a. $260.
    b. $77.50.
    c. $310.
    d. $215.
    e. none of the above.
15. If the firm stopped producing (produced zero units of output), its total cost:
    a. would be zero.
    b. would be $50.
    c. would be $150.
    d. could not be calculated.
    e. would be none of the above.
16. The marginal cost of the fifth unit of output:
    a. is $3.
    b. is $62.
    c. is $80.
    d. cannot be determined from the information given.
    e. is none of the above.
17. If the firm increases its output from three to four units, its total cost changes by:
    a. $60.00.
    b. $12.50.
    c. $3.00.
    d. $1.67.
    e. none of the above.
18. If the firm decided to increase its output from six to seven units, its total costs would rise by:
    a. $87.14.
    b. $80.00
    c. $6.67.
    d. $120.00.
    e. none of the above.
19. Suppose that when producing 10 units of output, a firm's AVC is $29.5, its AFC is $5.5, and its MC is $33. Based on this information we can say that
    a. the firm's AC is $33.
    b. the firm's AC is $52.
    c. the firm's TC is $350.
    d. the firm's TC is $330.
    e. none of the above.
20. Answer Questions 21-23 on the basis of the following cost data:

    Output	Total Cost
    0	$10
    1	24
    2	30
    3	38
    4	40

21. When Q = 2, the AFC is:
    a. $0.
    b. $5.
    c. $10.
    d. $30.
    e. none of the above.
22. The total variable cost of producing three units is:
    a. $12.66.
    b. $9.33.
    c. $6.67.
    d. $28.00.
    e. cannot be determined.
23. The marginal cost of producing the fourth unit of output is:
    a. $0.50.
    b. $2.00
    c. $38.00
    d. $.75.
    e. cannot be calculated.
24. The average cost function tells management:
    a. the cost per unit of input.
    b. the cost per unit produced.
    c. the cost per the last unit produced.
    d. the minimum cost associated with a certain quantity produced.
    e. none of the above.
25. Assume that in the short-run a firm which is producing 100 units of output has average total costs of $200 and average variable costs of $150. The firm's total fixed costs are:
    a. $5,000.
    b. $500.
    c. $0.50.
    d. $50.
    e. none of the above.
26. A study of the airline industry reports that "the largest carriers tend to have a higher level of unit costs, and that these higher costs are caused by the difficulties of managing an airline of large size." This means that, at present,
    a. There are increasing returns to scale in the airline industry
    b. The airline industry suffers from diminishing returns
    c. The larger airlines are not profitable
    d. Airlines are experiencing decreasing returns to scale
27. When economies of scale are present,
    a. Costs per unit decline as output expands
    b. Marginal cost rises as the firm increases production
    c. Average cost increases with output
    d. Average fixed cost increases with output

	5c	6d	7a	8d	9c	10b
	11c	12	13b	14c	15b	16c
	17a	18d	19c	20	21b	22d
	23b	24b	25a	26d	27a