Wednesday, 20 July 2011

Solutions for Topic 7: Outputs and Costs

Question 7.1
Suppose 40 employee-hours can produce 80 units of output.  Assuming the law of diminishing marginal returns is present, to produce 160 units of output will require
      A)        an additional 40 employee-hours.
      B)        a total of 80 or less employee-hours.
      C)        less than 40 additional employee-hours.
      D)        a total of 81 or more employee-hours.
      E)        a total of 80 employee-hours.

The correct answer is (D).
Diminishing returns means the workers are less productive due to insufficient physical capital.
Since 40 hours is needed to produce the first 80 units of output, it will take more than 40 hours to produce another 80 units of output to reach 160 units
Question 7.2
If the firm spends $200 to produce 17 units of output and spends $455 to produce 34 units, then the marginal cost of increasing production from 17 to 34 units is
      (A)       $13.38.
      (B)       $15.
      (C)       $7.50.
      (D)       $11.76.
      (E)       impossible to calculate due to a lack of information.
The correct answer is (B).
Marginal cost is change in total cost divided by change in output
Change in total cost is $455 - $200 = $255
Change in output is 34 units – 17 units = 17 units
So MC = $255/17 = $15
Question 7.3
Economies of scale exist when
      A)        constant returns to scale are present.
      B)        input prices are falling.
      C)        average costs fall as the scale of production grows.
      D)        a 10% increase in all inputs causes a 9% increase in output.
      E)        firms become extremely large.
The correct answer is (c).
Economies of scale means when the scale of production increases, total output increases by more than total cost due to efficiency in using resources
Thus the average total cost decreases. Refer to the Long Run AC curve

Question 7.4
Suppose, a firm has $1500 of variable costs and $500 of fixed cost when it produces 500 units of output and sells them for $5 per unit.
(1) Calculate the average fixed cost, average variable cost and average total cost at this output level.
(2) Is this firm making a profit or incurring a loss at this output?
Total fixed cost (TFC) = $500, Total variable cost (TVC) = $1500, Total output (Q) = 500 units
(1) AFC = TFC/Q = $500/500 = $1
AVC = TVC/Q = $1500/500 = $3
ATC = AFC + AVC = $4
(2) Total revenue = $5 X 500 = $2500
Total cost = $500 + $1500 = $2000
The firm is making a profit of $500

Question 7.5
          Complete the following table and explain the relationship between marginal cost and average total cost.
Q
TVC
TC
MC
AFC
AVC
ATC
0
0
60
-
-
-
-
1
80
140
80
60
80
140
2
120
180
40
30
60
90
3
140
200
20
20
46.67
66.67
4
200
260
60
15
50
65
5
300
360
100
12
60
72
6
500
560
200
10
83.33
93.33


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