Homework SourseAn economist estimated that the cost function of a singlepro
An economist estimated that the cost function of a single-product firm is:
C(Q) = 50 + 25Q + 30Q2 + 5Q3.
Based on this information, determine the following:
a. The fixed cost of producing 10 units of output.
b. The variable cost of producing 10 units of output.
c. The total cost of producing 10 units of output.
d. The average fixed cost of producing 10 units of output.
e. The average variable cost of producing 10 units of output.
f. The average total cost of producing 10 units of output.
g. The marginal cost when Q = 10.
Solution
a) The fixed cost of producing 10 units of output = 50
b) The variable cost of producing 10 units of output
VC(q=10) = 25(10) + 30(10)2 + 5(10)3 = 250 + 3000 + 5000 = 8250
c)
C(q=10) = VC(q=10) + F = 8250 + 50 = 8300
d) AFC(q=10) = 50/10 = 5
e)
AVC(q=10) = 8250/10 = 825
f)
ATC(q=10) = AVC(q=10) + AFC(q=10) = 825+5 , = 830
g)
| Q=10 |
| Total cost is 8300/10 or , so average cost is 830 |
| At Q = 11, total cost is 9130/10 , average = 913 |
| At q=10, the cost of your next unit produced will be total cost at Q 11 minus total cost at Q 10 or 913 - 830 = 83 |
| MC is 83 for the 11th unit produced. |
