4. An economist estimated that the cost function of a single-product firm is C(Q
ID: 1192200 • Letter: 4
Question
4. An economist estimated that the cost function of a single-product firm is
C(Q) = 100 + 20Q + 15Q^2 +10Q^3
Based on this information, determine:
The fixed cost of producing 10 units of output.
The variable cost of producing 10 units of output.
The total cost of producing 10 units of output.
The average fixed cost of producing 10 units of output.
The average variable cost of producing 10 units of output.
The average total cost of producing 10 units of output.
The marginal cost when Q = 10.
*I think I have it, I just want to double check my work
Explanation / Answer
Solution :
The cost function of a single-product firm is
C(Q) = 100 + 20Q + 15Q 2 +10Q 3
a) The fixed cost of producing 10 units of output = $ 100
b) The variable cost of producing 10 units of output is
C(10) = 20 x 10 + 15 X 102 + 10 X 103
C(10) = $ 11,700
C) The total cost of producing 10 units of output.
Total cost C(10) = 100 + $ 20 X 10 + $ 15 X 102 + $10 X 103
Total cost C(10) = $ 11,800
d) C(Q) = 100 + 20Q + 15Q 2 +10Q 3
The average cost of producing 10 units is
Average cost = 100/10 + (20/10)Q + (15/10) Q2 + (10/10) Q3
Average cost = 10 + 2Q + 1.5 Q2 + Q3
e) The average variable cost of producing 10 units of output
Average variable cost = 2Q + 1.5 Q2 + Q3
Average variable cost = 2 X $ 10 + 1.5 X 102 + 103
Average variable cost = 20 + 150 + 1000
Average variable cost = $ 1,170
f) The average total cost of producing 10 units of output
Average total cost = 10 + 2Q + 1.5 Q2 + Q3
Average total cost = 10 + 2 X 10 + 1.5 X 102 + 103
Average total cost = $ 1,180
G) C(Q) = 100 + 20Q + 15Q^2 +10Q^3
Marginal cost dC/dQ = 20 + 30 Q + 30 Q2
The marginal cost when Q = 10.
Marginal cost dC/dQ = 20 + 30 X 10 + 30 X 102
Marginal cost dC/dQ = $ 3,320
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.