An economist estimated that the cost function of a single-product firm is:
C(Q) = 80 + 20Q + 25Q2 + 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.
$
a) The fixed cost of producing 10 units of output.
FC = "\\$ 80"
b. The variable cost of producing 10 units of output.
"VC(10) = 20\\times 10 + 25\\times 10\\\\^2 + 5\\times 10\\\\^3 =\\$ 7700"
Variable cost = "\\$ 7700"
c. The total cost of producing 10 units of output.
Total Cost "= FC + VC"
TC = "\\$80 +\\$ 7700 = \\$7780"
d. The average fixed cost of producing 10 units of output.
"AFC(10) = \\frac{80}{10} = \\$ 8"
e. The average variable cost of producing 10 units of output.
"AVC(10) = \\frac{7700}{10} = \\$770"
f. The average total cost of producing 10 units of output.
"ATC = 770 + 8 = \\$ 778"
g. The marginal cost when Q = 10.
"MC(10) = 20 + (2\\times 25)(10) + (3\\times5)(10)\\\\^2= \\$2,020"
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