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Unformatted text preview: Inclass cost function exercise
Chap. 5, problem #4
You estimate your demand function to be:
C(Q) = 50 + 25Q + 30Q2 + 5Q3
Based on this information, determine:
1) The fixed cost of producing 10 units of output
2) The variable cost of producing 10 units of output
3) The total cost of producing 10 units of output
4) The average fixed cost of producing 10 units of output
5) The average variable cost of producing 10 units of output
6) The average total cost of producing 10 units of output
7) The marginal cost when Q=10
a. (Hint: do this both as the derivative and as TC(10) – TC(9))
Solutions
1) FC = $50
2) VC(10) = 25(10) + 30(10)2 + 5(10)3 = $8,250
3) C(10) = 50 + 25(10) + 30(10)2 + 5(10)3 = $8300
a. Could also calculate at $8,250 + $50 in fixed costs
4) AFC(10) = $50 / 10 = $5
5) AVC(10) = VC(10) / 10 = $8250 / 10 = $825
6) ATC(10) = AFC(10) + AVC(10) = $830
a. Or could do $8300 / 10 = $830
b. Note: This is what you use to figure out econ of scale
c. This is also the “perunit cost!”
7) MC(10) = take derivative, and evaluate at 10
a. 25 + 60Q + 15Q2
b. MC(10) = 25 + 60(10) + 15(10)2 = $2,125
c. Doing this as total cost of 10 minus total cost of 9 (e.g. TC(10) – TC(9))
i) TC(10) = $8,300 (see problem #3)
ii) TC(9) = 50 + 25(9) + 30(9)2 + 5(9)3 = $6,350
iii) $8,300  $6,350 = $1,950 (NOTE: this is a different answer than you get
by taking the derivative!) //home/vdimitrov/16625/a084ca8296c1a39120e02944650e35c0a77ede48.doc ...
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This note was uploaded on 12/03/2011 for the course MANEC 387 taught by Professor Crawford,l during the Fall '08 term at BYU.
 Fall '08
 Crawford,L

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