Short-Run Economic Costs Suppose a firm has a short-run cost equation of C(q) =

Question

Short-Run Economic Costs Suppose a firm has a short-run cost equation of C(q) = 0.3q^3 - 15q^2 + 200q + 100, and short-run marginal cost equation of MC(q) = 0.9q2 - 30q + 200, if the firm produces 25 units of output: Solve for total fixed cost, total variable cost and total cost. Solve for the firm's average fixed cost, average variable cost and average total cost. Use the MC(q) equation to solve for the marginal cost of the last unit produced. Solve for whether the firm has short-run economies of scale or diseconomies of scale.

Explanation / Answer

a)C(q)=0.3q3-15q2+200q+100

TC=0.3(25)3 -15(25)2 +200(25) + 100
=0.3(15625)-15(625)+200(25) +100

=4687.5-9375+5000+100

=412.5

TVC=0.3(25)3 -15(25)2 +200(25)

=4687.5-9375+5000

=312.5

TFC=100

b)

TC=(0.3(q)3 -15(q)2 +200(q) + 100)/q

TAC=0.3q2-15q+200+100/q
=0.3(25)2-15(25)+200+100/25
=0.3(625)-375+200+4
=187.5-375+200+4
=16.5

AFC=100/q
=100/25
=4

AVC=0.3q2-15q+200
=0.3(25)2-15(25)+200
=187.5-375+200
=12.5

c)MC=0.9q2-30q+200

=0.9(625)-30(25)+200

=562.5-750+200

=12.5

d)MC=0.9q2-30q+200

=0.9(26)2-30(26)+200

=608.4-780+200=28.4

SInce marginal cost of production is increasing there is diseconomies of scale.

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