Question

# A perfectly competitive firm has the following total cost and marginal cost functions:      TC =...

A perfectly competitive firm has the following total cost and marginal cost functions:

TC = 100 + 10q – q2 + (1/3)q3

MC = q2 – 2q +10

a)    For quantities from 0 to 10 determine: TC, TFC, TVC, and MC.

b)    For quantities from 0 to 10 determine: ATC, AFC, and AVC.

c)    Assume P (MR) equals 45. For quantities from 0 to 10 determine: TR and profit.

d)    At what quantity is profit maximized? At this quantity what is true about the relationship between MC and MR?

a., b., c.

 Q TFC TVC TC MC ATC AFC AVC P TR Profit 0.00 100.00 0.00 100.00 45.00 0.00 -100.00 1.00 100.00 9.33 109.33 9.33 109.33 100.00 9.33 45.00 45.00 -64.33 2.00 100.00 18.67 118.67 9.33 59.33 50.00 9.33 45.00 90.00 -28.67 3.00 100.00 30.00 130.00 11.33 43.33 33.33 10.00 45.00 135.00 5.00 4.00 100.00 45.33 145.33 15.33 36.33 25.00 11.33 45.00 180.00 34.67 5.00 100.00 66.67 166.67 21.33 33.33 20.00 13.33 45.00 225.00 58.33 6.00 100.00 96.00 196.00 29.33 32.67 16.67 16.00 45.00 270.00 74.00 7.00 100.00 135.33 235.33 39.33 33.62 14.29 19.33 45.00 315.00 79.67 8.00 100.00 186.67 286.67 51.33 35.83 12.50 23.33 45.00 360.00 73.33 9.00 100.00 252.00 352.00 65.33 39.11 11.11 28.00 45.00 405.00 53.00 10.00 100.00 333.33 433.33 81.33 43.33 10.00 33.33 45.00 450.00 16.67

d.  quantity =7 at profit maximization. At this quantity MC = MR

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