The questions in this section refer to a competitive firm that has the cost function c(q) = q2 + 10q + 100

Economics Dec 11, 2020

The questions in this section refer to a competitive firm that has the cost function c(q) = q2 + 10q + 100.

At an output of q = 5, the firm's total variable cost is ,its average cost is and its average fixed cost is In the short run, the minimum price above which this firm would supply a positive output is In the short run if the price is p = 20, the firm supplies an output of and its profit is

Expert Solution

Cost function is C = q2 + 10q + 100

variable cost is q2 + 10q and fixed cost is 100

AVC is VC/q = q + 10 and ATC is C/q = q + 10 + 100/q

MC is 2q + 10

1) At q = 5, VC = 5^2 + 10*5 = 75

AC = 5 + 10 + 100/5 = 35

AFC = FC/q = 100/5 = 20

2) Minimum price is minimum AVC which is 10

3) At P = 20 MC = P gives 2q = 20 - 10 or q = 10/2 = 5 units

Firm supplies 5 units

Profit = revenue - cost

= 5*20 - (5^2 + 10*5 + 100)

= -75

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