archer runs a competitive detective agency with the short run cost function c(y)

Question

archer runs a competitive detective agency with the short run cost function c(y)= 16y^2+12y+100
a. if the market price is 100 what is the profit maximizing output b. calculate his breakeven price c. calculate his shutdown point archer runs a competitive detective agency with the short run cost function c(y)= 16y^2+12y+100
a. if the market price is 100 what is the profit maximizing output b. calculate his breakeven price c. calculate his shutdown point archer runs a competitive detective agency with the short run cost function c(y)= 16y^2+12y+100
a. if the market price is 100 what is the profit maximizing output b. calculate his breakeven price c. calculate his shutdown point

Explanation / Answer

Hi,

The correct answers are as follows:

a) total revenue = 100y

marginal revenue = 100

cost curve = 16y^2+12y+100

marginal cost =32y+12

profit maximizing output occurs when marginal cost = marginal revenue

32y+12 = 100

Y = 88/32

Y = 2.75 units

b) breakeven price occurs when revenue = cost

100y = 16y^2+12y+100

On solving the quadratic equation, we get

Y = $3.0 or 1.60

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