Bobby runs a competitive detective agency with the short-run cost function c ( y
ID: 1190200 • Letter: B
Question
Bobby runs a competitive detective agency with the short-run cost function c(y) = 16y2 + 12y + 100.
Write out the following equations for the firm: AVC, ATC, and MC. How much are the firm’s fixed costs?
If the market price for solving a mystery is $100, what is the profit maximizing output?
Calculate Bobby's breakeven price.
Calculate Bobby's shutdown price
Complying with more stringent international regulations increases bobby's fixed cost from 100 to 144. How would this change affect his firm’s supply curve and its output level?
Explanation / Answer
c(y) = 16y2 + 12y + 100
ATC = 16y+12+100/y
Variable cost wil not have fixed cost =100
TVC=16y2 + 12y
AVC=16y+12
MC = dTC/dy
MC = 32y+12
P=MC at competitive market
100=32y+12
88 = 32y
y=88/32
y= 2.75
TR = 2.75x100 = 275
TC=16x2.752 + 12x2.75 +100 = 374
TR=TC is the break even point
py = 16y2 + 12y + 100
p=MC
(32y+12)y = 16y2 + 12y + 100
32y2+12y = 16y2+12y+100
16y2 =100
Taking under root both the sides
4y = 10
y =10/4 = 2.5
y=2.5
MC = P = 32x2.5+12 =$92
SHut down point
AVC >P
P=MC
16y+12 = 32y+12
y = 0 is the shutdown point.
If fixed copst increases, the total cost curve would shift to theright. BUt marginal cost., that is the supply curve, will remain the same