Question

In: Economics

Consider an industry in the U.S. facing aggregate (inverse) demand function: p(y) = 1050 – 5y...

Consider an industry in the U.S. facing aggregate (inverse) demand function:

p(y) = 1050 – 5y

The industry is currently in long run equilibrium. The market price is $225 and there are n = 11 firms producing. Each firm’s variable cost is:

c_v(y) = 1/3 y³

What is each firm’s fixed cost?

Expert Solution

Let the fixed cost be F

Total Cost =TC(y)=F+(1/3)y^3

Marginal Cost=MC(y)=dTC(y)/dy=y^2

Average Cost=TC(y)/y=(F/y)+(1/3)y^2

Set MC(y)=AC(y) to determine the output level at which AC(y) is minimized

y^2=(F/y)+(1/3)y^2

(2/3)y^2=F/y

y^3=(3/2)F

y=(1.5F)^(1/3)

So, MC at this output is given by

MC(y*)=(1.5F)^(2/3)

Set MC(y*)=Long run price

(1.5F)^(2/3)=225

1.5F=225^(3/2)=3375

F=$2250 (Fixed Cost)

Rahul Sunny answered 2 years ago

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