Question

5. Consider the following information for Rancher John: (a) If the market price is $150, calculate the output level for Rancher John in the short run (b) If total fixed cost is $8000, should Rancher John shut down or continue to produce in the short run? Explain ybur decision.

Answer 1

Given

VC=40q+q²

a)

Marginal Cost can be calculated by differentiating VC with respect to q, we get

MC=dVC/dq=40+2q

A perfectly competitive firm sets its output level such that P=MC

So, Set MC=P

40+2q=150

2q=110

q=55

Optimal output is 55 units in short run.

b)

AVC=VC/q

AVC=(40q+q²)/q=40+q

Now let us calculate AVC at optimal output i.e. 55 units. Put q=55

AVC=40+55=$95

We find that AVC is less than market price of $150. We can say that firm is able to recover variable costs.

Total Revenue=P*q=150*55=$8250

VC=40q+q²

Put q=55

VC=40*55+55² =$5225

Total Cost=FC+VC=8000+5225=$13225

Profit=TR-TC=8250-13225=-$4975

We can see that firm is making loss. But AVC<Price,

So, firm should continue to produce in short run to minimize losses.