Question

You are working for a firm that is operating in a perfectly competitive market, and exhibits a cost function of TC = 4000 +500 Q – 2 Q2 + 0.02Q3. If the market equilibrium price is $515, should you operate? If so, what is the Profit? If the market price is $455, should you operate? Why? Finally, what is the price that would have you shutdown, layoff labor, and leave the plant idle in the short-run?

Answer 1

Hi

The answer of the following question is given below as follows :

TC=4000+500Q-2Q² + 0.02Q^​​2

MC= aTC/ so

500-4Q+0.06Q²

Now coming to the 1^st part of the question.

So the perfectly competitive firm that operates at the

Point P=MC.

515=500-4Q+0.06Q^​​2

0.06Q^​​2 -4Q+0.06Q^​​2

By solving this we get our ans as .

Q=70.2 units.

So at this point

TT=PQ-TC

TT=(515*70.2)-(400+500(70.2)-2(70.2)² +0.02(70.2)³.

ie TT= $9.89 .

ie AVC=TVC/Q.

=$458.2

NOW at this point we can say that P>AVC So the the firm must operates despite being in loss.

Now let's coming to the 2^nd point .

Assume the P=$455

P=MC

455=500-4Q+0.06Q^​​2

By solving the above equation we get the value of Q ie

Q= 52.34 units.

Now at this point AVC= $450.1

Since P>AVC the must operates..

Now let's discuss the last part of the question.

The Shut down point is MC=AVC

500-4Q+0.06Q^​​2

BY SOLVING THE ABOVE EQUATION WE GET THE VALUE OF Q as 50 units

Now let's find the P

P=mc.

500-4(50)+0.06(50)²

ie P= $450.

I HOPE I HAVE SERVED THE PURPOSE WELL.

THANKS.