Question

Suppose there are n firms in an industry with free entry. Each firm's marginal cost is MC(y)=2y and total cost is TC(y)=y²+1 for y>0 and TC(y)=0 for y=0. What is the smallest price at which the product will be sold in the industry in the long run?

Group of answer choices

neither one is correct

1

4

6

2

Answer 1

The smallest price at which the product will be sold in the industry in the long run is when P= minimum ATC.

And we know that ATC is at its minimum , when ATC=MC.

Here , ATC = TC/y = (y² +1)/y = y + 1/y

MC = 2y

ATC =MC

y + 1/y = 2y

y +1/y - 2y = 0

1/y - y = 0

(1-y²)/y = 0

1-y² =0

y² = 1

y = 1

This implies that when y=1 ,ATC is at its minimum.

ATC = y+ 1/y

= 1 + 1/1

= 1+ 1 = $2

So, the smallest price at which the product will be sold in the industry in the long run is $2. Hence, option(E) is correct.