Question

In: Economics

Consider a firm that operates in the perfectly competitive salmon farming industry. The short-run total cost...

Consider a firm that operates in the perfectly competitive salmon farming industry. The short-run total cost curve is TC(Q)=250+3Q+Q2 , where Q is the number of salmon harvested per month.

What is the equation for the average variable cost (AVC)?
Solve for the firm's operation condition, MC≥AVC.
Assuming MC≥AVC, what is the firm's short-run supply curve? Find the supply function, NOT the inverse supply function.
In light of the answer in part 2, What is the minimum price at which the firm operates?

Solutions

Expert Solution

TC = 250 + 3Q + Q2

TVC = 3Q + Q2

AVC = TVC/Q

= ( 3Q + Q2 )/Q

= 3 + Q

AVC = 3 + Q

MC = dTC/dQ = 3 + 2Q

MC = 3 + 2Q

MC AVC

3 + 2Q 3 + Q

subtracting 3 on both sides

2Q Q

subtracting Q on both sides

2Q - Q Q - Q

Q 0

Short run supply curve is given as

P = MC

P = 3 + 6Q

P - 3 = 6Q

Q = P/6 - 3/6

Q = P/6 - 1/2

The minimum price at which firm operates is given by

P = min.AVC and MC AVC

AVC is minimum where MC = AVC

3 + 2Q = 3 + Q

2Q - Q = 3 - 3

Q = 0

min.AVC = 3 + 0 = 3

So minimum price at which firm operates is P 3

Rahul Sunny answered 1 year ago

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