Question

Zoras’ is a commercial fishery whose costs are estimated as Cost = 400 + Output + Output² where output is the number of pounds of fish caught and sold. If we denote output by Q, the average and marginal costs are given by the formulas:

AC = 400/Q + 1 + Q

MC = 1 + 2 ∙ Q

1. In a single graph, draw the average and marginal cost curves.

2. Compute Zoras’ ES and their break-even price.

3. Compute the formula for Zora’s supply.

Next, imagine that the fish market consists of 49 other firms that are identical to Zoras.’ Thus, the supply side is made up of 50 clones of Zoras’.

4. Find the formula for the market supply.

Answer 1

1. The graph is provided below

2. First find the supply function. It is rising marginal cost function. Since MC is positive for all Q, supply function is MC = 1 + 2Q or P = 1 + 2Q.

ES = (1/coefficient of Q)*P/Q or ES = (1/2)*P/Q. Hence ES = 0.5P/Q.

Break even occurs when TR = TC

PQ = 400 + Q + Q^2

P =  400/Q + 1 + Q.

It can be found as

1 + 2Q =  400/Q + 1 + Q.

Q = 400/Q

Q^2 = 400

Q = 20 and break even price is P = 400/20 + 1 + 20 = $41. When P is 41 and Q is 20, ES = 0.5*41/20 =1.025

3. Compute the formula for Zora’s supply.

It is P = 1 + 2Q or Q = 0.5P - 0.5

4. Find the formula for the market supply.

This is given by Qs = 50Q = 50(0.5P - 0.5) or Qs = 25P - 25