Question

Assume a firm has the cost function given by

c(q)=q348−q24+10q+25c(q)=q348−q24+10q+25.
Answer the following:Write your answers to 2 decimal places.
a) Find the quantity level q∗>0q∗>0 that maximises the firm's profit, at the price level p=23p=23.
b) Calculate the short run shutdown quantity for the firm.

Answer 1

To find the quantity level that maximizes the firm's profit, calculate the firm's profit function and find the value of q that maximizes it. To calculate the short-run shutdown quantity, set the profit function equal to 0 and solve for q.

Step-by-step explanation:

To find the quantity level that maximizes the firm's profit, we need to first calculate the firm's profit function and then find the value of q that maximizes it. The profit function is given by:

profit(q) = (p - average cost(q)) * q

where p is the price and average cost(q) is the average cost at quantity level q. In this case, the price is given as $23. To find the average cost, we need to differentiate the cost function with respect to q and equate it to 0:

average cost'(q) = 0

Solving this equation will give us the quantity level q∗ that maximizes the firm's profit.

To calculate the short-run shutdown quantity, we need to find the quantity level at which the firm's profit becomes negative. This can be done by setting the profit function equal to 0 and solving for q:

profit(q) = 0

The obtained quantity level will be the short-run shutdown quantity for the firm.