Question

In the long run, all firms have the same cost function, with an avoidable fixed cost

c(q) = { 0 if q=0
64+q²+10q if q>0
​ Aggregate demand for the good is
D(p) = { 640−8p for p<80
0 for p≥80
1. Find the long-run, aggregate supply function, and the competitive equilibrium (p∗,Q∗) in the long run. How many firms are active in the market (i.e., how many firms produce positive units)?

Answer 1

In the long run, firms in a perfectly competitive market have zero economic profits. The long-run aggregate supply function is determined by finding the quantity at which firms have zero economic profits. This occurs when the price is equal to the minimum average avoidable cost.

Step-by-step explanation:

In the long run, firms in a perfectly competitive market will have zero economic profits. To determine the long-run aggregate supply function, we need to find the level of output at which firms in the market have zero economic profits. This occurs when the price is equal to the minimum average avoidable cost.

First, we need to determine the minimum average avoidable cost. The avoidable fixed cost function is given as c(q) = { 0 if q = 0 64 + q² + 10q if q > 0}. The minimum average avoidable cost occurs when the derivative of the avoidable fixed cost function with respect to quantity is equal to zero. So, we need to find the derivative of c(q) and set it equal to zero.

Next, we need to find the quantity at which the minimum average avoidable cost occurs. Using the value of q found in the previous step, we can substitute it back into the avoidable fixed cost function to find the minimum average avoidable cost.

Finally, the long-run aggregate supply function is given by setting the price equal to the minimum average avoidable cost function. We can substitute the value of the minimum average avoidable cost into the aggregate demand function to find the equilibrium quantity and price in the long run.