Consider three firms out of a competitive industry. They have the following technologies: C1 = y2...

Consider three firms out of a competitive industry. They have the following technologies: C₁ = y² + 9; C₂ = y² +y + 9; C₃ = y² + 2y + 9.

a. For each firm derive the SAC, SMC and AV C. Show these curves on three graphs, one for each firm.

b. Suppose that in the short run the market price is 7. Show each firm’s profit on your graphs. Should all of these firms produce? Explain.

Solutions

Expert Solution

We know that AVC = VC/y, SAC = C/y and MC = dC/dy.

Beginning with the first firm, the cost is C1 = y2 + 9. This firm has SAC = y + 9/y, AVC = y and SMC = 2y. The second firm has a cost function C2 = y2 + y + 9. This firm has SAC = y + 1 + 9/y, AVC = y + 1 and SMC = 2y + 1. The third firm has a cost function C3 = y2 + 2y + 9. This firm has SAC = y + 2 + 9/y, AVC = y + 2 and SMC = 2y + 2. The graphs are shown below.

b. Now that in the short run the market price is 7. This is equated against rising MC. Firm 1 produces where P = SMC = 7 and it gives the profit as shown by green coloured region in the graph. There is no economic profit for firm 2. The third firm bears an economic loss because the average cost exceeds the price. The firms should produce in all cases because the price is greater than the shut down price (minimum AVC),

Rahul Sunny answered 1 year ago

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