Question

Consider a publicly available technology of producing a good that is characterized by the variable cost...

Consider a publicly available technology of producing a good that is characterized by the variable cost function VC (Q) = (1/2)Q2 and fixed costs FC = 2 for a firm that operates the technology. In the short run, fixed costs are unavoidable. In the long run, fixed costs are avoidable and it is free for any firm outside of the market to enter, should it want to. In the short run, the set of firms in the market is fixed. The market demand curve is given by demand function, QD(P) = 40 − 20P

1. Write up a producer’s cost function.

2. Determine a producer’s efficient scale of production, Qe. (Hint: We have that MC(Qe) = AC(Qe), that is, at efficient scale it is necessarily the case that marginal cost equals average cost).

3. Determine a single producer’s short run supply curve (that is, the optimal choice of output given output price, P in the situation where fixed costs are unavoidable).

4. Consider a situation where there are 10 producers in the market, all operating this technology. Determine the short run market supply curve.

5. In short run market equilibrium, what is the equilibrium price and quantity? What is the profit level of each producer?

6. Suppose market demand increases to QD(P) = 120 − 20P. Determine the new short run competitive equilibrium (state the new equilibrium price, the aggregate quantity supplied and demanded, how much each producer is producing, and the profit level of each producer).

7. In the long run, there is free entry, and so the number of firms will adjust so that in the competitive equilibrium, firm profits are zero. Subject to the new demand function, what is the long run competitive equilibrium price level? How many firms are there in the market. How much is each firm producing?

8. In the long run equilibrium, calculate aggregate surplus. In addition calculate producer surplus and consumer surplus.

9. Suppose as social planners, we dictate that all existing firms in the long run equilibrium must each produce one additional unit of the good relative to what they were already producing, which is then consumed by the consumers. We hold the number of firms in the market fixed. What happens to aggregate surplus?

I searched and found a similar problem to this with different equations for VC and FC here on Chegg Study. Please do not just copy and give me that as I noticed that the solution to the problem is incorrect. Thank you

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