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An industry consists of many identical firms, each with the cost function C(q)=100+30q-8q^2+q^3 Derive the average...

An industry consists of many identical firms, each with the cost function C(q)=100+30q-8q^2+q^3

Derive the average cost, average variable cost, and marginal cost curves of a firm.

Compute the outputs at which the AC and AVC curves reach their minimums.

If the market price is $40, and each firm is a price-taker, how much output will each firm supply? How much profit or loss is each firm making at this price?

Show this area on the graph (label the three curves). If the market price is p derive the supply curve of the firm q(p). Point this out on the graph. You must show an output choice for every p≥0. If the government imposes a lumpsum tax of T dollars on every firm in the industry, how will it change the output choice of each firm in the short run? If the government imposed a percentage tax of t∈(0,1) on a firm’s profits, how would that change the output choice of each firm in the short run? If the government imposed a tax of t_u per unit produced by a firm, how would that change the output choice of each firm in the short run?

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