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The following shows the cost function of firm X: C(q) = a + bq + 0

Economics

The following shows the cost function of firm X: C(q) = a + bq + 0.5cq2 where q denotes the quantity of output. a) Derive the fixed cost and marginal cost of firm X respectively. b) Suppose firm X is a price-taking firm, what is the minimum price that it would produce output? Find the quantity of output q* that the firm would choose to produce, if the price has induced the firm to produce. If firm X is actually in a market with only one player, with market demand: p= d - 0.5eq where d and e are positive number c) Find the optimal amount of output for the monopolist to produce, as well as the corresponding price charged p and marginal cost ?. Compare q* and ? and explain the difference intuitively. The government is going to set a maximum price control on the market at ?. d) Explain the effect of the output level, if i > ii. >c 111. ?

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