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# competitive firms and the cost function

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In the market for widgets the market demand curve is given by:

P=50-0.05Q

The market is competitive and each firm has total costs given by:

C(q) = 640 + (0.1)q^2

(a) Find the equilibrium
i. output of each firm
ii. price
iii. market quantity
iv. Number of firms (throughout this question ignore the indivisibility problem that the number of firms must in reality be a whole number)

(b) Suppose the government imposes a fixed tax L per firm (e.g. A licensing fee). Explain the impact of this tax on the following variables
i. output of each firm
ii. price
iii. market quantity
iv. Number of firms

(c) Suppose the government imposes a fixed tax t per unit quantity on each firm. Explain the impact of this tax on the following variables
i. output of each firm
ii. price
iii. market quantity
iv. Number of firms

(d) Suppose the government imposes a price ceiling of 10 dollars. Determine the short run impact of this price ceiling on the following variables
i. output of each firm
ii. price
iii. market quantity
iv. Number of firms

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