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(a) Consider a profit-maximizing monopolist with costs of C(q) = cq and an inverse demand of p(Q) = a-bQ, where {a; b; c} > 0. What is the rm's objective equation as a function of q?
(b) What are the first- and second-order conditions associated with the rm's problem?
Using these conditions, demonstrate that the optimal quantity is Q* = (a-c)/2b.
(c) If a = 9, b = 2, and c = 3, by how much would the rm's quantity change if the firm were subjected to a per-unit tax of $2?
(d) If a = 9, b = 2, and c = 3, by how much would the rm's quantity change if the firm were subjected to a lump-sum tax of $4?
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The market price of hamburgers in a college town decreased recently, and the students in an economics class are debating the cause of the price decrease. Some students suggest that the price decreased because a new type of grill allows restaurants to..
Suppose that the cost of a unit of capital is r and the price of a unit of labor is w and the level of output is y. Write down the long-run total cost as a function of w, r, and y.
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