PS9(09)

PS9(09) - ECN 712 Fall 2009 Professor Schlee Problem Set...

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Unformatted text preview: ECN 712 Fall 2009 Professor Schlee Problem Set IX, Due 11 November For each problem assume that the monopolist posts a single price (for each good that it sells). 1. A monopolist produces a good according to a constant returns to scale technology with average cost of k > 0 per unit. The inverse demand p ( ) is nonnegative and nonincreasing on R + with p (0) > k ; on the set { q | p ( q ) > } , the inverse demand is continuously differentiable with p < 0. (a) What is the effect of an increase in k on the quantity and price? (Note that the objective function need not be concave.) (b) Use the following three examples to explore whether the price can rise by more than or less than the unit-cost increase (that is, whether p- k is can be increasing or decreasing in k ): (i) p ( q ) = a- bq ; (ii) p ( q ) = a- bln ( q ); and (iii) p ( q ) = aq- b for 0 < b < 1. 1 (c) If the good were produced by a competitive industry (with all firms producing according to constant returns technology with average cost of k ), then of course we would have p = k . Could the competitive comparative static relation dp/dk = 1 be used to distinguish between monopoly and competition? 2. An art museum operates according to the cost function c ( q ) = F + kq for q > 0, with c (0) = 0, where c is measured in dollars, q denotes the number of visits to the museum. The demand for museum visits is given by p = a- bq , where p is admission charge in dollars. The parametersis admission charge in dollars....
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PS9(09) - ECN 712 Fall 2009 Professor Schlee Problem Set...

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