# Pset5 - Ec115 Problem Set 5 [One-variable calculus] 1. For...

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Ec115 Problem Set 5 [One-variable calculus] (remember to check the second order condition) and sketch a graph of the func- tion: (a) y = x 2 6 x + 3 (b) y = 2 x 2 + 4 x 6 (c) y = 3 x 3 27 x 2 + 45 x + 15 (d) y = x 1+ x 2 : 2. (a) A monopolist faces (inverse) demand function p = 100 q where p is the price of the good and q is the quantity demanded. Suppose the unit cost of production is 10; i.e. the cost of producing output q is 10q. Explain why the ( q ) = q [100 q ] 10 q: What value of q, denoted q ; maximises the &rm±s pro&t? What is the corre- sponding price p charged by the monopolist? ( q ) q and price p . (c) Suppose now the unit production cost is c > 0 : maximising q and price p : Show that dp =dc > 0 and dq =dc <

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## This note was uploaded on 12/31/2011 for the course ECON MR 102 taught by Professor Huyduong during the Winter '11 term at RMIT Vietnam.

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Pset5 - Ec115 Problem Set 5 [One-variable calculus] 1. For...

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