PS14+exercises - Intermediate Microeconomics 2010 Problem...

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Intermediate Microeconomics, 2010 Problem Set 14: Exercises 1. Positive Externalities. Production of medicine often requires research that pro- duces new general insights, i.e., production of medicine has a positive externality. Consider the following quasilinear economy. A rm can produce medicine at costs c ( q s ) = 5( q s ) 2 . Production of q s units of medicine leads to an increase in our general knowledge k ( q s ) = 2 : 5 ( q s ) 2 . The consumer has preferences over medicine, knowledge, and money: U q s ; q d ; m = m + v q d + k ( q s ) = m + 90 q d 5 q d 2 + 2 : 5 ( q s ) 2 (a) Find the demand and supply functions, D ( p ) and S ( p ). Derive the compet- itive allocation x . What is the surplus in the competitive allocation? (The surplus with the externaility is S ( q ) = v ( q ) c ( q ) + k ( q )). (b) Given a subsidy t < 0, nd the competitive allocation with a subsidy t < 0, x t . (Note: A negative tax is not di erent from a positive tax. It implies that the rm supplies according to S ( p t ) while the consumer demands according to D ( p )).
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