h2answ08 - Department of Economics The Ohio State...

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Department of Economics The Ohio State University Econ 805—Homework #2 Answers Prof James Peck Winter 2008 1. (Note: I am changing the notation so that f rm g’s output of good y is denoted as y g . This was a typo.) Consider the following economy with one consumer, 2 f rms, and 3 goods. The three goods are two consumption goods, x and y , and leisure, c . The consumer receives no utility or disutility from leisure, as long as we have c 0 . The utility function is u ( x, y, c )=log( x )+log( y ) . The consumer is endowed with 1 unit of leisure and none of goods x and y : ω =(0 , 0 , 1) .F i rm f , producing good x , has production function x f = μ L f 8 1 / 2 where L f is the labor input used by f rm f in producing good x i r m g , producing good y , has production function y g = μ L g 8 1 / 2 where L g is the labor input used by f rm g in producing good y . The consumer owns both f rms. Note: This notation is di f e ren tfromwha tweu sedinc las s ,butyouw i l l often see articles that use notation like this. (a) What is the economy’s production possibilities frontier? That is, give an expression for the maximum amount of good y that can be produced, as a function of the amount of good x that is produced. (b) De f ne a competitive equilibrium for this economy. (c) Calculate the competitive equilibrium prices, allocation, and pro f ts.
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h2answ08 - Department of Economics The Ohio State...

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