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h6w03 - The Ohio State University Department of Economics...

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The Ohio State University Department of Economics Econ 805–Extra Problems on Production and Uncertainty Winter 2003 Prof. Peck (1) In the following economy, there are two consumers, two …rms, and two goods (labor/leisure and food). For i = 1,2, consumer i is endowed with zero units of food and 1 unit of leisure, ! i = (0 ; 1) . Letting x i denote consumer i’s consumption of food and ` i denote consumer i’s consumption of leisure, the utility function is: log( x i ) + log( ` i ) . Let y 1 denote …rm 1’s output of food and L 1 denote …rm 1’s labor input (so that L 1 must be nonnegative). Then …rm 1’s production function, the frontier of its production set, is given by: y 1 = AL 1 , where the parameter A is a positive real number. Firm 1 is owned by consumer 1. Let y 2 denote …rm 2’s output of food and L 2 denote …rm 2’s labor input (so that L 2 must be nonnegative). Then …rm 2’s production function, the frontier of its production set, is given by: y 2 = ( L 2 ) 1 = 2 . Firm 2 is owned by consumer 2.
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