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101_HW-4

# 101_HW-4 - W,C 1 • Find the utilities of the workers and...

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Economics 11, Winter 2011: HW #4 Due Tuesday March 1 at beginning of class 1. Total capital is K = 4 and total labor is L = 25. Production functions are x = K 1 / 2 L 1 / 2 y = K 1 / 2 L 1 / 2 Find and sketch the Production Possibility Frontier. 2. Total capital is K = 4 and total labor is L = 25. Production functions are x = K 2 / 3 L 1 / 3 y = K 1 / 3 L 2 / 3 Find and sketch the Production Possibility Frontier. 5. As in class, consider an economy with two production goods K,L (cap- ital and labor) and two consumption goods x,y . Consumption goods are produced from production goods according to the production func- tions x = min { K,L } y = K + L There are W workers, each endowed with 1 unit of L (labor) and noth- ing else; worker utility functions are u W ( x,y ) = xy . There is one capitalist who is endowed with C units of K capital and nothing else; the capitalist utility function is u C ( x,y ) = xy . Find the competitive equilibrium; your answer will involve

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Unformatted text preview: W,C . 1 • Find the utilities of the workers and the capitalist at competitive equilibrium. • How do these utilities change if C increases (keeping W ﬁxed)? 6. As in class, consider an economy with two production goods K,L (cap-ital and labor) and two consumption goods x,y . Consumption goods are produced from production goods according to the production func-tions x = min { K,L } y = K + L There are W workers, each endowed with 1 unit of L (labor) and noth-ing else; worker utility functions are u W ( x,y ) = xy . There are C capitalists, each endowed with 1 unit of K capital and nothing else; capitalist utility functions are u C ( x,y ) = xy . Assume W > 2 C . Find the competitive equilibrium. (You can assume that p K > p L .) 2...
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101_HW-4 - W,C 1 • Find the utilities of the workers and...

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