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Please explain the logic behind solving these two questions
(a) Two commodities, X and Y, are produced with identical technology and are
sold in competitive markets. One unit of labour can produce one unit of each of
the two commodities. Labour is the only factor of production; and labour is
perfectly mobile between the two sectors. The representative consumer has the
utility function: U = XY ; and his income is Rs. 100/-. If 10 units of labour are
available, find out the equilibrium wage in the competitive labour market.
(b) Consider an economy producing a single good by a production function
Y = min {K, L}
where Y is the output of the final good. K and L are input use of capital and labour
respectively. Suppose this economy is endowed with 100 units of capital and
labour supply s L is given by the function
L w s = 50 ,
where w is the wage rate.
Assuming that all markets are competitive find the equilibrium wage and rental
rate.
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