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There are 800 consumers in an economy that each have the same utility function given by...

There are 800 consumers in an economy that each have the same utility function given by U(c, l) = 32√ c − (24 − l)2 where c is their consumption and l is the number of hours they spend for leisure. A single firm serves the market with production function Y = 32L1/2K1/2 . The firm cannot choose its capital stock, which is fixed at K = 1600. You can assume the price level is equal to 1 so real and nominal wages are equivalent

Question: Solve for an individual consumer’s labor supply as a function of the real wage and total supply of labor hours for the economy in one day as a function of the real wage (hint: you will need to use the budget constraint to cancel out consumption)

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