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In: Economics

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)0.5 − (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 = 32L0.5K0.5. 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.

What is the equilibrium real wage and equilibrium total number of hours worked per day?
How many hours does each consumer work per day?

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