Consider the one consumer, one producer economy, with two goods, x (output) and L (leisure). The production function is of the form ??= √? where z is the labour input. The total utility function of the consumer is given by U(x, L) = log x + log L and the total endowment of labour is L* = z + L. Note that total endowment of labour time can be used either for more work z (as labour input in production process) or for more leisure L. Then compute equilibrium prices, profits and consumption quantities.
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