4. (15 points) Suppose the production function is given by YzKaN(1-a) where N is labour inputs,...

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4. (15 points) Suppose the production function is given by YzKaN(1-a) where N is labour inputs, K is capital, a is the factor share of capital, andz is total factor productivity. (a) What is the marginal product of labour, MPN, of the firm? (b) Solve the for firms problem for the equation describing the units of labour the firm will demands for any given wage, w. What is this function called? (c) Does the amount of labour the firm demands go up or down when the wage goes up? Prove it (one way is to derive and). (d) Let w = 1, k = 1, a = 0.3, and z = 5. What is the amount of labour demanded by the firm? Round to the nearest unit. (e) No let w = 1, k = 2, a = 0.3, and z = 5. What is the amount of labour demanded by the firm? Round to the nearest unit. 4. (15 points) Suppose the production function is given by YzKaN(1-a) where N is labour inputs, K is capital, a is the factor share of capital, andz is total factor productivity. (a) What is the marginal product of labour, MPN, of the firm? (b) Solve the for firms problem for the equation describing the units of labour the firm will demands for any given wage, w. What is this function called? (c) Does the amount of labour the firm demands go up or down when the wage goes up? Prove it (one way is to derive and). (d) Let w = 1, k = 1, a = 0.3, and z = 5. What is the amount of labour demanded by the firm? Round to the nearest unit. (e) No let w = 1, k = 2, a = 0.3, and z = 5. What is the amount of labour demanded by the firm? Round to the nearest unit.