16. An equilibrium model of labour demand and output pricing leads to the pair of equations: $pF'(L) - w = 0$; $pF(L) - wL - B = 0$
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It states that the marginal product of labor (F'(L)) times the price of output (p) must equal the wage rate (w). Show more…
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Consider a perfectly competitive firm that produces output from labor according to the function q = f(L) and chooses labor employment (L) to maximize the following profit function: π(L) = p0f(L) - (c0 + w0L), where f'(L) > 0 and f''(L) < 0, for all L > 0, and p0 (the unit price of the firm's product), w0 (the unit price of labor), and c0 (the firm's fixed cost) are all exogenously given and positive. a. What equation describes the "first-order necessary condition" for the profit maximizing choice of L? b. Does the quantity of labor that solves the FONC, necessarily always maximize profit for this firm? Why or why not? c. Write down the total differential of the FONC equation from (a). d. Based on your answer to (c), how would an exogenous increase in the unit price of the firm's product affect its demand for labor, all else equal? Explain.
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A firm faces a perfectly elastic demand for its product at a price of 10 euros per unit. The firm is also confronted with an upward-sloping labor supply curve specified as w = 10 + 2L, where L is the number of workers hired per hour and w is the hourly wage. Each hour of labor produces 5 products. Assume that the firm only uses labor to produce its products. Also assume that the firm is profit-maximizing. a) How many workers should the firm hire each hour? b) What wage will the firm pay and how much profit does it make? c) What happens to employment and profits if a minimum wage of 40 is introduced? d) What happens to profits if the firm does not adjust employment in response to the minimum wage?
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Suppose the representative household has preferences given by u(c,l) = log(c) + θ log(l), where c is consumption, l is leisure and θ > 0 is a parameter. There is no capital in this model. Firms only use labor as an input into production. The production function is given by F(L) = AL^{1-α}, where A > 0 is productivity parameter, L is labor hired by the firms, and 0 < α < 1 is a parameter. Firms hire workers in a competitive labor market where the wage is w: 1. What will be the equilibrium wage? (Hint: Solve for labor supply equation from the household first order condition, and firm's labor demand condition. Then equate labor demand to labor supply to derive equilibrium wage)
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