University of Miami Competitive Labor Market Question

I need an explanation for this Economics question to help me study.

1. Suppose a firm purchases labor in a competitive labor market and sells its product in a competitive product market. The firms elasticity of demand for labor is -0.6. Suppose the wage changes by 16%. The amount of labor hired by firm will change by ___ %

2. Suppose the hourly wage rate is $13, the rental price of capital is $3 and the price of output is constant at $30 per unit. Firm’s production technology is q = 4K^0.25E^0.75, the marginal product of employment is MP_E =3K^0.25E^-0.25 and the marginal product of capital is MP_K = K^-0.75E^0.75. What is firm’s optimal demand of labor if firm plans to produce q=20 units of outputs in the long-run? (please keep 1 decimal place in your answer)

3. You are hired by the government to evaluate the impact of a policy change that affects one group of individuals but not another. Suppose that before the policy change, members of a group affected by the policy averaged 15,251 in earnings, and members of a group unaffected by the policy averaged 15,665. After the policy change, members of the affected group averaged 17,329 in earnings while members of the unaffected group averaged 16,430 in earnings. What is the estimated effect of the policy on individuals’ earnings? Your answer should be a numerical number (positive or negative).

4. A firm would hire 24,823 workers if the wage rate is $10 and would hire 14,253 workers if the wage rate is $28. What is the firm’s elasticity of labor demand?

5. When the wage was $16 per hour, a group of workers supplied 88 hours of work per week on average. The wage then increased to $25 per hour, and the same group of workers supplied 61 hours of work per week on average. What is the elasticity of labor supply for this group of workers? (please calculcate to 2 decimal places)

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