MPL is the marginal product of labour, MRPL is the marginal revenue product of labour, and x denotes multiplication. What is the profit-maximizing condition for a monopoly hiring workers in the short run?

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BlackTom AI · Accepted Answer

We start by restating the setup: MPL is the marginal product of labor, MRPL is the marginal revenue product of labor, and x denotes multiplication. In a short-run monopoly hiring decision, the firm chooses employment where the wage equals the value of the marginal product of labor, i.e., w = MRPL.

Option a. w = p(1+1/e)MPL
- This option expresses w in terms of MPL multiplied by p(1+1/e). Since MRPL = MR × MPL, and MR ≈ p(1+1/e) under a monopoly (where e is the price elasticity of demand, typically negative so 1/e is negative, depending on sign convention), this form is consistent with w = MR × MPL when MR is written as p(1+1/e). In other words, if MR = p(1+1/e), then MRPL = p(1+1/e) × MPL, matching this option. This aligns with the fundamental condition w = MRPL for profit maximization.
- Potential confusion: ensure you’re not mixing MRPL with MRPL scaled again by p; here MPL is multiplied by p(1+1/e), which already contains MR through MR = p(1+1/e).

Option b. w = p × MPL
- This would set w equal to the price times the marginal product of labor, i.e., w = p × MPL. This ignores the revenue effect of selling additional output. In a monopoly, the extra output changes price, so the correct condition uses MR, not p, times MPL. Therefore this is incorrect.

Option c. w = p(1+1/e)MRPL
- Here w is set proportional to MRPL again, but with an extra factor of MRPL included inside. This double-counts MRPL (MRPL is already MR × MPL). Writing w as p(1+1/e)MRPL would imply w scales with MRPL again, which is inconsistent with the standard condition w = MRPL. In short, it overcounts the revenue effect and is not correct.

Option d. w = p × MRPL
- This says w equals p times MRPL. But MRPL already equals MR × MPL, where MR is the marginal revenue, not the market price p. In a monopoly, MR ≠ p unless elasticity is infinite. Therefore this form misplaces the MR factor and is not the correct profit-maximizing condition.

Summary note: the key idea is that the wage equates to the marginal revenue product of labor, MRPL = MR × MPL. If MR is expressed as p(1+1/e) in your setup, then MRPL becomes p(1+1/e) × MPL, which corresponds to option a. The other options fail because they either omit MR, double-count MRPL, or wrongly multiply by p without the MR adjustment.

SESS0007_24-25 LSA Test

MPL is the marginal product of labour, MRPL is the marginal revenue product of labour, and x denotes multiplication. What is the profit-maximizing condition for a monopoly hiring workers in the short run?

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