Under perfect competition, the equilibrium price of labor used to produce cloth will be equal to

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Question restatement: Under perfect competition, the equilibrium price of labor used to produce cloth will be equal to which of the following? Options: A) the slope of the production possibility frontier. B) the price of cloth divided by the marginal product of labor in the production of cloth. C) the marginal product of labor in the production of cloth times the price of cloth. D) the ratio of the marginal product of labor in the production of cloth to the marginal product of labor in the production of food times the ratio of the price of cloth to the price of food. E) the average product of labor in the production of cloth times the price of cloth.

Option A: The slope of the production possibility frontier (PPF) reflects opportunity costs between two outputs and is not the wage of labor. In perfect competition, wages are determined by the value of the marginal product of labor, not by the PPF slope. Misconception: confusing opportunity cost with input pricing.

Option B: Price of cloth divided by the marginal product of labor (P_c / MPL) has incorrect units and interpretation. Wage equals the value of the marginal product of labor, which is MPL times the good’s price, not price divided by MPL. This reverses the correct relationship and mixes up the relevant variables.

Option C: Marginal product of labor in the production of cloth times the price of cloth (MPL_c × P_c) expresses the value of the additional output produced by one more unit of labor in cloth production. This is exactly the value of the marginal product of labor (VMPL) for cloth and is the standard wage condition under perfect competition when factors are paid their VMPL. Correct conceptually, tying MPL to the product price yields wage equal to VMPL.

Option D: This expression combines the MPLs for cloth and food and the relative prices into a ratio that does not correspond to the wage of labor in cloth production. It mixes cross-sector marginal products and price ratios in a way that does not represent the wage in a perfectly competitive single-output labor market for cloth.

Option E: Average product of labor times the price of cloth would give the value of average output per worker, not the value of the next unit of output produced by the next worker. Wages are driven by the marginal product, not the average product, so this is incorrect.

Summary: The wage in a perfectly competitive labor market producing cloth equals the value of the marginal product of labor for cloth, which is MPL_cloth × P_cloth. The remaining options misconstrue the relation between input pricing, output value, and marginal vs. average measures, or misapply PPF concepts to input pricing.

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Under perfect competition, the equilibrium price of labor used to produce cloth will be equal to

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