Assume a firm purchases resources a and b under purely competitive conditions and combines these resources to produce X. Product X is sold in a purely competitive market. The MPs of a and b are 6 and 3, respectively, and the prices of a and b are $12 and $6, respectively. If profit-maximizing equilibrium exists, the price of X will be

A) $1.
B) $0.5.
C) $2.
D) $5.

Question

skittlez_and _twiztid · Accepted Answer

Final Answer : C, Explanation :  The profit-maximizing condition for a firm in a competitive market is to equate the marginal product per dollar spent on each resource. For resource a, MPa/Pa = 6/$12 = 0.5. For resource b, MPb/Pb = 3/$6 = 0.5. Since the marginal product per dollar is equal for both resources, the firm is in equilibrium. The price of X must be such that the value of the marginal product (VMP) equals the marginal cost (MC). VMP is found by multiplying the MP of the resource by the price of the product (P). Given that the MPs are 6 and 3 for a and b respectively, and their ratios to the prices are equal, we can infer that the price of X (P) must be such that P*MP = price of the resource. Since we don't have direct information about the total costs or the specific production function, we focus on the equilibrium condition. The question doesn't provide a direct way to calculate the price of X solely based on the given information without making assumptions about the production function or the quantity produced. However, the equilibrium condition suggests that the firm is efficiently allocating resources based on their marginal products and prices, aiming to maximize profit. The price of X would be determined by the market conditions for X, reflecting the costs of inputs and the productivity of those inputs in producing X. Given the information, we cannot directly calculate the price of X without additional details about the demand for X or the total cost of production. The correct answer is inferred based on the principle of profit maximization in competitive markets, which requires equalizing the marginal product per dollar across inputs.

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