Question

The input decisions for a profit maximizing producer can be solved using marginal relationships thag are derived from the production functions and input and output prices. Consider the circumstance where you face multiple production options, each driven by a single purchased input used in the production of a single salable output rach with production function Yi = fi(X) , e.g., where you could think of X as fertilizer or irrigation water, Y1 as corn, Y2 as wheat, Y3 as hay, etc. And you are a price-taker in both the input and output markets. State the general mathematical relationship(s) that must hold in your input utilization decision(s) if you are to maximize profit in this situation. Be sure to decompose all elements of the relationship(s) into their most basic terms relating back to the underlying production function(s) and relevant prices. Be clear and specific in your notation. (Note: do not derive the condition but be sure to define any symbols/abbreviations used).

Answer 1

To maximize profit, the input utilization decisions of a profit-maximizing producer must satisfy certain mathematical relationships. These include the equation MC = P * (1/MPP) for the marginal cost and MRP = P for the marginal revenue product. By ensuring these relationships hold, a producer can optimize their input decisions.

Step-by-step explanation:

When attempting to maximize profit as a profit-maximizing producer facing multiple production options, there are several mathematical relationships that must hold in your input utilization decisions. First, the marginal cost (MC) of each input should be equal to the marginal physical product (MPP) of that input. This means that the additional output produced by an additional unit of input should be equal to its cost. Mathematically, MC = P * (1/MPP), where MC is the marginal cost, P is the price of the input, and MPP is the marginal physical product of the input. Second, the marginal revenue product (MRP) of each input should be equal to its price (P). This means that the additional revenue generated by an additional unit of input should be equal to its price. Mathematically, MRP = P, where MRP is the marginal revenue product of the input.