# Marginal Cost Problem

1. Assume a manufacturing process can be captured by the following production function:

Q = 5,000 + 100X - 0.5X2

Where Q is the number of units of output produced weekly and X is the variable input used in the production process. Assume further that the cost of each unit of input X used is $100 (marginal factor cost, MFC = $100) and that the marginal revenue of each unit sold of output Q is constant at $2.00 (so that P = MR = $2.00).

a) What is the marginal product of input X?

b) What is the expression for the marginal revenue product of input X (MRPX)?

c) Using the rule for optimal resource utilization, what is the optimal amount of input X to use in the production process?

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#### Solution Preview

a) What is the marginal product of input X?

MPx = dQ/dX = 100 - X

b) What is the expression for the marginal revenue ...

#### Solution Summary

The rule for optimal resource utilization is applied.