A firm's production function is given by q = min{M, L^1/2}, where M is the number of machines and L is the amount of labor that it uses.The price of labor is $1and the price of machines is $4 per unit.The firm's long-run marginal cost curve is A)upward sloping and gets flatter as Q increases. B)a straight line with slope 2. C)a straight line with slope 1. D)upward sloping and gets steeper as Q increases. E)a straight line with slope 4.

Question

Quizplus · Accepted Answer

The production function suggests a Cobb-Douglas form, which typically results in constant returns to scale. Given constant returns to scale and the prices for labor and machines, the long-run marginal cost curve would be linear, reflecting constant marginal costs. The specific slope depends on the combination of input costs and the production function, but the description provided does not allow for determining the exact slope without additional information. However, the correct choice among the given options for a Cobb-Douglas production function in the long run is a straight line, indicating constant marginal costs.

A Firm's Production Function Is Given by Q = Min{M