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 $2 per unit.The firm's long-run marginal cost curve is A)a straight line with slope 2. B)upward sloping and gets flatter as Q increases. C)upward sloping and gets steeper as Q increases D)a straight line with slope 1. E)a straight line with slope 2

Question

Quizplus · Accepted Answer

The production function described suggests a linear relationship between inputs and output, implying constant returns to scale. In the long run, where all inputs are variable, the firm can adjust both labor and machine inputs to minimize costs. Given the prices of labor and machines, the firm's cost of production will increase linearly with output, leading to a straight line marginal cost curve. The slope of this line depends on the input cost ratios and technology, but without specific details on these, the most accurate answer given the options is a straight line, indicating constant marginal cost. The specific slope value cannot be determined from the given information, making the choice of slope 2 (A) as arbitrary as slope 1 (D), but since the question seems to mistakenly repeat the option for a straight line with slope 2, the correct choice based on the options provided and assuming a typo or error in the question formulation is A.

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