Microeconomic Theory (Isoquants)

Question

A firm uses capital (K) and Labor (L) and these are perfect substitutes. One unit of output can be produced using 1 unit of capital or 3 units of labor. What is the equation for the production function? Show the isoquant map. 

I am confused about how to go about answering this question, an explanation would be helpful.

Answer 1

Here is the production function you are looking for:

Q = f(K,L) = min(K, 3L)

When a firm can produce with either input, it will choose the combination of inputs that creates the most output per dollar spent. For example, if the firm has more capital than labor, it will use capital to produce output, while if it has more labor than capital, it will use labor.

The isoquant map for this production function is a straight line with a slope of -1/3. This is because the marginal rate of substitution between capital and labor (the rate at which the firm is willing to trade one input for the other) is constant and equal to 1/3.