Question

3. Suppose that the production of one widget requires that three units of labor (L) be used in conjunction with two units of capital (K).

a. Write down the production function q = f(L, K) that represents this production technology.

b. Graph the isoquant associated with 12 widgets.

c. Does this production technology exhibit decreasing, constant, or increasing returns to scale?

Answer 1

(a) This is a fixed proportion production function of the form

q = f(L, K) = min{2K, 3L}

(b) When q = 12,

12 = min{2K, 3L}

A fixed-proportion production function has L-shaped isoquants where optimal bundle lies on the point of inflection. In following graph, Q0 represents such an isoquant.

(c) If both L and K are doubled, new production function becomes

q1 = min{(2 x 2L), {2 x 3K}]

q1 = min{4L, 6K}

q1 = 2 x min{2L, 3K} = 2 x q

q1 / q = 2

Since doubling both inputs exactly doubles output, there is constant returns to scale.