Question

Problem 5. Suppose that a firm’s production function is f(x, y) = 20x 0.7y 0.3 . Starting from the input bundle (x, y) = (40, 60), how much extra output will the firm get if it increases x from 40 to 41? How many units of output will the firm lose if x decreases from 40 to 39

Answer 1

A firm’s production function is f(x, y) = 20x ^0.7y ^0.3

The input bundle (x,y) = (40,60)

Extra output the firm will get if it increases x from 40 to 41 can be obtained by calculating the marginal product of input x (MP_x) . Marginal product of an input is defined as the change in output resulting from employing (or removing) an additional unit of that input in (or from) production.

Now,

When the initial input bundle is (40, 60), MP_x = 15.8 (approx.)

Hence, starting from the input bundle (x, y) = (40, 60), the firm will get 15.8 unit of extra output if it increases x from 40 to 41.

Also, from the definition of MP_x, we get,

The firm will lose 15.8 units of output if x decreases from 40 to 39.