Question

A firm is currently producing 100 widgets using 4 units of labor and 12 units of capital. The firm's production
function exhibits constant returns to scale. How many units of labor and capital are needed to produce 350 widgets?

Answer 1

Answer

Let a firm is producing output Q by using two factors, labor(L), and capital(K).

So, the production function of the firm is as follows,

Q = f(L.K).....(1)

The constant returns to scale means if the inputs are increased by a certain proportion, the output will also increase by that proportion, i.e.,if the inputs are increased by '' times, the output will also increase by '' times.

So, if labor is increased by '' times, the number of labor will be, *L or L.

Similarly, if capital is increased by '' times, the number of capital will be, *K or K.

So, equation (1) would be,

Q = f(L , K)

Or, Q = * f(L,K)

Or, Q = Q

Now, the firm is currently producing 100 widgets using 4 units of labor and 12 units of capital., and the firm's production function exhibits constant returns to scale.

So, when the firm will produce 350 widgets , its production will rise by 35 times (350/100).

As the firm's production function exhibits constant returns to scale, so the labor and capital will also increase by 35 times.

So labor employment will be = 4 * 35 = 140

and, the capital employment will be 12 * 35 = 420

So, 140 units of labor, and 420 units of capital are needed to produce 350 widgets.

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