Question

Classical theory assumes the economy’s production function exhibits constant returns to scale. An example is the Cobb-Douglas production function presented on pp. 61-62:

Y = AKαL1-α

MPL = (1 – α)Y/L MPK = αY/K

A is greater than zero and measures the productivity of the available technology. The parameter α is a constant between 0 and 1 and measures capital’s share of income.

1. Assume A = 1, α = 0.5, L = 64 and K = 4. Find the values for Y, MPL and MPK.

2. Now suppose that the employment of labour doubles, while A, α and K remain the same.

   Find the values for Y, MPL and MPK.

3. Suppose instead, that the employment of capital doubles, while A, α and L remain the same. Find the values for Y, MPL and MPK.

4. Examine the results. You should find that when the employment of labour rises relative to the employment of capital, MPL falls and MPK rises. And when the reverse is the case (i.e., K rises relative to L), MPK falls and MPL rises. Why is this so?

Answer 1

given,

solution with given information

the solution with doubled L

the solution with doubled k

it is found that when the employment of labour (L) increases then MPl falls and MPk rises; and when the employment of capital increases then MPk falls but MPl rises. this happens due to the law of diminishing return from an additional unit of a factor.

let's take this situation when the employment of capital (K) increases with a given unit of labour (L), then the marginal product arises out from an additional unit of capital declines (from the law of diminishing marginal product), but the marginal product of labour increases, because now the labours will have better divisibility and with addition of new capital stock they will be able to produce more. similarly, the vice-versa happens.