Question

Illustrate and discuss the difference between constant, Increasing and decreasing returns to scale.

Answer 1

Increasing Returns to Scale

When our inputs are increased by m and our output increases by more than m.

Constant Returns to Scale

When our inputs are increased by m and our output increases by exactly m.

Decreasing Returns to Scale

When our inputs are increased by m and our output increases by less than m.

For example.

1) Q = 3K + 4L. We will increase both K and L by m and create a new production function Q1. Then we will compare Q1 to Q.

Q1 = 3(K*m) + 4(L*m) = 3*K*m + 4*L*m = m(3*K + 4*L) = m*Q

After factoring I replaced (3*K + 4*L) with Q . Since Q1 = m*Q we note that by increasing all of our inputs by the multiplier m we've increased production by exactly m. So we have constant returns to scale.

2) Q=.4KL Again we put in our multipliers and create our new production function.

Q1 = .4(K*m)*(L*m) = .4*K*L*m² = Q * m²

Since m > 1, then m² > m. Our new production has increased by more than m, so we have increasing returns to scale.

3) Q=K^0.3L^0.2Again we put in our multipliers and create our new production function.

Q1 = (K*m)^0.3(L*m)^0.2 = K^0.3L^0.2m^0.5 = Q* m^0.5

Because m > 1, then m^0.5 < m, in this case our new production has increased by less than m, so we have decreasing returns to scale.