Question

A firm has a production function f(x,y)=1.4(x⁰.⁶+y⁰.⁶ )²

where x>0 and y>0. Investigate, whether the firm has increasing, decreasing or constant returns to scale.

Answer 1

The firm with the production function f(x,y)=1.4(x⁰.⁶+y⁰.⁶)² has constant returns to scale as the output scales up proportionally with the inputs.

Step-by-step explanation:

A student inquired whether the firm with the production function f(x,y)=1.4(x0.6+y0.6)2 has increasing, decreasing, or constant returns to scale. To investigate this, we examine how the output changes when all inputs are scaled up by the same proportion.

Let's scale up inputs by a factor k, where k > 0. The new production function would be:

f(kx, ky) = 1.4((kx)0.6 + (ky)0.6)2

= 1.4(k0.6x0.6 + k0.6y0.6)2

= 1.4k1.2(x0.6 + y0.6)2

If k1.2 > k, the firm has increasing returns to scale. If k1.2 < k, the firm has decreasing returns to scale. Here, since 1.2 = 1, the firm has constant returns to scale, as the production function scales up proportionally with inputs.

This concept relates to a constant cost industry where despite the increase in market demand and price, the long-run equilibrium intersects at the same market price due to perfectly elastic supply curves and an elastic supply of inputs such as labor.