Question

Find the values of K and L that maximizes income with the following production function and budget constraint. Also, does this production function exhibit increasing returns to scale, constant returns to scale, or decreasing returns to scale? Why?

• max Y = 100K^0.25N^0.75
• subject to 200N + 250K = 50,000
• where 200 is the real wage, 250 is the rental rate of capital, & 50,000 is the firm’s budget constraint.

Answer 1

A function exhibit constant returns to scale if F(tK,tN) = t*F(K,N)

Here F(K,N) = 100K^0.25N^0.75

=> F(tK,tN) = 100(tK)^0.25(tN)^0.75 = t(100K^0.25N^0.75) = t*F(K,N)

Hence, F(tK,tN) = t*F(K,N)

Hence, this function exhibits constant returns to scale.