Question

1) The production function Q = 50K^0.25L^0.25 exhibits

A. increasing returns to scale. B. constant returns to scale.

C. decreasing returns to scale. Answer

D. increasing, then diminishing returns to scale.

E. negative returns to scale.

2) The production function Q = 50K^0.25L^0.75 exhibits

A. increasing, then diminishing returns to scale. B. increasing returns to scale.
C. decreasing returns to scale.

D. constant returns to scale. Answer

E. negative returns to scale.

could you please explaing me the reason of those answers.

Thank you

Answer 1

1.
Q = 50K^0.25L^0.25
multiplying a factor m in both sides
Qm=50(mK^0.25)(mL^0.25)
Factoring m out
Qm=50m^(0.25+0.25)(K^0.25L^0.25)
Qm=50m^0.5(K^0.25L^0.25)
Now when we multiplied m its value was m^1, after factoring it out we see its value has decreased to m^0.5
Thus we can say this production function has decreasing returns to scale.

2.

Q = 50K^0.25L^0.275
multiplying a factor m in both sides
Qm=50(mK^0.25)(mL^0.75)
Factoring m out
Qm=50m^(0.25+0.75)(K^0.25L^0.75)
Qm=50m^1(K^0.25L^0.75)
Now when we multiplied m its value was m^1,after factoring it out we see its value is still m^1
Thus we can say this production function has constant returns to scale.