Question

13. Following are different algebraic expressions of the production function. Decide whether

each one has constant, increasing, or decreasing returns to scale.

a. Q = 75L0.25K0.75

b. Q = 75A0.15B0.40C0.45

c. Q = 75L0.60K0.70

d. Q = 100 + 50L + 50K

e. Q = 50L + 50K+ 50LK

f. Q = 50L2 + 50K2

Answer 1

a). Q = 75L0.25K0.75

$0.25+0.75=1$

Constant returns to scale

b). Q = 75A0.15B0.40C0.45

$0.15+0.40+0.45=1$

Constant returns to scale

c). Q = 75L0.60K0.70

$0.60+0.70=1.30$

Increasing returns to scale

d). Q = 100 + 50L + 50K

Assumes 10 units of each input;

$Q=100+(50\times10)+(50\times10)=1100$

If 20 units of each input;

$Q=100+(50\times20)+(50\times20)=2100$

So, $EQ<1$

Decreasing returns to scale

e). Q = 50L + 50K+ 50LK

Assumes 10 units of each input;

$Q=(50\times10)+(50\times10)+(50\times10\times10)=6000$

If 20 units of each input;

$Q=(50\times20)+(50\times20)+(50\times20\times20)=22000$

So, $EQ>1$

Increasing returns to scale

f). Q = 50L2 + 50K2

Assumes 2 units of each input;

$Q=(50\times2^2)+(50\times2^2)=400$

In case of using 4 units of each input;

$Q=(50\times4^2)+(50\times4^2)=1600$

So, $EQ>1$

Increasing returns to scale