Question

Given the Cobb Dougless Equation Q=4K^(0.5)L^(0.7)

What kinds of returns to scale does the function have?

What is the output elasticity of labor? Interpret the results.

Answer 1

For Cobb Douglas Equation, Q(L,K) =

if $\alpha + \beta$ > 1 there will be increasing returns to scale. If $\alpha + \beta$ < 1 there will be decreasing returns to scales. And, if $\alpha + \beta$ = 1 there will be constant returns to scale

$\alpha + \beta$ $\alpha + \beta = 0.5 + 0.7 = 1.2$ , so there will be increasing returns to scale.

Interpretation - The output increases more than proportionately when all the inputs increase proportionately.

Output elasticity of labor = $\beta$ = 0.7

Interpreation - $\beta$ is 0.7, so if labor increases in 10%, output will increase 7%.