# Recall that a Cobb-Douglas production function has the form P = cL(^alpha) K(^beta) with c,...

## Question:

Recall that a Cobb-Douglas production function has the form {eq}P = cL^\alpha K^\beta{/eq} where {eq}c, \alpha, \beta > 0{/eq}.

Economists talk about increasing returns to scale if doubling {eq}L{/eq} and {eq}K{/eq} more than doubles {eq}P{/eq}, constant returns to scale if doubling {eq}L{/eq} and {eq}K{/eq} exactly doubles {eq}P{/eq}, and decreasing returns to scale if doubling {eq}L{/eq} and {eq}K{/eq} less than doubles {eq}P{/eq}.

What conditions in the sum {eq}\alpha + \beta{/eq} lead to:

(a) constant returns to scale?

(b) decreasing returns to scale?

## Returns to Scale:

Returns to scale in economics measure the changes in output with respect to changes in inputs. In particular:

• If the quantity of all inputs is increased by a constant proportion, and the output increases by the same proportion, production is said to have constant returns to scale.
• If the output increases by less than the same proportion, then production is said to have decreasing returns to scale.
• If the output increases by more than the same proportion, then production is said to have increasing returns to scale.