# Let a firm’s production function be z=f(x,y)=xayb where z is the output level and x and y are fac… 1 answer below »

Let a firm’s production function be

*z=f(x,y)=x ^{a}y^{b}*

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Let a firm’s production function be z=f(x,y)=xayb where z is the output level and x and y are fac…
1 answer below »

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where z is the output level and x and y are factor inputs and a

and b are exogenous parameters, a,b>0. Prices on factors are

given, p_{x} and p_{y} and the product price is

p.

a) Show that this production function exhibits constant returns

to scale if a+b=1, increasing returns if a+b>1 and decreasing

returns if a+b<1

b) Derive the cost function for this production function

c) Derive, using the Envelope Theorem, the Shephard’s Lemma for

this production function.

Please explain, and show workings, thank you.