# Production functions production Function

 Date 16.04.2016 Size 84.3 Kb.

• ## To study variation in a single input, we define marginal physical product as the additional output that can be produced by employing one more unit of that input while holding other inputs constant    • ## In general, we assume diminishing marginal productivity    ## Average Physical Product (AP) • ## Labor productivity is often measured by average productivity Note that APl also depends on the amount of capital employed

## f(k,l) = q0

• Each isoquant represents a different level of output

• output rises as we move northeast

• ## Take the total differential of the production function:  • Along an isoquant dq = 0, so   • ## Since RTS = fl/fk    • ## Using the fact that dk/dl = -fl/fk along an isoquant and Young’s theorem (fkl = flk)  ## q = f(k,l) and all inputs are multiplied by the same positive constant (t >1), then  • ## This implies that the marginal productivity functions are homogeneous of degree zero

• ### Geometrically, all of the isoquants are radial expansions of one another. Along a ray from the origin (constant k/l), the RTS will be the same on all isoquants • ## The elasticity of substitution () measures the proportionate change in k/l relative to the proportionate change in the RTS along an isoquant ## The value of will always be positive because k/l and RTS move in the same direction Both RTS and k/l will change as we move from point A to point B

• ## All isoquants are straight lines

• ### =

Capital and labor are perfect substitutes

• ## Because k/l is constant, = 0

k per period

k/l is fixed at b/a

= 0
q3/a

q3

q2
q1
l per period

q3/b
Substitution between capital and labor is not possible.

k per period

q3

q1

q2

l per period