Describing Technology

• IsoquantsTwo inputs one output

Illustrates marginal rates of substitution between inputs

• Production functionMany inputs one output

• x = f(k,l,m)

Returns to scale: increase all inputs by factor a

f(ay1,ay2,…,ayn) > af (y1,y2,…,yn) increasing returns

f(ay1,ay2,…,ayn) = af (y1,y2,…,yn) constant returns

f(ay1,ay2,…,ayn )< af (y1,y2,…,yn) decreasing returns

Isoquants

Isoquants and Cost Minimization

Isoquants and Cost Minimization

• Get Equal Bang–Per–Buck from your inputs• Let k = kapital input r1 = unit cost of kapital• l = labor input r2 = unit cost of labor• m = materials input r3 = unit cost of materials

• At input combination that results in minimum cost M for given output x

For each pair of inputs• Slope of output isoquant = slope of iso-cost line

MPPl/MPPk = (M/r1)/(M/r2) = r2/r1

Then

MPPk/r1 = MPPl /r2 = MPPm/r3