L15 Technology

Technology Producers: have a technology A technology - a process converting inputs to an output Typical Inputs: labor, physical and human capital, land, R&D, marketing capital To make our life simpler: only two inputs capital ( ) and labor ( ) Technology given by production function

Production function: Geometry L z All bundles in I1 are strictly preferred to all in I2. K

Production function: Geometry L z All bundles in I1 are strictly preferred to all in I2. K

Production function: Geometry L z All bundles in I1 are strictly preferred to all in I2. K

Production function: Geometry 5 L 3 z All bundles in I1 are strictly preferred to all in I2. K

Production function: Geometry f(K,L) y 5 L 3 All bundles in I1 are strictly preferred to all in I2. K

3 Classic Examples Cobb-Douglass Fixed Proportions Perfect Substitutes

Marginal Product MPK and MPL Economic Interpretation of MPK – how much product goes up if K increases by 1 Geometric Interpretation MPL analogous but for L

MPK Increasing, Constant, Decreasing? Cobb-Douglass More generally

MPK Increasing, Constant, Decreasing? Fixed Proportions Perfect Substitutes

Technical Rate of Substitution TRS: slope of isoquant Interpretation: Formula:

What’s new? Long run and Short run ( fixed) Monotone transformation? Nooooo! Returns to Scale (Idea)

Returns to scale Constant Returns to Scale (CRS) Increasing (IRS), Decreasing (DRS)

CRS: Geometry L 2z z K All bundles in I1 are strictly preferred to all in I2. K

Marginal Product and Returns to Scale

Marginal Product and Returns to Scale