Representing technology 1

 

·     Production plan: y = (yj,-x)

·     Production possibility set, Y, is all  (yj,-x)

·     Input requirement set V(y)

·     Short run PPS:Y|z

·     Production function: y = f(x)

o   Concave and convex functions

o   Quasi-concave functions

·     Isoquant

·     Transformation function

 

Representing technology 2

 

·     •Monotonic technologies

·     •Convex technologies

·     •Regular technology

·     •Parametric representation

·     •Technical rate of substitution, TRS

·     •Elasticity of substitution

·     •Output elasticity of a factor

 

Representing technology 3

 

·        Returns to scale

o       Constant returns to scale

o       Increasing returns to scale

o       Decreasing returns to scale

·     Elasticity of scale

·     Homogeneous functions

·     Positive monotonic transformation

·     Homothetic function

•

Representing technology 4

 

·     Models v complex reality

·     Judging models

·     Categories

·     Communication of results

o   Rhetoric and simple writing

[F]ew important conclusions of economic analysis cannot be expressed in simple language. The challenge is to find how to do that. Many intellectuals, many economists, use obscure language when they write. Sometimes it is a way of disguising that they are not saying a heck of a lot.

"Interview with Gary Becker", Federal Reserve Bank of Minneapolis, _The Region_, June 2002.

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·     Parametric representations

·     Unit isoquant representation

·     Homotheticity

·     Scale

Profit functions

 

·     Profit function

·     Short run profit function

·     Cost function

·     Short run cost function

·     Profit maximization: FOC and SOC

·     Interior solutions and comparative statics

·     Corner solutions and KT conditions

 

Factor demands and output supply

 

·     Factor demands as a function of prices

·     Supply function

·     Properties of factor demands

·     Properties of supply function

·     WAPM

·     IRTS and profit maximization

·      

Profit functions 2

 

·     Properties of profit functions

o   Reaction to output and input prices

o   H1

o   Convex in p

o   Continuous in p

·     Examples of profit functions

·     Deriving supply and factor demands from the profit function

o   Hotelling’s lemma

o   Deriving comp static results from PF

·     The Envelope theorem

·     Le Chatelier principle

 

Cost functions

·     The program

·     Solving by substitution or constrained minimization

·     2nd order conditions for constrained optimization

·     Conditional factor demands

·     Average and marginal cost

·     Short run and long run

·     Envelope theorem for constrained optimization

·     Properties of the cost function

·     Comparative statics using cost function

Duality (Briefest of looks)

 

·     Dual problems

·     “Reverse engineering” from the cost function to the technology

·     Example