Tutorial 5 Production Possibility Frontiers Matthew Robson Introduction

Tutorial 5: Production Possibility Frontiers Matthew Robson

Introduction

Perfect Substitutes

Perfect Complements

Edgeworth Box

Edgeworth Box – Perfect Substitutes; Firm 1

Edgeworth Box – Perfect Substitutes; Firm 2

Edgeworth Box – Perfect Complements; Firm 1

Edgeworth Box – Perfect Complements; Firm 2

Production Possibility Frontier -Find the Contract Curve (locus of efficient points) -Take any isoquant for Firm 1 and find the point where the Output of Firm 2 is the highest (n. b. for Perfect Complements this will be an area not a point) -Repeat for all isoquants for Firm 1 -Explain why this Contract Curve is where it is -Construct the Production Possibility Frontier -Take each point on the contract curve -Plot the Output of Firm 2 against the Output of Firm 1, for these points -Notice a kink point, is this optimum in any sense?

Edgeworth Box – Perfect Substitutes

Edgeworth Box – Perfect Complements

Production Possibility Frontier; Perfect Substitutes

Production Possibility Frontier; Perfect Complements

Cobb-Douglas Technology

Cobb-Douglas Technology

Cobb-Douglas; Lagrange (1) (2)

Cobb-Douglas; Quantities From (1) (3) From (2) (4) (3) = (4) (5)

Cobb-Douglas; Output

y 2 Cobb-Douglas; Possibility Production Frontier y 1

y 2 Cobb-Douglas; Possibility Production Frontier y 1

y 2 Cobb-Douglas; Possibility Production Frontier y 1

Cobb-Douglas; Price Takers