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Microeconomics Corso E

Microeconomics Corso E. John Hey. Summary of Chapter 8. The contract curve shows the allocations that are efficient in the sense of Pareto.

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Microeconomics Corso E

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  1. MicroeconomicsCorso E John Hey

  2. Summary of Chapter 8 • The contract curve shows the allocations that are efficient in the sense of Pareto. • There always exist the possibility of mutually advantageous exchange if preferences are different and/or endowments are different (unless the endowment point is on the contract curve). • Perfect competitive equilibrium (with both individuals taking the price as given) always leads to a Pareto efficient allocation. • If one of the individuals chooses the price the allocation is not Pareto efficient.

  3. The competitive equilibrium depends on the preferences and the endowments. • If one individual changes his or her preferences in such a way that he or she now prefers more a particular good than before... • ... the relative price of that good rises. • If an individual is endowed with more of a good than before... • ... the relative price of that good falls.

  4. Part 1 and Part 2 • Part 1: an economy without production... • ... just exchange • Part 2: an economy with production... • ... production and exchange.

  5. Part 1 • Reservation prices. • Indifference curves. • Demand and supply curves. • Surplus. • Exchange. • The Edgeworth Box. • The contract curve. • Competitive equilibrium. • Paretian efficiency and inefficiency.

  6. Part 2 • Chapter 10: Technology. • Chapter 11: Minimisation of costs and factor demands. • Chapter 12: Cost curves. • Chapter 13: Firm’s supply and profit/surplus. • Chapter 14: The production possibility frontier. • Chapter 15: Production and exchange.

  7. Chapter 10 • Firms produce... • ...they use inputs to produce outputs. • In general many inputs and many outputs. • We work with a simple firm that produces one output with two inputs... • ...capital and labour. • The technology describes the possibilities open to the firm.

  8. Individuals Buy goods and ‘produce’ utility… …depends on the preferences… …which we can represent with indifference curves.. …in the space (q1,q2) Firms Buy inputs and produce output… …depends on the technology… …which we can represent with isoquants .. …in the space (q1,q2) Chapter 5 Chapter 10

  9. The only difference? • We can represent preferences with a utility function ... • ... but this function is not unique... • ... because/hence we cannot measure the utility of an individual. • We can represent the technology of a firm with a production function ... • ... and this function is unique… • …because we can measure the output.

  10. An isoquant • In the space of the inputs (q1,q2)it is the locus of the points where output is constant. • (An indifference curve – the locus of the points where the individual is indifferent. Or the locus of points for which the utility is constant.)

  11. Two dimensions • The shape of the isoquants: depends on the substitution between the two inputs. • The way in which the output changes form one isoquant to another – depends on the returns to scale.

  12. Perfect substitutes 1:1 • an isoquant: q1 + q2 = constant • y = A(q1 + q2) constant returns to scale • y = A(q1 + q2)0.5decreasing returns to scale • y = A(q1 + q2)2increasing returns to scale • y = A(q1 + q2)breturns to scale decreasing (b<1) increasing (b>1)

  13. y = q1 + q2 : perfect substitutes 1:1 and constant returns to scale

  14. y = (q1 + q2)2 : perfect substitutes 1:1 and increasing returns to scale

  15. y = (q1 + q2)0.5 : perfect substitutes 1:1 and decreasing returns to scale

  16. Perfect Substitutes 1:a • an isoquant: q1 + q2/a = constant • y = A(q1 + q2/a) constant returns to scale • y = A(q1 + q2/a)breturns to scale decreasing (b<1) increasing (b>1)

  17. Perfect Complements 1 with 1 • an isoquant: min(q1,q2) = constant • y = A min(q1,q2) constant returns to scale • y = A[min(q1,q2)]breturns to scale decreasing (b<1) increasing (b>1)

  18. y = min(q1, q2): Perfect Complements 1 with 1 and constant returns to scale

  19. y = [min(q1, q2)]2Perfect Complements 1 with 1 and increasing returns to scale

  20. Y = [min(q1, q2)]0.5: Perfect Complements 1 with 1 and decreasing returns to scale

  21. Perfect Complements 1 with a • an isoquant: min(q1,q2/a) = constant • y = A min(q1,q2/a) constant returns to scale • y = A[min(q1,q2/a)]breturns to scale decreasing (b<1) increasing (b>1)

  22. y = q10.5 q20.5: Cobb-Douglas with parameters 0.5 and 0.5 – hence constant returns to scale

  23. y = q1 q2: Cobb-Douglas with parameters 1 and 1 – hence increasing returns to scale

  24. y = q10.25 q20.25: Cobb-Douglas with parameters 0.25 and 0.25 – hence decreasing returns to scale

  25. Cobb-Douglas with parameters a and b • an isoquant: q1aq2b = constant • y = A q1aq2b • a+b<1 decreasing returns to scale • a+b=1 constant returns to scale • a+b>1 increasing returns to scale

  26. Individuals The preferences are given by indifference curves …in the space (q1,q2) .. can be represented by a utility function u = f(q1,q2)… …which is not unique. Firms The technology is given by isoquants …in the space (q1,q2) ..can be represented by a production function … y = f(q1,q2)… … which is unique . Chapter 5 Chapter 10

  27. Chapter 10 • Goodbye!

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