GENERAL EQUILIBRIUM. Wanna Download D. Salvatore, International Economics for free? Gr8, visit now jblogger2016.wordpress.com

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4 Wanna Download D. Salvatore, International Economics for free? Gr8, visit now jblogger2016.wordpress.com PDF Version of Lecture Notes by jblogger2016 GENERAL EQUILIBRIUM

5 FIRM AND HOUSEHOLD DECISIONS Input and output markets cannot be considered separately or as if they operate independently.

6 PARTIAL EQ VS GENERAL EQ ANALYSIS Partial equilibrium analysis is the process of examining the equilibrium conditions in individual markets, and for households and firms, separately. General equilibrium is the condition that exists when all markets in an economy are in simultaneous equilibrium.

7 GENERAL EQUILIBRIUM THEORY Partial equilibrium model all prices other than the price of the good being studied are assumed to remain fixed. General equilibrium model all prices are variable and equilibrium requires that all markets clear (all of the interactions between markets are taken into account)

8 ASSUMPTIONS 1. 2*2*2 modelfop (L and K), products(x and Y), Consumers (A,B) 2. Two consumers A and B Preference assumption Ordinal Indifference curves are convex to the origin. Diminishing marginal rate of substitution(mrsxy)

9 ASSUMPTIONS

10 ASSUMPTIONS 3. Two Factors of Production L and K-fixed in supply 4. Two goods/products X and Y The isoquants are smooth and convex to the origin diminishing MRTSLK 5. Technology is given 6. X less capital intensive K/L in X <K/L in Y 7. Consumers maximize utility firms max profits

11 8. Absence of government interference-free markets 9. Perfectly competitive product and factor markets -Prices of L, K, X and Y are given 10. No externalities in consumption or production

12 STATIC PROPERTIES OF GENERAL EQUILIBRIUM Efficient allocation of resources among firms/equilibrium in production Efficient Distribution of commodities produces between consumers/equilibrium in consumption Efficient combination of production/simultaneous equilibrium of production and consumption

13 1. Equilibrium in production

14 COST CONSTRAINT (-) w/r K C/r C=wL+rK Slope of the isocost = K/ L= K/ L= (-) w/r C/w L

15 EQUILIBRIUM K e C wl rk L

16 EQUILIBRIUM Slope of isoquant = Slope of isocost MRTS = (-) w/r or MPL/MPK = (-) w/r

17 CapitalX KX X=1.5 X=1 0 LaborX LX

18 CapitalY KY Y=3 Y=2 0 LaborY LY

19 We can combine the information of these two figures into one figure KY KX 0 LX 0 LY

20 We can combine the information of these two figures into one figure KX 0 LX

21 We can combine the information of these two figures into one figure KX 0 LX

22 We can combine the information of these two figures into one figure KX 0 LX

23 We can combine the information of these two figures into one figure LY 0 KX KY 0 LX

24 Kx Ly Oy The origin of good X is in the southwest corner The origin of good Y is in the northeast corner A Ly and Ky are measured relative to the Oy corner Lx and Kx are measured relative to the Ox corner Ox Ky Lx

25 EDGEWORTH BOX DIAGRAM IN PRODUCTION An Edgeworth box shows every possible way the existing k and l might be used to produce x and y any point in the box represents a fully employed allocation of the available resources to x and y 22

26 EDGEWORTH BOX DIAGRAM Labor in y production A Capital in x production Ox Labor in x production Total Labor Capital for y Oy Capital in y production Capital for x Labor for y Total Capital Labor for x 23

27 Which points represent efficient allocations inside the Edgeworth box?

28 EDGEWORTH BOX DIAGRAM Point A is inefficient because, by moving along y1, we can increase Oy x from x1 to x2 while holding y constant Total Capital y1 y2 A Ox Total Labor x2 x1 25

29 EDGEWORTH BOX DIAGRAM We could also increase y from y1 to y2 while holding x constant by moving along x1 Oy Total Capital y1 y2 A Ox Total Labor x2 x1 26

30 An allocation of resources is efficient in production (or technically efficient ) if no further reallocation would permit more of one good to be produced without necessarily reducing the output of some other good.

31 THE PARETO CRITERION Pareto optimal: the term used to describe situations in which it is impossible to increase production of one good without reducing the output of other commodity When isoquants are tangent Slope of x isoquant = slope of Y isoquant MRTS X l,k MRTS Y l,k w r 18w-

32 EDGEWORTH BOX DIAGRAM At each efficient point, the RTS (of k for l) is equal in both Oy x and y production y1 Total Capital p4 y2 p3 x4 y3 p2 y4 x3 p1 x1 Ox Total Labor x2 29

33 PRODUCTION POSSIBILITY FRONTIER The locus of efficient points shows the maximum output of y that can be produced for any level of x we can use this information to construct a production possibility frontier shows the alternative outputs of x and y that can be produced with the fixed capital and labor inputs that are employed efficiently 30

34 PRODUCTION POSSIBILITY FRONTIER Each efficient point of production becomes a point on the production possibility frontier Quantity of y Ox y4 y3 p1 p2 The negative of the slope of the production possibility frontier is the rate of product transformation (RPT) p3 y2 p4 y1 x1 x2 x3 x4 Oy Quantity of x 31

35 RATE OF PRODUCT TRANSFORMATION The rate of product transformation (MRPT) between two outputs is the negative of the slope of the production possibility frontier The rate at which one output can be transformed into another MRPT (of x for y) slope of production possibility frontier dy MRPT (of x for y) (along OxOy ) dx 32

36 Where on the ppc to produce?

37 PRODUCTION POSSIBILITY CURVE y Where on the PPC? How much X and how much Y should be produced? x

38 PRODUCTION POSSIBILITY CURVE Points lie inside the curve are (Pareto) inefficient y x

39 PRODUCTION POSSIBILITY CURVE y Slope of the PPC = y/ x How many units of Y that have to given up in order to produce one more unit of X Marginal rate of product transformation (MRPT or MRT)

40 We can prove that under pcm in equilibrium the slope of PPC= MCx/MCy= Px /Py

41 GENERAL EQUILIBRIUM y The slope of the PPF = Px/Py Px/Py x

42 GENERAL EQUILIBRIUM Claim: In equilibrium, firms will produce at the point on the production possibility curve at which MRPT = Px/Py If MRPT < Px/Py produce more X and less Y If MRPT > Px/Py produce less X and more Y

43 2. EQUILIBRIUM IN CONSUMPTION

44 EDGEWORTH BOX Total amount of Y U U 1A Individual A Total amount of X A 2

45 EDGEWORTH BOX Total amount of X U 1B U B 2 Individual B Total amount of Y Individual A

46 EDGEWORTH BOX Total amount of X Individual B Total amount of Y Individual A Each point within the box represents a particular allocation of the two products between the two individuals

47 PARETO EFFICIENT ALLOCATION Pareto Efficient Allocation: Each individual is on the highest possible indifference curve, given the indifference curve of the other individual.

48 EDGEWORTH BOX Total amount of Individual B a Y b Individual A XA X Total amount of YB

49 PARETO INEFFICIENT ALLOCATION a and b are Pareto inefficient allocations. Why? Because there exists changes in allocations, starting from a or b, that would make at least one individual better off without making the other individual worse off.

50 EDGEWORTH BOX Individual B Total amount of Y g is a pareto efficient point g Individual A X Total amount of

51 PARETO EFFICIENT ALLOCATION At point/allocation g: Individual A is on the higher possible indifference curve given B s indifference curve and Individual B is on the highest possible indifference curve given A s indifference curve. Therefore, g is a pareto efficient allocation Note: The two indifference curves are tangential to each other

52 PARETO EFFICIENT ALLOCATIONS Individual B Total amount of e g Y Individual A X Total amount of e and are also Pareto efficient allocations

53 CONTRACT CURVE Individual B Total amount of e g Y Individual A X Total amount of Joining up these Pareto efficient points yields the contract curve

54 THE CONTRACT CURVE IN CONSUMPTION All the points in the Edgeworth box where the indifference curves are tangent describes the entire set of Pareto-optimal allocations. A line connecting all these points of tangency is call the contract curve. Efficiency in consumption requires that MRS is identical for all individuals. In other words, the allocation to individual consumers of the goods produced in an economy must be Pareto-optimal.

55 CONTRACT CURVE The curve connecting all Pareto efficient allocations is known as the contract curve. At each point on the contract curve, the MRS s for A and B are equal, i.e. MRSAxy = MRSBxy In PCM prices are given MRSAxy = MRSBxy = Px/Py

56 EXCHANGE EDGEWORTH BOX: SUMMARY XB Individual B Total amount of Y YB YA Individual A PX PY XA X Total amount of

57 3. Equilibrium in product mix

58 Technical efficiency is not a sufficient condition for Pareto efficiency demand must also be brought into the picture In order to ensure Pareto efficiency, we must be able to tie individual s preferences and production possibilities together

59 EFFICIENCY IN PRODUCT MIX The condition necessary to ensure that the right goods are produced is MRS = MRPT the psychological rate of trade-off between the two goods in people s preferences must be equal to the rate at which they can be traded off in production 56

60 GENERAL EQUILIBRIUM y Recall the Edgeworth box Y Px/Py X x

61 GENERAL EQUILIBRIUM y Individual B Y Px/Py Individual A X x

62 GENERAL EQUILIBRIUM y Individual B Y Px/Py Individual A X x

63 GENERAL EQUILIBRIUM Recall that y MRSxy= Px/Py Individual B Y Px/Py Individual A X x

64 GENERAL EQUILIBRIUM y MRS = MRPT = Px/Py Y Px/Py UA Px/Py UB X x

65 GENERAL EQUILIBRIUM Three Conditions for General Equilibrium: (1) A MRS XY (2) MRTS X LK B MRS XY MRTS (3) MRPT XY Y LK PX PY PL w PK r PX MRS XY PY

66 SHAPE OF THE PRODUCTION POSSIBILITY FRONTIER The production possibility frontier shown earlier exhibited an increasing RPT this concave shape will characterize most production situations RPT is equal to the ratio of MCx to MCy 63

67 DETERMINATION OF EQUILIBRIUM PRICES We can use the production possibility frontier along with a set of indifference curves to show how equilibrium prices are determined the indifference curves represent individuals preferences for the two goods 64

68 DETERMINATION OF EQUILIBRIUM PRICES If the prices of x and y are px and py, society s budget constraint is C Quantity of y C Output will be x1, y1 y1 Individuals will demand x1, y1 y1 U3 U2 U1 x1 x1 C slope px py Quantity of x 65

69 DETERMINATION OF EQUILIBRIUM PRICES There is excess demand for x and excess supply of y Quantity of y C The price of x will rise and the price of y will fall y1 excess supply y1 U3 U2 U1 x1 x 1 excess demand C slope px py Quantity of x 66

70 DETERMINATION OF EQUILIBRIUM PRICES The equilibrium prices will be px* and py* Quantity of C* y C The equilibrium output will be x1* and y1* y1 y1 * y1 U3 U2 U1 C* x 1 x1* x1 px* slope py* C slope px py Quantity of x 67

71 COMPARATIVE STATICS ANALYSIS The equilibrium price ratio will tend to persist until either preferences or production technologies change If preferences were to shift toward good x, px /py would rise and more x and less y would be produced we would move in a clockwise direction along the production possibility frontier 68

72 GENERAL EQUILIBRIUM CLOSED ECONOMY-AUTARKY EQUILIBRIUM Food I1 I2 I A 200 p Clothing

73 CONDITIONS FOR AUTARKY EQUILIBRIUM Producers must be happy producing what they are producing: Px/PY=MRTS relative price of X equals opportunity cost in production. Consumers must be happy consuming what they are consuming: Px/PY=MRS relative price of X equals the marginal rate of substitution. Market clearance: supply equals demand.

74 SUMMARY OF CONDITIONS Each of the three efficiency conditions is necessary for an efficient allocation of resources: Efficiency in consumption requires that MRS is identical for all individuals. Efficiency in production requires that the MRTS must be identical for all firms. Efficiency in the product mix requires that each consumer s MRS be identical to the economy s MRT.

75 SOURCES OF INEFFICIENCY What produces an inefficient allocation of resources? There are many potential sources of inefficiencies, one is a monopoly. Others are Externalities, Public goods For a monopoly the first 2 efficiency conditions still hold: 1. Because all firms face the same input prices, each chooses an input bundle so that MRTS=w1e/w2e

76 MONOPOLY AND INEFFICIENCY For a monopoly the first 2 efficiency conditions still hold: Because all firms face the same input prices, each chooses an input bundle so that MRTS=w1e/w2e Because all consumers face the same product prices, each chooses a bundle at which the MRS=p1e/p2e

77 MONOPOLY AND INEFFICIENCY For a monopoly the inefficiency arises from a distortion of the product mix. The inefficiency arises because the profit maximizing monopolist produces where MR<P and P>MC Therefore for all consumers, the MRS>MRT and the allocation of resources is inefficient.