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Chapter 17. General Equilibrium and Welfare Economics. Figure 17.1
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Chapter 17... General Equilibrium and Welfare Economics
Figure 17.1 General Equilibrium Implications of a Reduction in the Demand for New Domestically Produced Automobiles The impact or partial equilibrium effect of a reduction in the demand for new domestically produced automobiles is to reduce price from P to P¢and quantity from Q to Q¢ [panel (a)]. This reduces the demand for (and price and quantity of) steel [panel (b)] and gasoline [panel (c)], and the demand for (and wages and employment of) workers in the automobile [panel (d)] and other affected industries. This, in turn, has spillover effects on the market for steaks [panel (e)] and other commodities, and feedback effects on the domestic automobile industry itself [panel (f)].
Figure 17.2 Edgeworth Box Diagram for Exchange A point such as C indicates that individual A had 3X and 6Y (viewed from origin 0A), while individual B has 7X and 2Y (viewed from origin 0B) for a total of 10X and 8Y (the dimensions of the box). A’s indifference curves (A1, A2, and A3) are convex to 0A, while B¢s indifference curves (B1, B2, and B3) are convex to 0B. Starting from point C where A1 and B1 intersect, individuals A and B can reach points on DEF, where one or both individuals gain. Curve 0ADEF0B is the contract curve for exchange. It is the locus of tangencies of the indifference curves (at which the MRSXYare equal) for the two individuals and the economy is in general equilibrium of exchange.
Figure 17.3 Edgeworth Box Diagram for Production A point such as R indicates that 3L and 8K (viewed from origin 0X) are used to produce X1 of commodity X, and the remaining 9L and 2K (viewed from origin 0Y) are used to produce Y1 of Y. The isoquants for X (X1, X2, and X3) are convex to 0X, while the isoquants of Y (Y1, Y2, and Y3) are convex to 0Y. Starting from point R, where X1 and Y1 intersect, the economy can produce more of X, more of Y, or more of both by moving to a point on JMN. Curve 0X JMN0Yis the contract curve for production. It is the locus of tangencies of the isoquants (at which the MRTSLKare equal) for both commodities, and the economy is in general equilibrium of production.
Figure 17.4 Production-Possibilities Frontier The production-possibilities frontier or transformation curve TT is derived by mapping the production contract curve of Figure17.3 from input to output space. Starting from point R¢, the economy could increase its output of X (point N¢), of Y (point J¢), or of both X and Y (point M¢). The absolute slope or MRTXY= 3/2 at point M¢ means that 3/2 of Y must be given up to produce one additional unit of X. MRTXYincreases as we move down the frontier. Thus, at point N¢, MRTXY= 3.
Figure 17.5 General Equilibrium of Production and Exchange Production-possibilities frontier TT is that of Figure 17.4. Every point on TT is a point of general equilibrium of production. Starting from point M¢ (10X, 8Y) on the production-possibilities frontier, we constructed in Figure 17.4 the Edgeworth box diagram for exchange between individuals A and B shown in Figure 17.2. Every point on contract curve 0ADEF0B is a point of general equilibrium of exchange. Simultaneous general equilibrium of production and exchange is at point E, at which MRTXY= MRSXY= MRSXY= 3/2. A B
Figure 17.6 Efficiency in Production and Exchange in a “Robinson Crusoe” Economy In a single-person economy, economic efficiency in production and exchange (and maximum social welfare) is achieved at point M*, at which indifference curve A2 for individual A (the only individual in society) is tangent to his or her production-possibilities frontier, T¢T¢. Output is 6X and 3Y, and MRTXY= MRSXY= 3/2.
Figure 17.7 Graphic Analysis of General Equilibrium with Trade The production-possibilities frontier is AA for nation A and BB for nation B. In the absence of trade, nation A is at point C and nation B is at point C¢. Since MRTXY= PX/PY(the absolute value of the slope of the production–possibilities frontier) is lower at point C than at point C¢, nation A has a comparative advantage in X while nation B has a comparative advantage in Y. With trade, A produces at point D, exchanges 40X for 40Y with B, and consumes at E > C. Nation B produces at point D¢, exchanges 40Y for 40X with A, and consumes at E¢ > C¢.
Figure 17.8 Utility-Possibilities Frontier Utility-possibilities frontier UM¢UM¢ shows the various combinations of utilities received by individuals A and B (i.e., UA and UB) when the economy composed of individuals A and B is in general equilibrium or Pareto optimum in exchange. The frontier is obtained by mapping exchange contract curve 0ADEF0B in Figure17.5 from output or commodity space to utility space. Specifically, if A1 refers to UA = 200 utils and B3 to UB = 600 utils, point D in Figure 17.5 can be plotted as point D¢ in this figure. Point E can be plotted as point E¢, and point F as F¢. By joining points D¢E¢F¢, we get utility-possibilities frontier UM¢UM¢.
Figure 17.9 Grand Utility-Possibilities Frontier Utility-possibilities frontier UM¢UM¢ is that of Figure 17.8. Utility-possibilities frontier UN¢UN¢.is derived from the contract curve for exchange in the Edgeworth box diagram constructed from point N¢ on the production-possibilities frontier of Figure17.5. By joining E¢, H¢, and other Pareto optimum points of production and exchange similarly obtained, we get grand utility-possibilities frontier GE¢H¢G.
Figure 17.10 Measuring Changes in Social Welfare A movement from point C* to a point from E¢ to H¢ on grand utility-possibilities frontier GG benefits one or both individuals and harms no one. Thus, the movement increases social welfare according to the Pareto criterion. A movement from point C* to point Z increases social welfare according to the Kaldor–Hicks criterion, since individual B could fully compensate individual A for his or her loss and still retain some gain. However, since this type of reasoning is based on interpersonal comparisons of utility, social welfare need not be higher.
Figure 17.11 Lorenz Curves A Lorenz curve gives the cumulative percentages of total income (measured along the vertical axis) for various cumulative percentages of the population or families (measured along the horizontal axis). The after-taxes and after-transfers Lorenz curve has a smaller curvature (or outward bulge from the diagonal) than the before-taxes and before-transfers Lorenz curve, indicating a smaller income inequality after taxes and transfers than before.
