尼克尔森中级微观经济学第九版答案ch12

CHAPTER 12 GENERAL EQUILIBRIUM AND WELFARE The problems in this chapter focus primarily on the simple two-good general equilibrium model in which “supply” is represented by the production possibility frontier and “demand” by a set of indifference curves. Because it is probably impossible to develop realistic general equilibrium problems that are tractable, students should be warned about the very simple nature of the approach used here. Specifically, none of the problems does a very good job of tying input and output markets, but it is in that connection that general equilibrium models may be most needed.  The Extensions for the chapter provide a very brief introduction to computable general equilibrium models and how they are used. Problems 12.1–12.5 are primarily concerned with setting up general equilibrium conditions whereas 12.6–12.10 introduce some efficiency ideas. Many of these problems can be best explained with partial equilibrium diagrams of the two markets. It is important for students to see what is being missed when they use only a single-good model. Comments on Problems 12.1    This problem repeats examples in both Chapter 1 and 12 in which the production possibility frontier is concave (a quarter ellipse). It is a good starting problem because it involves very simple computations. 12.2    A generalization of Example 12.1 that involves computing the production possibility frontier implied by two Cobb-Douglas production functions. Probably no one should try to work out all these cases analytically. Use of computer simulation techniques may offer a better route to a solution (it is easy to program this in Excel, for example). It is important here to see the connection between returns to scale and the shape of the production possibility frontier. 12.3    This is a geometrical proof of the Rybczynski Theorem from international trade theory. Although it requires only facility with the production box diagram, it is a fairly difficult problem. Extra credit might be given for the correct spelling of the discoverer’s name. 12.4    This problem introduces a general equilibrium model with a linear production possibility frontier. The price ratio is therefore fixed, but relative demands determine actual production levels. Because the utility functions are Cobb-Douglas, the problem can be most easily worked using a budget-share approach. 12.5    This is an introduction to excess demand functions and Walras’ Law. 12.6    This problem uses a quarter-circle production possibility frontier and a Cobb-Douglas utility function to derive an efficient allocation. The problem then proceeds to illustrate the gains from trade. It provides a good illustration of the sources of those gains. 12.7    This is a fixed-proportions example that yields a concave production possibility frontier. This is a good initial problem although students should be warned that calculus-type efficiency conditions do not hold precisely for this type of problem. 12.8    This provides an example of efficiency in the regional allocation of resources. The problem could provide a good starting introduction to mathematical representations of comparative versus absolute advantage or for a discussion of migration. To make the problem a bit easier, students might be explicitly shown that the production possibility frontier has a particularly simple form for both the regions here (e.g., for region A it is  ). 12.9    This problem provides a numerical example of an Edgeworth Box in which efficient allocations are easy to compute because one individual wishes to consume the goods in fixed proportions. 12.10    A continuation of Problem 12.9 that illustrates notions of the core and exchange offer curves. Solutions 12.1    a.    b.    9x2 = 900; x = 10, y = 20 c.    If x = 9 on the production possibility frontier, If x = 11 on the frontier, Hence, RPT is approximately 12.2    I have never succeeded in deriving an analytical expression for all these cases. I have, however, used computer simulations (for example with Excel) to derive approximations to these production possibility frontiers. These tend to show that increasing returns to scale is compatible with concavity providing factor intensities are suitably different (case [e]), but convexity arises when factor intensities are similar (case [d]). 12.3    a.    Draw the production possibility frontier and the Edgeworth box diagram. Find where P line is tangent to PPF; then go back to the box diagram to find input ratio. See Corn Law Debate example in the text. b.    P given, land/labor ratio is constant. Equilibrium moves from E to E '. Cloth  (OC E' > OC E)    Wheat  (OW'E' < OWE)