专业课 尼科尔森微观经济学基本原理与扩展全套资料 尼克尔森微观经济理论-基本原理与扩展 第九版答案 ch06

Chapter 6/Demand Relationships Among Goods v 25CHAPTER 6 DEMAND RELATIONSHIPS AMONG GOODS Two types of demand relationships are stressed in the problems to Chapter 6: cross-price effects and composite commodity results. The general goal of these problems is to illustrate how the demand for one particular good is affected by economic changes that directly affect some other portion of the budget constraint. Several examples are introduced to show situations in which the analysis of such cross-effects is manageable. Comments on Problems 6.1Another use of the Cobb-Douglas utility function that shows that cross-price effects are zero. Explaining why they are zero helps to illustrate the substitution and income effects that arise in such situations. 6.2Shows how some information about cross-price effects can be derived from studying budget constraints alone. In this case, Giffens Paradox implies that spending on all other goods must decline when the price of a Giffen good rises. 6.3A simple case of how goods consumed in fixed proportion can be treated as a single commodity (buttered toast). 6.4An illustration of the composite commodity theorem. Use of the Cobb-Douglas utility produces quite simple results. 6.5An examination of how the composite commodity theorem can be used to study the effects of transportation or other transactions charges. The analysis here is fairly intuitivefor more detail consult the Borcherding-Silverberg reference. 6.6Illustrations of some of the applications of the results of Problem 6.5 6.7This problem demonstrates a special case in which uncompensated cross-price effects are symmetric. 6.8This problem provides a brief analysis of welfare effects of multiple price changes. 6.9This is an illustration of the constraints on behavior that are imposed by assuming separability of utility. 6.10This problem looks at cross-substitution effects in a three good CES function.Solutions 6.1a. As for all Cobb-Douglas applications, first-order conditions show that. Hence b.Because indifference curves are rectangular hyperboles (ms = constant), own substitution and cross-substitution effects are of the same proportional size, but in opposite directions. Because indifference curves are homothetic, income elasticities are 1.0 for both goods, so income effects are also of same proportionate size. Hence, substitution and income effects of changes in pm on s are precisely balanced. c.But d.From part a: 6.2Since a rise in pr implies that pr r definitely rises. Hence, must fall, so j must fall. Hence, . 6.3a.Yes, b.Since c.Since changes in pb or pt affect only pbt , these derivatives are also zero. 6.4a.Amount spent on ground transportation b.Maximize U(b, t, p) subject to ppp + pbb + ptt = I. This is equivalent to Max U(g, p) = g2p Subject to . c.Solution is d.Given pbg, choose pbb = pbg/2 ptt = pbg/2.6.5a.Composite commodity = b.Relative price Relative price 0 and Uii 0). c.Again, using , a rise in px will cause x to fall, MUx to rise. So the direction of change in is indeterminate. Hence, the change in y is also indeterminate. d.If But Hence, the first case is not separable; the second is. 6.10a.Example 6.3 gives clearly so these are gross comp