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All Textbook Solutions for Microeconomic Theory

2.1P 2.2P 2.3P 2.4P 2.5P 2.6P 2.7P 2.8P 2.9P 2.10P 2.11P 2.12P 2.13P 2.14P 2.15P 2.16P 3.1P 3.2P 3.3P 3.4P 3.5P 3.6P 3.7P Find utility functions given each of the following indifferencecurves [defined by U()=k ]: a. z=k1/x/y/ b. y=0.5x24(x2k)0.5x c. z=y44x(x2yk)2xy22x 3.9P 3.10P 3.11P 3.12P 3.13P 3.14P 3.15P 4.1P 4.2P 4.3P 4.4P 4.5P 4.6P 4.7P 4.8P 4.9P 4.10P 4.11P 4.12P 4.13P 4.14P 5.1P 5.2P 5.3P 5.4P 5.5P 5.6P 5.7P 5.8P 5.9P 5.10P 5.11P 5.12P 5.13P 5.14P 5.15P 6.1P 6.2P 6.3P 6.4P 6.5P 6.6P 6.7P 6.8P 6.9P 6.10P 6.11P 6.12P 6.13P 6.14P 7.1P 7.2P 7.3P 7.4P 7.5P 7.6P 7.7P 7.8P 7.9P 7.10P 7.11P 7.12P 7.13P 7.14P 7.15P 8.1P 8.2P 8.3P 8.4P 8.5P 8.6P 8.7P 8.8P 8.9P 8.10P 8.11P 8.12P 9.1P 9.2P 9.3P 9.4P 9.5P 9.6P 9.7P 9.8P 9.9P 9.10P 9.11P 10.1P 10.2P 10.3P 10.4P 10.5P 10.6P 10.7P 10.8P 10.9P 10.10P 10.11P 10.12P 11.1P 11.2P 11.3P 11.4P 11.5P 11.6P 11.7P 11.8P 11.9P 11.10P 11.11P 11.12P 11.13P 11.14P 11.15P 12.1P 12.2P 12.3P 12.4P 12.5P 12.6P 12.7P 12.8P 12.9P 12.10P 12.11P 12.12P 12.13P 12.14P 13.1P 13.2P 13.3P 13.4P 13.5P 13.6P 13.7P 13.8P 13.9P 13.10P 13.11P 13.12P 13.13P 13.14P 14.1P 14.2P 14.3P Suppose the market for Hula Hoops is monopolized by a single firm. a. Draw the initial equilibrium for such a market. b. Now suppose the demand for Hula Hoops shifts outward slightly. Show that, in general (contrary to the competitive case), it will not be possible to predict the effect of this shift in demand on the market price of Hula Hoops. c. Consider three possible ways in which the price elasticity of demand might change as the demand curve shifts: It might increase, it might decrease, or it might stay the same. Consider also that marginal costs for the monopolist might be increasing, decreasing, or constant in the range where MR=MC Consequently, there are nine different combinations of types of demand shifts and marginal cost slope configurations. Analyze each of these to determine for which it is possible to make a definite prediction about the effect of the shift in demand on the price of Hula Hoops.14.5P 14.6P 14.7P 14.8P 14.9P 14.10P 14.11P 14.12P 14.13P 15.1P 15.2P 15.3P 15.4P 15.5P 15.6P 15.7P 15.8P 15.9P Inverse elasticity rule Use the first-order condition (Equation 15.2 ) for a Cournot firm to show that the usual inverse elasticity rule from Chapter 11 holds under Cournot competition (where the elasticity is associated with an individual firm's residual demand, the demand left after all rivals sell their output on the market). Manipulate Equation 15.2 in a different way to obtain an equivalent version of the inverse elasticity rule: pMCp=sieQ,p , where si=qi/Q is firm i's market share and eQp is the elasticity of market demand. Compare this version of the inverse elasticity rule with that for a monopolist from the previous chapter.15.11P 15.12P 15.13P 16.1P 16.2P 16.3P 16.4P 16.5P 16.6P 16.7P 16.8P 16.9P 16.10P 16.11P 16.12P 17.1P 17.2P 17.3P 17.4P 17.5P 17.6P 17.7P 17.8P Precautionary saving and prudence The Query to Example 17.2 asks how uncertainty about the future might affect a person's savings decisions. In this problem we explore this question more fully. All of our analysis is based on the simple two-period model in Example 17.1. a. To simplify matters, assume that r= in Equation 17.15. If consumption is certain, this implies that u(c0)=u(c1) or c0=c1. But suppose that consumption in period 1 will be subject to a zero-mean random shock, so that c1=c1p+x, where c1p is planned period- 1 consumption and x is a random variable with an expected value of 0. Describe why, in this context, utility maximization requires u(c0)=E[u(c1)] . b. Use Jensen's inequality (see Chapters 2 and 7 ) to show that this person will opt for c1pc0 , if and only if u is convex-that is, if and only if u0 . c. Kimball" suggests using the term "prudence" to describe a person whose utility function is characterized by u0 . Describe why the results from part (b) show that such a definition is consistent with everyday usage. d. In Example 17.2 we showed that real interest rates in the U.S. economy seem too low to reconcile actual consumption growth rates with evidence on individuals willingness to experience consumption fluctuations. If consumption growth rates were uncertain, would this explain or exacerbate the paradox?Wonopoly and natural resource prices Suppose that a firm is the sole owner of a stock of a natural resource. a. How should the analysis of the maximization of the discounted profits from selling this resource (Equation 17.63 be modified to take this fact into account? b. Suppose that the demand for the resource in question had a constant elasticity form q(t)=a[p(t)]b . How would this change the price dynamics shown in Equation 17.67? c. How would the answer to Problem 17.7 be changed if the entire crude oil supply were owned by a single firm?17.11P 17.13P 18.1P 18.2P 18.3P 18.4P 18.5P 18.6P 18.7P 18.8P 18.9P 18.10P 18.11P 18.12P A firm in a perfectly competitive industry has patented a newprocess for making widgets. The new process lowers the firm’saverage cost, meaning that this firm alone (although still aprice taker) can earn real economic profits in the long run. a. If the market price is $20 per widget and the firm’s marginalcost is given by MC=0.4q , where q is the dailywidget production for the firm, how many widgets willthe firm produce? b. Suppose a government study has found that the firm’snew process is polluting the air and estimates the socialmarginal cost of widget production by this firm to be. If the market price is still $20, what is thesocially optimal level of production for the firm? Whatshould be the rate of a government-imposed excise tax tobring about this optimal level of production? c. Graph your results.19.2P 19.3P 19.4P 19.5P 19.6P 19.7P 19.8P 19.9P 19.10P 19.11P 19.12P

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