Department of Agricultural and Resource Economics University of California, Davis ARE 100A Problem Set IIIWinter 2010 Richard Howitt Quiz on January 29 1.Assume an individual consumes three goods, food, clothing, and automobiles. Denote the quantities of these goods as Q1, Q2, and Q3. the individual’s utility function is given by: 12( )5ln4ln10ln(1)UQQ=+++i3Q. The prices of the three goods are: 12310,20,20,000PPP===, and individuals total income is $60,000. Automobiles must be bought in discrete units, that is, Q3must be equal to 0, 1, or 2. Given these constraints, how will an individual allocate their income to maximize utility. Discuss the corner solution in inherent in this problem. (A graph may help your explanation.) 2.Assume that Warren Buffet enjoys the consumption of cigars (C), and brandy ( B) according to the following utility function. 22(,)20183U C BCCBB=−+−(a)How many glasses of brandy and cigars does Warren consume during an evening? (Remember who he is.) (b)Now assume that Warren’s doctor advises him that he should limit his consumption so that the sum of brandy and cigars consumed in the day is less than or equal to
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