Consider a consumer with CES utility u(x1; x2) = x 1 + x 2. (a) Does this consumer have preferences the "increasing di§erence property" between the two goods? How about the strict increasing di§erence property? Make a detailed argument. (b) for the case that = :5; show using the arguments on monotone com- parative statics in class that both goods are normal.
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11) A consumer's preferences over two goods (x1,x2) are represented by the utility function u(x1,x2) = x1^(1/2) + x2^(1/2). The income he allocates to the consumption of these two goods is m > 0. The price of the two goods are p1 and p2, respectively. a) Determine the monotonicity and convexity of these preferences and explain your reasoning. Briefly define monotonicity and convexity. b) Calculate the marginal rate of substitution (MRS(x1,x2)) between the two goods for this consumer. For the bundle (x1,x2) = (1,4), interpret the MRS. c) For any p1,p2, and m, calculate the demand functions of x1 and x2 including the corner solutions if there are any. Clearly state which assumptions you used to achieve your solutions. If there is no corner solution, discuss why this is the case. d) Consider a price increase in x1 from p1 to p1'. Find expressions for the substitution and income effects on x1 as a function of p1,p2, and m, and determine their signs. What do the signs of the substitution and income effects and the sign of the aggregate demand change tell you about these goods? Discuss.
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