11) A consumer's preferences over two goods (x1,x2) are represented by the utility function u(x1,x2) =...

 

Transcribed Image Text:

11) A consumer's preferences over two goods (x1,x2) are represented by the utility function u(x1,x2) = x 1/2 + x 1/2. The income he allocates to the consumption of these two goods is m > 0. The price of the two goods are p and p2, respectively. a) Determine the monotonicity and convexity of these preferences and explain your reasoning. Briefly define monotonicity and convexity. (10 marks) 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. (15 marks) c) For any P1, P2, and m, calculate the demand functions of x 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. (30 marks) d) Considera price increase in x from p to p. Find expressions for the substitution and income effects on x 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. (45 marks) 11) A consumer's preferences over two goods (x1,x2) are represented by the utility function u(x1,x2) = x 1/2 + x 1/2. The income he allocates to the consumption of these two goods is m > 0. The price of the two goods are p and p2, respectively. a) Determine the monotonicity and convexity of these preferences and explain your reasoning. Briefly define monotonicity and convexity. (10 marks) 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. (15 marks) c) For any P1, P2, and m, calculate the demand functions of x 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. (30 marks) d) Considera price increase in x from p to p. Find expressions for the substitution and income effects on x 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. (45 marks)