Question

4. Mehmet drinks only pure spring water, but he can purchase it in two different-sized containers: 0.5 liter and 2 liter. The water is identical in both containers. Assume that Mehmet's utility depends only on the quantity of water consumed. That is, the containers themselves yield no utility. (a) Write down Mehmet's utility function in terms of quantities of 0.5 liter containers (x) and 2 liter containers (y). (b) Write Mehmet's demand function for x in terms of price of x, P.x, price of y, Py, and his income, I. Clearly explain your answer. (c) By using your answer in part (b), find the indirect utility function V(Px, Py, I). (d) Graph the uncompensated demand curve for x, holding I and Py constant. (e) Suppose that initially I = 10 TL and P, =1 TL. What will happen to the demand curve if Mehmet's income decreases to I' = 8, while keeping P., and Py same? (f) Suppose that initially I = 10 TL and Py =1 TL. What will happen to the demand curve if the price of good y, Py, increases to 2 TL, while keeping Px and I same? (g) Formulate the expenditure minimization problem of this agent to at- tain a fixed utility level Ū for any Px, Py and I. (h) Find the compensated demand curve for x and draw it on a graph?

Answer 1

ANSWER mehmet's utility fonction iyis equivalent to honits of alt Contained is cauivalent to a contained ofs. Marginal utility (ru). Prom Ixis 4 times, Thus Mou from lx u= x+48 Huy - 4. Hox=1, MRS.X, Ya Mux THUY Si 114 OR MRs > Pxlpy or 25 > pulpy Mux (Px > Muylpy only xis Consumed R MRS. Ralpy x*=0

X=(!lpe, 025) Pulp] 0.25 Py 15. (0,025 2pxlpy] © UCP.Po, Clox, 825) = Pelp.] = { 4*ily 025 28«/?y] 7 0.25Ry M2D = Income Demanda coduc ofx. r. Il px "A - - - . please like Thanking you