Mehmet drinks only pure spring water, but he can purchase it in two different-si
ID: 1103172 • Letter: M
Question
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 Mehmetís utility depends only on the quantity of water consumed. That is, the containers themselves yield no utility.
(b) Write Mehmetís demand function for x in terms of price of x, Px; 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) Formulate the expenditure minimization problem of this agent to attain a fixed utility level U for any Px, Py and I.
Explanation / Answer
The two bundles are identical and are perfect substitutes thus the utility function will be such that x:y = .5/2 = 1/4
U(x,y) = x+1/4y
In this case Budget line is :
Pxx+Pyy=I
(b)
The demand for x will be when I/Px > 1/4(I/Py)
x= I/Px
The demand for x will be when I/Px < 1/4(I/Py)
y = I/Py
(c) V(Px, Py, I) = I/Px+(1/4)*I/Py
(d) E = Px*x+Py*y
now since x and y are perfect substitutes.
E = Px*x if I/Px >= 1/4(I/Py)
E = Py*y if I/Px =< 1/4(I/Py)