LONG QUESTION No. 2: Each sub-question (a-e) is worth 1 markeach
Ishmael's utility function is u = 10 x^​2 Y. The price of X is Rs.20 and price of Y is Rs. 5. His money income
is M = 300.

a. Write down the preference maximization (or utilitymaximization) problem of Ishmael and set up the
Lagrangian of this problem?
b. What is the preference maximizing (or utility maximizing) bundlefor Ishmael at income = Rs. 300.?

c. If the price of X decreases to Rs. 10 while the price of Yremains the same, what will be the new utility
maximizing bundle of Ishmael (income is still Rs. 300)?
d. In a clearly labelled indifference curve-budget line diagramshow the initial and new equilibrium for
Ishmael.
e. In the above diagram clearly identify the price-consumptioncurve for the good X.