Problem 1. (Consumer Choice)
Lionel watches movies x1 while drinking beer, x2. His utility function from consuming the two types of goods is
given by
U(x1; x2) = 2 ln(x1) + ln(x2)
a) Plot Lionel's indi erence curve map (graph). Find his MRS analytically (give formula). Find the value of
MRS at the consumption bundle (2; 4) and depict it in the graph.
b) Using \magic formulas," nd the optimal level of consumption of x1 and x2 if p1 = p2 = 4 and m = 15. Plot
carefully the optimal point along with the budget line and the indi erence curve passing through the optimal point
(a graph + two numbers).
c) Argue that the commodities are neither gross complements nor gross substitutes (argue using the magic formula,
one sentence).
For the rest of the problem suppose that Lionel's preferences change and now they are given by U(x1; x2) =
3x1 + 3x2.
d) In a separate graph plot his indi erence curves, and nd MRS for consumption bundle (2; 1). (a graph +one
number).
e) Find Lionel's optimal choice given prices p1 = p2 = 4 and m = 15 (two numbers). Is the optimal choice unique?
(yes/no answer)