中国人民大学老师考研出题题库之一 微观+宏观经济学题库

中国人民大学老师考研出题题库之一 微观+宏观经济学题库

有几年老师从里面出题，供参考

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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 indierence 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 indierence 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 indierence 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)