NAME.......................................................
INTERMEDIATE MICROECONOMICS
Midterm Exam
(90 minutes)
1) For each of the questions below indicate whether the statement given is TRUE or FALSE. Briefly
explain the reason for your answer. (5 pts each)
a) A consumer has preferences represented by the utility function U(x1, x2) = 10(x21 + 2x1x2 + x22) – 50.
For this consumer, goods 1 and 2 are perfect substitutes.
b) Ceyda'’s utility function is U(x, y) = (x + 2)(y + 1). If her consumption of both x and y are doubled,
then her marginal rate of substitution between x and y remains constant.
c) A consumer has a utility function given by U = min{x1, 2x2}. If good 2 has a price of zero, the
consumer will always prefer more of good 2 to less.
d) It is possible for a consumer to satisfy the weak axiom of revealed preference but violate the strong
axiom of revealed preference.
2) Max has the utility function U(x, y) = x(y + 1). The price of x is $2 and the price of y is $1. Income is
$10. How much x does Max demand? How much y? If his income doubles and prices stay unchanged,
will Max’s demand for both goods double?
3) Cahit consumes caviar and bread. Cocoa is sold in an unusual way. There is only one supplier, and the
more caviar you buy from him, the higher the price you have to pay per unit. In fact y units of caviar will
cost Cahit y2 dollars. Bread is sold in the usual way at a price of 2 dollars per unit. Cahit’s income is 20
dollars and his utility function is U(x, y) = x + 2y, where x is his consumption of bread and y is his
consumption of caviar.
a) Sketch Cahit’s budget set.
b) Sketch some of his indifference curves and show the point that he chooses.
c) Calculate the amount of bread and the amount of caviar that Cahit demands at these prices and this
income.
4) Şükrü’s utility function is U(x, y) = x2y. He has $150 and the price of x and the price of y are both 1.
Şükrü’s boss is thinking of sending him to another town where the price of x is 1 and the price of y is 2.
The boss offers no raise in pay. In the absence of a raise Şükrü complains bitterly. He says that although
he does not mind moving for its own sake, having to move is as bad as a cut in pay of $A. He also says
he would not mind moving if when he moved he got a raise of $B. What are A and B?
5) In an isolated peasant village, the only crop is corn. Good harvests alternate with bad harvests. This year
the harvest will be 1,000 bushels. Next year it will be 150 bushels. There is no trade with the outside
world. Corn can be stored, but rats will eat 25% of what is stored in a year. The villagers have the CobbDouglas utility function 𝑈 𝑐! , 𝑐! = 𝑐! 𝑐! , where c1 is consumption this year and c2 is consumption next
year.
a) Draw a budget line for the village with this year’s consumption on the horizontal axis and next
year’s consumption on the vertical axis. On your graph show the quantities at which the budget line
intercepts the vertical and horizontal axes.
b) How much will the villagers consume this year?
c) How much will the rats eat?
d) How much will the villagers consume next year?