EC 203.01PS: CH 4FALL 2005
1.With quasilinear preferences, the slope of indifference curves is constant along all rays through the origin.FALSE
2.Angela's utility function is U(x1, x2) = (x1 + x2)3. Her indifference curves are downward-sloping, parallel straight lines.TRUE
3.Maximilian consumes two goods, x and y. His utility function is U(x, y) = max{x, y}. Therefore x and y are perfect substitutes for Max.FALSE
4.Ike's utility function is U(x, y) = 25xy. He has 12 units of good x and 8 units of good y. Ben's utility function for the same two goods is U(x, y) = 4x + 4y. Ben has 9 units of x and 13 units of y.
a. Ike prefers Ben's bundle to his own bundle, but Ben prefers his own bundle to Ike's.
b. Ben prefers Ike's bundle to his own, but Ike prefers his own bundle to Ben's.
c. Each prefers the other's bundle to his own.
d. Neither prefers the other's bundle to his own.
e. Since they have different preferences, there is not enough information to determine who envies whom.A
5.Harmon's utility function is U(x1, x2) = x1x2. His income is $100. The price of good 2 is p2 = 4. Good 1 is priced as follows. The first 15 units cost $4 per unit and any additional units cost $2 per unit. What consumption bundle does Harmon choose?
a. (12.5, 12.5)
b. (25, 12.5)
c. (12.5, 25)
d. (15, 10)
e. None of the above.A
6.Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through 35 apples and 18 bananas will also pass through the point where he consumes 5 apples and
a. 131 bananas
b. 137 bananas
c. 21 bananas
d. 42 bananas
e. 126 bananas, E
7.Joe Bob's cousin Peter consumes goods 1 and 2. Peter thinks that 4 units of good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is the only one that would not represent Peter's preferences?
a. U(x1, x2) = min{2x1, 4x2}.
b. U(x1, x2) = 20x1 + 40x2 - 10,000.
c. U(x1, x2) = 2x1 + 4x2 + 1,000.
d. U(x1, x2) = 4x12 +16x1x2 + 16x22
e. More than one of the above does not represent Peter's preferences. Answer: A
8. Harry Mazzola has the utility function U(x1, x2) = min{x1 + 2x2, 2x1 + x2}. He has $40 to spend on corn chips and french fries. If the price of corn chips is $3 per unit and the price of french fries is $4, then Harry will
a. definitely spend all of his income on corn chips.
b. definitely spend all of his income on french fries.
c. consume at least as many corn chips as french fries but might consume both.
d. consume at least as many french fries as corn chips but might consume both.
e. consume equal amounts of french fries and corn chips. Answer: E
9. Use separate graphs to draw indifference curves for each of the following utility functions:
a. U(x, y) = min{2x + y, 2y + x}.
b. U(x, y) = max{2x + y, 2y + x}.
c. U(x, y) = x + min{x, y}.
In which of these cases are preferences convex?
If you take a point on the line x = y and draw two lines through it, one with a slope of -1/2 and the other with a slope of -2, the outer envelope of these lines will be an indifference curve for (a) and the inner envelope will be an indifference curve for (b). The indifference curves for (c) passing through a point on the line x = y consist of a line segment going down and to the right with slope -1 and a line segment going up and to the left with slope -2. Cases (a) and (c) display convex preferences, and case (b) does not.
10. Herr Daum has the utility function , where x1 is his consumption of corn chips and x2 is his consumption of french fries. You have a graph with corn chips on the horizontal axis. Label both axes for values within the range [0,8].
a) Draw the locus of all points along which . Show the locus of all points for which . Also draw the locus of all points for which .
b) On the graph shade in the region where both of the following inequalities are satisfied: and . At the bundle (x1,x2)=(8,2) one sees that ____ and ____ . Therefore u(8,2)=_____ .
c) Sketch in the indifference curve along which Herr Daum’s utility is 12. Sketch in the indifference curve for utility of 6.
d) At the point where Herr Daum is consuming 5 units of corn chips and 2 units of French fries, how many units of corn chips would he be willing to trade for one unit of French fries?