Economics 100A: Microeconomics A Midterm 1 Solutions: Spring 2022
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Economics 100A: Microeconomics A
Midterm 1 Solutions: Spring 2022
1. (30 pts) Emmanuel’s preferences between the following bundles are
A B, B C and C A .
Bundle A Bundle B Bundle C
Bagels per week
1
1
5
Oatmeal per week
5
2
2
a. Illustrate each bundle in a single graph. Put bagels per week on the x-axis and oatmeal per week on they-axis.
0 1 2 3 4 5 x1
b. Is it possible that Emmanuel’s preferences are monotonic? If so, sketch
one or more indifference curve(s) in the above graph that illustrates his
preferences and is monotonic. Label this/these indifference curve(s) with (b)’s. Ifnot, clearly explain why not.
No. He prefers B over C even though C has strictly more bagels and the same amount ofoatmeal as B does.
c. Is it possible that Emmanuel’s preferences are convex? If so, sketch one or
more indifference curve(s) in the above graph that illustrates his preferences and is convex. Label this/these indifference curve(s) with (c)’s. Ifnot, clearly explain why not.
Yes.
d. Is it possible that Emmanuel’s preferences are rational? Briefly explain. Yes. His preferences could be complete and transitive.
e. Is it possible that Emmanuel’s preferences are well-behaved? Briefly explain.
No. His preferences are not monotonic.
2. (30 pts) Becky’s utility function is U x, y x y
a. Is x a good, a bad, a satiation good or something else? Is y a good, a bad, a satiation good, or something else? What can we say about the direction in which utility is increasing? Clearly demonstrate your logic.
x
y
3
x
y 2 y
x is a good.
y is a bad.
Utility is increasing right and down.
b. What is Becky’s marginal rate of substitution between x andy?
3x2
MUx y 3y
MU x3 x
y
c. Ifher indifference curves have negative slopes, determine how the magnitude ofthe marginal rate of substitution changes as we move down and to the right along an indifference curve. Ifher indifference curves have positive slopes, determine how the magnitude ofthe marginal rate of substitution changes as we move up and to the right along an
indifference curve. Clearly demonstrate your logic. (Hint: Start by writing the equation for one of her indifference curves.)
U x, y x k
y
3
x
x3
MRS 6x
x k
The magnitude of her MRS increases as we move up and right along an indifference curve.
d. V(x, y) = aln(x) + bln(y). Find a value for a and a value for b such that V(x,
y) represents Becky’s preferences. Show your work. If no such values exist, clearly demonstrate why not.
The two utility functions represent the same preferences if V(x, y) is a monotonic transformation of U(x, y). (Or vice-versa.)
Consider the monotonic transformationf(U) = ln(U).
V(x, y) =f[U(x, y)] = 3ln(x) – ln(y) if a = 3 and b = –1.
(Any positive value of a that equals –3b works.)
3. (25 pts) Bruce gets utility from chocolate covered peanut butter cookies. He only likes to eat cookies where the amount of peanut butter (P) is equal to the amount of chocolate (C) squared. Extra peanut butter without extra chocolate is of no value to Bruce, just as extra chocolate without extra peanut butter is of no value to him.
a. Is his utility function u(P, C) = min[P2, C] or min[P, C2]? Clearly demonstrate your logic.
Min[P, C2]
He is consuming in the correct proportions when P = C2 .
b. Draw two ofBruce’s indifference curves for peanut butter and chocolate. Place ounces of peanut butter (P) on the x-axis and ounces of chocolate
(C) on the y-axis. Indicate the coordinates for any significant points on the indifference curves. Clearly indicate the direction in which his utility increases.
4. (15 pts) Jamie has $60 to spend on dinner. She can buy chicken wings (W) for $2 each and tater tots (T) for $5 per cup.
a. Graph her budget constraint. Place chicken wings (W) on the x-axis and cups of tots (T) on the y-axis. Label both axes and the intercepts.
b. What is her marginal rate of transformation (MRT)?
MRT
pT 5
c. Illustrate how her budget constraint will change if her Aunt Kristen gives her a $6 gift certificate that can only be used for the purchase of chicken wings (W). Label the key points. The gift certificate cannot be used for the purchase of tater tots (T) and cannot be sold. (You may add this constraint to your graph in (a) as long as it is clear which constraint goes with which
part. Or you can make a new graph for this part.)
Illustrated above in green.
2022-05-10