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Unformatted text preview: NAME , Student ID Number Northwestern University First Midterm Economics 3101 _
Winter Quarter, 20002001 Professor Braeutigam
INSTRUCTIONS: (1) Write your name and student ID number in the Spaces at the tog of this gage.
(2) This a 50 minute. closedbook examination..Answer all questions. (3) The examination is worth 100 points. The potential score on each question is indicated in parentheses at
the beginning of each question. ' .(4) Show all work clearly and concisely in the sgace provided after each Question. '
You must support your answer with clearly demonstrated reasoning to receive any credit. However, for work in the right direction partial credit will be given. Question 1 (25 points possible )
Question 2 (25 points possible)
Question 3 (25 points possible ) V Question 4 (25 points possible ) Total Score (100 points possible) Circle the nameof your Teaching Assistant and Section Day: Marc Fusaro  Thursday
 Marc Fusaro  Friday
Nick Kreisle  Thursday Nick Kreisle  Friday 209 Economics 3101, Professor Braeutigam Page 2 First Midterm, Winter 20002001 1) Suppose the supply curve for cotton is given by ClS = 2P, where QS is the quantity offered for sale when
the price is P. The demand curve for cotton is QD = 200(M/P), where O0 is the quantity purchased when M
is the income in the market andP is the price. Assume M is exogenous. a) (8 points) What are the equilibrium price and quantity of cotton when income is 100? .b) (9 points) What are the following elasticities at the equilibrium you determined in (a)? v
The own price elasticity of demand
The income elasticity of demand
The own‘price elasticity of supply c) (8 points) Find the reduced form equation that shows how the equilibrium price depends on the level
of income. Use this reduced form to determine how you would expect a small increase in income to affect
the equilibrium price when M = 100 (Le. ﬁnd the value of dP/dM when M = 100). 210 Economics 310—1, Professor Braeutigam Page 3 First Midterm, Winter 20002001 2) Sam consumes two goods. food (measured by F) and clothing (measured by C). To survive, he needs at
least 10 units of clothing and 20 units of food each year. If he receives less clothing than 10 units or less
food than 20 units, he dies (and gets inﬁnitely negative utility). When F320and 0310, his utility function is _ . . .. . JFZO #010
U 2JF 20JC 10, With the marginal utilities MUC m and MUF m .
The price of food (P;) is 1, and he has an income of l = 200 per year. The price of clothing is PC.
a) (7 points) If"the price of clothing is too high. Sam will not be able to survive. What is the range of prices
V for clothing for which he can survive?  For the rest of this problem assume that the price of clothing is low enough so that Sam can purchase more
than the minimum amounts of food and clothing necessary to survive. b') '(8 points) Show whether he has a diminishing marginal rate of substitution of clothing for food. c) (10 points) Derive an algebraic expression for Sam's demand for clothing. that is, express C as a
function of Pc (assuming l=200 and PF = 1). 211 Economics 3101, Professor Braeutigam Page 4 First Midterm, Winter 20002001 3) a) (7 points) A consumer buys only goods x and y. Her indifference map is shown below. She has an
income of $100 per week and the price of y is $1, Using the graph. draw the price consumption curve
between the lowest and highest indifference curves on the graph. 'y Indifference curves
' 10% .
i , ‘\ i t
: 1 ‘ 0246810121416182022 b) (10 points) Using the information contained in the optimal choice diagram in (a), draw a picture of the
consumer's demand curve for x. Your demand curve should contain 4 points, one corresponding to each
indifference curve. Label the coordinates of the points. 212 Economics 310—1, Professor Braeutigam Page 5 ,First Midterm. Winter 20002001 c) (8 points) The graph is repeated below for your convenience. On the graph show how you would
measure the equivalent variation resulting from an increase in the price of x from $5to $10. Provide a numerical estimate of the equivalent variation (an exact measure is not necessary. but be clear in showing
how you arrive at your estimate). y » Indifference curves
10 ‘ i
l l.
l mm...—
, , x
O246810121416182022 4) Answer each of the following in the space provided.
a) (10 points) A consumer buys two goods, X and Y. and always likes more of both goods. When he faces
budget line BL1, his optimal choice is A. Given budget line BL2. he chooses B. Using revealed preference, what can you say about the way the consumer ranks A and B? If you cannot infer a ranking, explain why
not. 213 Economics 310—1. Professor Braeutigam Page 6 First Midterm. Winter 20002001 b) (7 points) Joe likes root beer and ice cream in his root beer floats. but he wantsthe ratio of ice cream
and root beer to be ﬁxed: exactly one scoop of ice cream for each 8 ounces of root beer. On a graph with
scoops of ice cream on the horizontal axis and ounces of root beer on the vertical axis. draw two
indifference curves. Label the lower indifference curve U1 and the higher indifference curve U2. c) (8 points) Alexis consumes root beer (R) and cokes (C). Her preferences are characterized by a
constant marginal rate of substitution of root beer for cokes, MRSRC = 4. The price of a Coke is 1 and the
price of a root beer 3. To maximize her satisfaction. should she buy only cokes. only root beer, or a
combination of the two? Explain. ' ' 214 Economics 3101, Professor Braeutigam Page 7 First Midterm. Winter 20002001 Solutions: 1) a) When M = 100. demand is_ QD = 200(100/P) = 20,000/P. ln equﬂibrium Qs = Q0. Thus 2P=20,000/P, or P2 = 10,000, with P = 100. _  . The equilibrium quantity can be calculated either by looking at the supply curve or the demand curve at the
. equilibrium price. Using the supply curve. Qs = 2P = 2(100) = 200. Equivalently, using the demand curve we see that QD = 200(M/P) = 200(100/100) =' 200. b) The demand curve is a constant elasticity curve, of the form Q = APEM’.. where e is the own price
elasticity of demand and f is the income elasticity of demand (i.e.. Q = 200P'1M‘). The own price elasticity
of demand is —1, and the income elasticity of demand is 1. Supply elasticity: Em, = (dQs/dPXP/Q) = 2(100/200) = 1. c) In equilibrium Qs = 00. Thus 2P=200M/P, or P2 = 100M. This means that P = 10M”. As M increases, the
demand curve shifts out and the equilibrium price rises. The rate of change in P as M increases is dP/dM = 5/M°‘5. So, for example. when M = 100, dP/dM = 5/(100)°'5 = 5/10 = 0.5. So when M rises by 1 unit, P will
rise by about 0.5. _____—_—_—_______———
2‘) a) Using the budget line, we know that PFF + PCC 5 I, or F + PCC 5 200. When he just receives enough
food and clothing to survive, F = 20 and C = 10. So 20+ Pc(10) 5 200. This means that Pc 5 18. If the price
of clothing exceeds 18, he cannot purchase enough of the two goods to survive. b)
F20
MRSCF JAE: V010 =12.
 MUF i/c.1o (>10 JFZO
the MRS” diminishes. Therefore he has a diminishing MRS”. As he consumes more clothing (and less food) along an isoquant, 0) At an optimum, two conditions must be satisﬁed: F20 P F—20 7 ~
1 MRS =——=—° => —=P =5 F=P c1o +2
H C" c1o PF c1o ° °( ) 0 (2) F+PCC=200 90+5Pc Substituting (1)into (2) :> Pc(C10)+20+PCC=200 :> C=
. c 3) a) x
8 10 '12 14 16 18 20 22 215 Economics 3101, Professor Braeutigam Page 8 First Midterm, Winter 20002001 b) When P)( = 20, the optimal basket is A, with x = 2.
When P, = 10, the optimal basket is B, with x = 4.
When P, = 6.67, the optimal basket is C, with x = 6.
When P, = 5, the optimal basket is E, with x = 8. The demand curve appears as follows: PX
22
20
18
16
14
12
10 ' 0 2 4  6 8 10
Baskets A, B, C, and E in the optimal choice diagram correspond respectively to Points A, B, C, and E on
the demand curve. c) The graph below shows: _a) the initial budget line and optimal basket A. b) the ﬁnal budget line and the ﬁnal basket C. c) the decomposition budget line for determining the equivalent variation (parallel to the initial budget
line and tangent to the final indifference curve) and the decomposition basket D.
Since p, = 1, the difference between the vertical intercept of the initial budget line and the decomposition
budget line is the equivalent variation, or about $24 in this example. The equivalent variation is negative
because the higher price decreases the consumer’s welfare. ' yE Equivalent 1 0
“Variation
about $24 Decomposition
BL for equivalent
variation Initial BL 0 246810121416182022 216 Economics 3101; Professor Braeutigam Page 9 First Midterm, Winter 20002001 4) a) We cannot infer a ranking. Given BL1, the consumer selects A when he could have chosen F. So A is weakly preferred to F. Since F lies to the northeast of B, F is strongly preferred to 8. Thus. on the basis of
his behavior given BL1, the consumer must strictly prefer A to B.
However, given BL1, the consumer selects B when he could have chosen E. 80 B is weakly preferred to
E. Since E lies to the northeast of A, E is strongly preferred to E. Thus. on the basis of his behavior given '
8L2, the consumer must strictly prefer B to A.
' It cannot be true simultaneoUsly that A is strongly preferred to B and B is strongly preferred to A. This
violates the axiom of transitivity. The consumer cannot simultaneously be choosing an optimal basket given each budget line.’ b) Ounces of
root beer m Scoops of ice cream c) MRSRC = 4 = MUR/MUC > PR/Pc = 3/1. Cross multiplying tells us that MUR/PR >MUc/Pc. Therefore, the
, marginal utility per dollar spent on root beer will always be greater than the marginal utility per dollar spent
on coke. She should substitute root beer for coke until she consumes only root beer. 217 ...
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