MPP 801: Microeconomics Fall 2007

Assignment 2 KEY Kevin Wainwright

1. The Following are TRUE or FALSE statements. In each case, use Budget Constraint-Indi¤erenceCurve analysis to determine whether they are true or false. (marks only for explanation)

(a) If a decline in the price of tomatoes results in a reduction in consumption of tomatoes by tomatofarmers, then we can conclude that tomatoes are inferior goods to the tomato farmers FALSE -ANSWER:

First:an inferior good is one where demand falls as income rises and demand rises when incomefalls. This is referred to as a "Negative Income E¤ect"Second,The substitution e¤ect states that people will substitute towards relatively cheaper goodsand away from relatively exensive goods (this includes farmers!)Farmers earn income selling tomatoes

If tomato prices fell, then farmers should substitute towards consuming more tomatoes since theopportunity cost of eating tomatoes is lower.The substitution e¤ect is unambiguous and holds forall goods.

A fall in the price of tomatoes also reduces farmer incomes. IF tomatoes are an inferior good,then farmers should also want to consume more tomotes due to the negative income e¤ect of beingan inferior good.

SINCE Demand actually FELL, it can only be due to the income e¤ect of a NORMAL goodThe answer can be formally shown in a budget constraint and indi¤erence curve graph.

Graph

1

(b) If the price of x falls and the consumption of x remains at the same level as before the price fall,then x is neither a normal good or an inferior good.FALSE -x is inferior SE says "buy more"so IE must say "Buy"less"

(c) Skippy consumes only two goods, X and Y, with a �xed budget. If the cross price elasticity ofdemand for Y with respect to the price of X is zero, Then the own price elasticity of demand forX is -1.TRUE. In a two good world, since total spending on y is unchanged, the totalspending on x is unchanged. This would only happen if the % change in quantityequaled the % change in price, thus unit elastic

(d) In a two good world a consumer initially faces the prices Px = Py = 1 and he is buying 10 unitsof each. Suppose the Px rises to $3 and Py rises to $2 while the consumer�s income rises by $30.The quantity of x consumed may fall.TRUE: With all the changes, consumer can STILLa¤ord the exact same bundle, but the relative price of x is higher (budget line issteeper)

see graphGraph for Question 1-d

2. Mary has an income of $10 per week, which she spends on Marmite which costs $4 a jar, and bread,which costs $2 per loaf.

(a) Draw Mary�s budget line? What is the slope of her budget line?

(b) Show the e¤ect on the budget line of halving the price of Marmite to $2 per jar.

(c) Show that a 50 per cent reduction in the price of both Marmite and bread (to $2 a jar and $1 perloaf) has the same e¤ect on Mary�s budget line as a doubling of Mary�s income to $20 per week.

(d) Suppose the government, due to a national shortage of brewers yeast (the main ingredient inMarmite) decides to ration Marmite consumption to one jar per week. Show the e¤ect of therationing on the original (part a) budget constraint.

3. Myrtle has $200 per month to spend on Transit (X) and all other goods (Y). She currently buys a buspass for $50 and rides 40 times per month.If she didn�t buy the pass, bus rides would cost $2/ride.Myrtle is o¤ered to join a Transit program that would allow her to pay a membership fee and thencould ride the bus for $1 per trip. The most Myrtle would pay for the membership is $20. and thenshe would ride 15 times a month. If she were given the membership for free, she would ride the bus 18

2

Figure 1: Graph for Question 3

times per month. Myrtle also reveals that she would be indi¤erent between a free membership (and$1 per ride) versus simply having the traditional bus pass reduced to $25 per month (�at rate), whereshe would again choose to ride the bus 40 times a month.

(a) Using all the information provided, draw all the relevant budget constraints and indi¤erencecurves. Be sure to label all equilibrium points and have a legend that explains each point (in oneor two sentences).

(b) Calculate her CV (compensating variation) Two answers acceptable $20 fee; or $30 di¤erencebetween the Pass ($50), and the most she would pay for $1 rides ($20)

(c) Calculate her EV (equivalent variation)-25$

4. Skippy has the following utility function: u = xy and faces the budget constraint: M = pxx + pyy.

Her associated marginal rate of substitution is MRS =y

x

(a) Use the MRS = px=py and the budget constraint to �nd Skippy�s demand functions.

x =M

2px; y =

M

2py

indirect utility function is

v =

�M

2px

��M

2py

�=

M2

4pxpy

v tells you the utility number for any given budget and prices

3

(b) Suppose M = 120, Py = 1 and Px = 4: What is Skippy�s optimal x; y and utility number? If theprice of x was lowered to 2 what would be her x; y and utility number

xold = 15; yold = 60; uold = 900

xnew = 30; ynew = 60; uold = 1800

(c) What is the most Skippy would pay to have Px lowered to 2? USE INDIRECT UTILITY

v =M2

4pxpy

900 =(M � F )2

4(2)(1)

7200 = (120� F )2

120� F =p7200 = 84:9

F = 120� 84:9 = 35:1

(d) Suppose M = 120, Py = 1 and Px = 4: How much additional income would Skippy need to be aswell o¤ as if the price of x had fallen to 2? USE INDIRECT UTILITY

v =M2

4pxpy= 1800

1800 =(M + S)

2

4(4)(1)

28800 = (120 + S)2

120 + S =p28800 = 169:7

S = 169:7� 120 = 49:7

4