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Lecture 2

MGEB02H3 Lecture Notes - Lecture 2: Engel Curve, Problem Set, Slutsky Equation

Economics for Management Studies
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MGEB02F Problem Set 2 Professor Michael Krashinsky
1. Suppose that there are only two goods - food and housing. The diagram labelled 2.1
shows the consumption bundles chosen by a consumer with indifference curves I1, I2, I3,
and I4, when faced with different combinations of income (I) and prices for the two goods
(PF and PH). The bundles are:
Point A B C D E F G H J K
Food 7 16 40 22 30 42 24 40 22 45
Housing 39 21 5 27 17 9 39 20 57 30
The diagram labelled 2.2 duplicates diagram 2.1, leaving out the indifference curves (this
may show the points and lines more clearly).
a) If PF = 2, PH = 2, derive a table showing all the points on the Engel Curve for food.
Repeat if PF = 3, PH = 2. Sketch each Engel curve. For PF = 3, PH = 2, sketch the Engel
curve for housing.
b) If I = 360 and PF = 6, derive a table showing the demand schedule for housing, and
sketch the demand curve. Now instead set PF = 6 and hold utility constant on the I2
indifference curve. Derive a table showing the compensated demand curve for housing,
and sketch the curve on the same diagram as the regular demand curve. How are the two
curves related?
c) If I = 120 and PH = 2, derive the demand schedule for food.
d) Is either good ever inferior? Is either good always normal? Is either good ever a
Giffen good? Explain your answers.
e) When I = 300, PH = 4, suppose that PF rises from 4 to 6. Using the points on the
diagram, divide the change in the consumption of food into an income and a substitution
effect. Explain in words what is signified by each effect. How much is this consumer
harmed by this price rise (that is, how much additional income would we have to give
this consumer to compensate for the price rise?)?

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