Lecture notes
Microeconomics 1 Block 1 Topics in Consumer Theory Lecture Notes 20/21
- Module
- Microeconomics 1
- Institution
- The University Of York (UOY)
Microeconomics 1 Block 1 Topics in Consumer Theory Lecture Notes 20/21
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Micro Block 1: Topics in Consumer Theory1.1 Consumer theory
Bundles
A consumption bundle is denoted (x1, x2,… , xn), where n is the number of di erent goods that can
be consumed and xi is the quantity of good i in the bundle. For now, we focus on the case where
n = 2, that is, there are only two goods to consume. We use only two moods because we can then
represent the consumer’s choice graphically.
Budget constraint
Assume the price of good 1 is p1 and the price of good 2 is p2. Assume that the consumer has m
pounds to spend on consumption. The budget constraint is p1x1 + p2x2 ≤ m. Any bundle (x1, x2)
that satis es this equation is a ordable and all these a ordable bundles make up the budget set
of the consumer.
To represent the budget set graphically, we rst need to plot the budget line. The budget line is
formed by all the bundles that use all the money available, that is p1x1 + p2x2 = m x2 = m/p2 -
(p1/p2) x1.
We recognise the equation of an a ne function with intercept m/p2 and slope - (p1/p2). The
intercept is the maximal amount of good 2 we can buy. The slope of the budget line is the
opportunity cost of good 1; it is how much of good 2 the consumer must give up in order to
consume one more unit of good 1.
Figure 1: the budget set and budget line
In this gure, m = 10, p1 = 1 and p2 = 2.
1
fi fi ff ffi fi ff ff
, EXAMPLE From the example in gure 1, the budget constraint is x1 + 2x2 = 10. Once, the budget
line is x2 = 5 - 1/2(x1) where the slope is - (p1/p2) = 1/2.
Changing the prices of the goods will change the slope of the budget line. Increasing the amount
of money available will shift the budget line away from the origin (conversely, decreasing the
amount of money will shift the budget line closer to the origin). Figure 2 shows what happens
when we decrease the amount of money available from m to m’.
Figure 2: shifting the budget line
In this gure, m = 10, m’ = 6, p1 = 1 and p2 = 2.
Preferences
Preferences are relationships between bundles. Consider two bundles, say (x1, x2) and (y1, y2).
Whenever (x1, x2) is strictly preferred to (y1, y2), we write (x1, x2) ≻ (y1, y2). Whenever (x1, x2) and (y1,
y2) are regarded as indi erent, we write (x1, x2) ~ (y1, y2). Finally, whenever (x1, x2) is at least as
good as (y1, y2), we write (x1, x2) ≿ (y1, y2).
We will make the following assumptions on preferences:
• Completeness: any two bundles can be compared
• Re exivity: any bundle is at least as good as itself
• Transivity: take any three bundles, X, Y, Z, then if X ≿ Y and Y ≿ Z, then X ≿ Z.
Throughout the lecture, we will put special emphasis on well behaved preferences, which satisfy
these two additional properties:
• Monotonicity, or “more is better”: all else equal, more of a commodity is better than less of it
• Convexity: averages are preferred to extremes.
Indi erence curves
2
fl ff fi ff fi
, An indi erence curve graphs the set of bundles that are indi erent to some bundle, as shown in
gure 3. With well behaved preferences, indi erence curves will have the following properties:
• Bundles on indi erence curves farther from the origin are preferred to those on indi erence
curves closer to the origin (by monotonicity)
• Indi erence curves slope downwards (by monotonicity)
• Indi erence curves cannot cross (by transitivity)
• Indi erence curves are convex (by convexity).
Marginal rate of substitution
The marginal rate of substitution (MRS) is the slope of the indi erence curve. The MRS tells us
how much of good 2 the consumer is willing to give up to increase their consumption of good 1,
while staying on the same indi erence curve.
Figure 3: indi erence curves
In this gure, the consumer is indi erent between any two bundles located on this curve. The
utility function is u(x1, x2) = √x1√x2, and the utility level associated with the indi erent curve is
equal to 3.
Utility functions
A utility function u(x1, x2) assigns numbers to bundles so that more preferred bundles get higher
numbers. We could easily construct a utility function from indi erence curves by assigning to each
indi erence curve a number: the farther away from the origin the indi erence curve is, the higher
the number.
Conversely we can construct an indi erence curve from the utility function by nding all the
bundles that give the same utility level, that is, we need to nd all the bundles (x1, x2) such that
u(x1, x2) = u* to construct the indi erence curve associated with the utility level u*.
3
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