Consumer Theory and X1

Topics: Consumer theory, Indifference curve, Preference Pages: 8 (1056 words) Published: April 23, 2013

Hal R. Varian. Intermediate Microeconomics, A Modern Approach. W. W. Norton & Company, Inc.

1 BUDGET CONSTRAINT

Consumer theory ---- how consumers buy their goods?
Economists assume: consumers choose the best bundle of goods they can afford. Two aspects:
----Consumers choose the most preferred goods.
----They are limited by economic condition.

The Budget Constraint
Consumption bundles: （消费束，商品组合）: a list of numbers of goods and services. X = (x1, x2, …, xn,)
In the case of two goods: good 1 and good 2.
Bundle of goods: X = (x1, x2)
Prices of goods: (p1, p2),
The amount of money the consumer has to spend: m.
The consumer’s affordable consumption bundles, (x1, x2) satisfy p1x1 + p2x2 ≤ m.
----The budget set of the consumer (预算集) .

good 2

m/p2

O m/p1 good 1

Two Goods Are Often Enough
Composite good ----take x2 as everything else, the dollars spent on other goods. For example, x1: consumption of milk in quarts per month. The budget constraint will take the form
p1x1 + x2 ≤ m.

The case of n goods
Budget constraint:
p1x1 + p2x2+…+ pnxn ≤ m.

Properties of the Budget Set
Budget line（预算线）:
p1x1 + p2x2 = m.
Vertical intercept: m/p2
Horizontal intercept: m/p1.
Slope: – p1/p2
Economic interpretation of slope:
For the bundle (x1, x2):
p1x1 + p2x2 = m.
After a change in bundle (△x1, △x2):
p1(x1+△x1) + p2(x2+△x2) = m.

good 2

x2
△x2
△x1

O x1 good 1

Subtracting the first equation from the second gives
p1△x1 + p2△x2 = 0.
This gives

The number of good 2 the consumer must give up when he increases his consumption of good 1 by 1 unit, and keeps the money spent unchanged. Opportunity cost of consuming good 1---- in order to consume more of good 1 you have to give up some consumption of good 2.

Budget Line Changes
How the budget line changes when prices and incomes change?

Change in income
Change in m results in a parallel shift of the budget line. Intercepts m/p2 and m/p1 will change.
Slope – p1/p2 keeps unchanged.

good 2

m/p2

O m/p1 good 1

Changes in prices
Increasing p1 will not change the vertical intercept,
but p1/p2 will become larger.

good 2

m/p2

O m/p1 good 1

What happens to the budget line when we change the prices of good 1 and good 2 at the same time? Proportionally:
(tp1)x1 + (tp2)x2 = m.

What happens to the budget line when we change the prices of good 1 and good 2 and the consumers’ income at the same time?

good 2

m/p2

O m/p1 good 1

Proportionally:
(tp1)x1 + (tp2)x2 = tm.

Some observations:
If one price declines and all others stay the same, the consumer must be at least as well-off. If the consumer’s income increases and all prices remain the same, the consumer must be at least as well-off as at the lower income A perfectly balanced inflation cannot change anybody’s optimal choice.

2 PREFERENCES

Consumer Preferences（消费者偏好）
Consumer ranks consumption bundles by his satisfaction from use of goods, irrelevant to the prices.

The case of two goods...

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