Budget Constraint Flashcards
What do you mean by budget constraint, consumption bundle, budget set
Consumers consumption bundle - (x1,x2). Price of the two goods (p1,p2). And the amount of money the consumer has to spend “m”.
Then the budget constraint of the consumer can be written:-
p1x1 + p2x2 <_ m
Good 2 often represents all other goods the consumer might want to buy. Its price is set to $1 because dollars directly measure the money spent on those other goods, simplifying the equation to:
p1x1 + x2 <_m
The consumers affordable consumption bundles are those that don’t caused any more than m we call this set of portable consumption bundles at prices (p1,p2) and income m the “budget set” of the consumer.
What is the budget line and budget set in a two-good model?
The budget line shows all combinations of two goods that exactly use up the consumer’s income:
p1x1 p2x2 = m
The budget set includes all bundles that cost less than or equal to the consumer’s income.
What are the intercepts and slope of the budget line?
Vertical intercept (x₂): m/p2
Horizontal intercept (X2): m/p1
Slooe: - p1/p2
This shows the trade off between the two goods
What is the rearranged formula for the budget line?
The budget line rearranged:
x2 = m/p2 - p1/p2 . x1
This tells how much of good 2 can be consumed when 𝑥1units of good 1 are bought.
How do you draw a budget line? What does the slope of the budget line represent?
Calculate vertical intercept: m/p2 (if all money spent on good 2).
Calculate horizontal intercept:m/p1 ( if all money spent on good 1).
Connect these points with a straight line (this is the budget line).
Slope = - p1/p2
It shows the opportunity cost: how much of good 2 must be given up to consume more of good 1.
If you buy more of good 1, you can afford less of good 2.
How does income or price change affect the budget line?
Increase in income: shifts the budget line outward (parallel shift).
Increase in price of good 1: makes the budget line steeper.
Both prices increase: the budget line shifts inward.
What is the numeraire price?
When we set one price to 1, that price is the numeraire (reference price).
It simplifies calculations by reducing the number of variables.
What happens when prices of both goods change by a factor 𝑡 ?
If both prices increase by a factor of 𝑡, the budget line shifts inward.
Equation:
t.p1x1 + t.p2x2 = m
= p1x1 + p2x2 = m/t
Multiplying both prices by
𝑡
t is like dividing income by
𝑡
t, shrinking the budget set.
Effects of Taxes and Subsidies on the Budget Line
1) Quantity Tax:
Imposed per unit of a good purchased.
Effectively increases the price from p1 to p1 + t Steepens the budget line, making the good more expensive for the consumer.
2) Value Tax (Ad Valorem Tax):
Based on the price of the good, expressed as a percentage (e.g., sales tax).
If good 1 is priced at 𝑝1 and taxed at rate r, the effective price becomes (1+r) .p1
Similar to a quantity tax, it raises the effective price, tilting the budget line inward.
Subsidies and Their Impact on the Budget
1) Quantity Subsidy:
The government pays a fixed amount s per unit purchased.
Lowers the effective price from p1 to p1-s. Flattens the budget line, making the good cheaper for consumers.
2) Ad Valorem Subsidy:
A percentage-based subsidy reducing the price of good 1.
With a subsidy rate o , the effective price becomes (1- o) .p1 .
3) Lump-Sum Taxes and Subsidies:
Lump-Sum Tax: Reduces income by a fixed amount, shifting the budget line inward without changing prices.
Lump-Sum Subsidy: Increases income by a fixed amount, shifting the budget line outward, enhancing purchasing power.
How does rationing modify the budget set?
Rationing restricts the quantity of good 1 a consumer can buy, e.g., a cap of ____
The budget set beyond____is lopped off, meaning consumers cannot purchase beyond that limit, even if they have the income.
How does a tax or subsidy above a certain quantity affect the budget line?
A tax applied to consumption above___changes the slope of the budget line.
Left of___, the slope is -p1/p2, right of ___, its - ( p1+t /p2), making it steeper.
How did the Food Stamp Program affect the budget line?
Pre-1979, consumers could buy $153 worth of food stamps for $25, leading to an 84% subsidy on food.
The budget line had a slope of -0.16 until $153 was spent on food. After that, the slope returned to -1.
Post-1979, food stamps were given as a grant, shifting the budget line outward by $200 for food without affecting spending on other goods.
How do you construct an indifference curve for a given bundle?
Pick a consumption bundle (x₁, x₂), adjust the quantities of goods to keep the consumer indifferent, and repeat this for different bundles. Connecting these points forms the indifference curve.
