Exogenous variable: variable is taken as determined by factors not discussed in the given model
Ex: Outer-ring of apartments
Endogenous variable: A variable that is caused by one or more variable in the model.

Optimization Principle: People try to choose the best patterns of consumption that they can afford
Equilibrium Principle: Prices adjust until the amount that people demand of something is equal to the amount that is supplied

Reservation Price: A person’s maximum willingness to pay for something
Demand Curve: A curve that relates the quantity demanded to price.
Supply Curve: Measures how much people wish to supply at each price

Equilibrium Price: p*; price where the quantity of apartments demanded equals the quantity supplied
Comparative Statics: asking how price changes when various aspects of the market change

Four possible ways of allocating apartments to people: (Apt example)
The competitive market – Pareto Efficient
A discriminating monopolist – Pareto Efficient
An ordinary monopolist – Pareto Inefficient
Rent control – Pareto Inefficient

Pareto efficiency or economic efficiency
Pareto Improvement: If we can find a way to make some people better off without making anybody else worse off.
Pareto Inefficient: If an allocation allows for a Pareto improvement
Pareto Efficient: If an allocation is such that no Pareto improvements are possible

Short run: Fixed supply of variable
Lon run: Supply of variable can change

Budget constraint: use the case of two goods. Requires that the amount of money spent on the two goods be no more than the total amount the consumer has to spend
Consumption bundle: (x1,x2); tells us how much of each good the consumer is choosing to consume m; The amount the consumer has to spend
Budget constraint: p1x1+p2x2 m p1x1 is amount consumer spends on good 1 p2x2 is amount consumer spends on good 2
Affordable consumption bundles are those that don’t cost any more than m
Budget set: affordable consumption bundle at prices (p1,p2) and income m
Can often interpret one of the goods as representing everything else the consumer might want to consume p1x1+x2 m ; price of good 2 will automatically be $1
Composite good: good 2, stands for everything else that the consumer might want to consume other than good 1
Budget line is the set of bundles that cost exactly m p1x1+p2x2=m Exhaust the consumer’s income x2=(m/p2)-((p1/p2)(x1)) vertical intercept of m/p2 slope of –p1/p2
Formula tells us how many units of good 2 the consumer needs to consume in order to satisfy the budget constraint if she is consuming x1 units of good 1
Deciding to change consumption of either x1 or x2 p1x1+p2x2=m p1(x1+x1)+p2(x2+x2)=m p1(x1)+p2(x2)=0 (x2/x1)= -(p1/p2)
Slope of the budget line
Negative because x1 and x2 must always have opposite signs

Budget Line Changes
Changes in Income
Increase in income will result in a parallel shift outward of the budget line, similarly a decrease in income will cause a parallel shift inward
Change in one price
Changes the slope of the budget line
Change in both prices
Both horizontal and vertical intercepts change p1x1+p2x2=m tp1x1+tp2x2=m t; both prices become t times as large p1x1+p2x2=m/t Change in income and price

The Numeraire
The budget line is defined by two prices and one income, but one of these variables is redundant
Can divide standard equation by one of the variables to make a fixed value (pegged to 1)
Numeraire price: The price we set to 1
The price relative to which we are measuring the other price and income
Numeraire good also exists

Taxes, Subsidies, and Rationing
Quantity Tax: The consumer has to pay a certain amount to the government for each unit of the good purchased
From consumer’s viewpoint it changes p1 to (p1+t); quantity tax (t)
Value Tax: Tax on the valuethe priceof a good
Usually expressed in percentage terms; ex: sales tax
Aka ad valorem
Sales tax rate,
Actual price for customer: (1+)p1
Subsidy: Government gives an amount to the consumer that depends on the amount of the good subsidized; s (quantity subsidy)
Opposite of a tax
(p1-s); makes the budget line flatter
Ad Valorem subsidy: based on the price of the good being subsidized;
Actual price to customer: (1-)p1
Lump-sum tax or subsidy
Government takes away some fixed amount of money, regardless of the individual’s behavior
Lump sum tax: budget line of a consumer will shift inward because his money income has been reduced
Lump sum subsidy: Budget line will shift outward
Quantity taxes and value taxes tilt the budget line one way or the other depending on which good is being taxed, but a lump-sum tax shifts the budget line inward
Government-imposed rationing constraints: level of consumption of some good is fixed to be no larger than some amount
Ex: WW2 U.S. Government rationed butter and meat
Rationed good x-bar
Change Budget Line and Budget set to be cut off vertically
Example: Food Stamp Program 1964 – lump-sum subsidy
Provided a subsidy on food for poor people
The rate at which food was subsidized depended on the household income
Since we are measuring each good in terms of the money spent on it, the “price” of each good is automatically 1, and the budget line will therefore have a slope of -1
In 1979 the program was modified. Instead of requiring that the households purchase food stamps, they are now simply given to qualified households
Budget line slope will not change; cannot sell food stamps. The max amount that it can spend on other goods does not change
Budget Line Changes
Perfectly balanced inflation: one in which all prices and all income rises at the same rate