Microeconomics

2. Household Theory
2.1 Budget Constraint and Preferences
An indifference map describes a person’s preferences for various combinations of goods and services. But preferences do not explain all ofconsumer behavior. Individual choices are also affected by budget constraints, which limit people’s ability to consume in light of the prices they must pay for various goods and services.
The budgetconstraint of the consumer can be written as
p1x1+p2x2≤m
Where p1x1 is the amount of money the consumer is spending on good 1, and p2x2 is the amount of money the consumer is spending on good 2. Itrequires that the amount of money spent on the two goods be no more than the total amount the consumer has to spend.
The consumer’s budget line describes the combinations of goods that can bepurchased given the consumer’s income and the prices of the goods.
The budget line is the set of bundles that cost exactly m
p1x1+p2x2=m
We can see the budget set in the next figure. The heavy line isthe budget line (the bundles that cost exactly m) and the bundles below this line are those that cost strictly less than m.

x2=mp2-p1p2x1
This is the formula for a straight line with a verticalintercept of m/p2 and a slope of -p1/p2. Where x2 is how many units of the good 2 the consumer needs to consume in order to just satisfy the budget constraint.
If there’s an increase in the income, thevertical intercept will increase and won’t affect the slope of the line, i.e. an increase in income will result in a parallel shift outward of the budget line. Similarly, a decrease in income willcause a parallel shift inward.

If price 1 increases and price 2 and income hold fixed, increasing p1will not change the vertical intercept, but it will make the budget line steeper since p1/p2 willbecome larger.

If both prices increase at the same time, supposing they become t times as large, we got
p1x1+p2x2=mt
Thus multiplying both prices by a constant amount t is just like dividing...