EC 270 - Tue Sep 15, 2026 - Lecture 02

Before class

• Read Chapter 2

In class

Lecture notes

• Consumer theory about understanding individual's choices
• Economists assume consumers make choices about the best bundle of goods they value and can afford

Building a model on the budget constraint

• Consumption choice set: collection all consumption choices there are
• If there are $n$ different consumption goods $x_i$ to choose from:
  • Consumption Bundle = $\text{X}=({\text{x}}_1,{\text{x}}_2,\dots ,{\text{x}}_n)$
• There are lots of constraints for consumption choice like budget time, etc. but we focus solely on the price constraint
• For each commodity $x_i$, there is a price ($p_i$) associated with it
  • Prices = $({\text{p}}_1,{\text{p}}_2,\dots ,{\text{p}}_n)$

We assume consumers have income $m$ (how much money they have to spend)

• Expenditures <= (disposable) income:

Budget constraint: is formed by the consumption bundles that are only just affordable
if all items in the consumption bundle are $\ge 0$ and all prices are $\ge 0$ and $p_1{x}_1+p_2{x}_2+\cdots +p_n{x}_n\le m$

• The budget constraint is the upper bound

WE WILL BE LOOKING AT THE TWO-GOOD APPROACH

• It's very general

• Often, x_2 represents "everything else" which makes our model simpler and still allows us to develop theory
• Composite goods are a collection of goods (often, everything else)

Graphically

• m/p_2 is the vertical intercept and is the amount of goods if we bought only good 2
• m/p_1 is the horizontal intercept and is the amount of goods if we bought only good 1
• Any point along the budget constraint is "just affordable"

Properties of the Budget Set

• Vertical intercept: $\frac{m}{p_2}$
• Horizontal intercept: $\frac{m}{p_1}$
• Slope: $-\frac{p_1}{p_2}$
  • The slope tells us how much of $x_2$ I can exchange in the market to get one more unit of $x_1$
  • Opportunity cost: the next best alternative forgone and in this case, the slope of the budget line measures the opportunity cost of consuming $x_1$
    • OC of an extra unit of $x_1$ is $-\frac{p_1}{p_2}$ of $x_2$

Changes in Income

• If $m$ increases, then the entire budget line shifts outwards/up in a parallel manner and are able to afford more
  • Remember, the slope of the budget line is $-\frac{p_1}{p_2}$, and thus income changes (holding prices constant) shift the budget line either in or out in a PARALEL manner
• Vice versa for decrease

Changes in Price

• What happens if $p_1$ increases?
  • Doesn't affect the vertical intercept because the price of good 1 doesn't affect it. By definition, $x_1$ is set to 0
  • You can afford less of good 1, thus your budget constraint is reduced and your horizontal intercept is lower and thus the slope gets steeper.
    
• Vice versa

The Numeraire

• Means "Unit of account"
• CHANGING THE NUMERAIRE DOES NOT AFFECT THE BUDGET LINE OR BUDGET SET
• We could peg one o the prices, or the income to some fixed value

or

Numeraire price: The price relative to which we are measuring the other price and income
Numeraire good: The good used to measure the value of other goods

Ad Valorem Sales Taxes

• It is a tax on the value of goods (e.g. HST)
• Harmonized Sales Tax (HST) is a 13% ad valour tax -> increases price from p to (1 + 0.13)p = 1.13p
• Assume the Ad Valorem tax is applied uniformly to all goods
• If the ad valour tax rate is $t$
  Then we have:

or

• This causes a shift inwards

Quantity Tax

• Consumer has to pay a certain amount to the government for each unit of the good they purchase
  • Changes the price of good from $p$ to $p+1$

Lump sum Tax

• Consumers must pay a fixed amount of money, regardless of their behavior
  Subsidies: "negative" taxes
• Taxes increase the price to the consumer $(p+1)$
• Subsidies decrease the price to the consumer $(p-1)$

What if prices are non-linear?

• e.g. bulk buying discounts, price penalties for buying "too much"
• You have to adapt your slope depending on what x is
• How do you find your x-intercept though? You look at how much you've already spent on good 1 and then add whatever is remaining

After class

• Tutorial questions for this chapter (exam-level - these are the real practice)