Here we analyze how demand changes when prices and income changes.
Types of Goods
Here we will define two main types of Goods:
- Normal Goods: The demand increases linearly with the income.
- Inferior or Ordinary Goods: The demand decreases when the income is higher, one example is low quality food.
- Necessary Good: The demand is increases sublinearly (e.g. constantly) with respect to the income.
- Luxury Good: The demand increases more than linearly with the income.
- Giffen Good: The decrease in price leads to a decrease in demand.
Curves of Demand
Income offer curve
It is quite intuitive to visualize: just expand the income while keeping utility and priced fixed, you will see the optimal point translating along the curve.
Engel Curve
This curve shows the relationship between the income and the quantity of a single good demanded, with all prices held constant. This graph is a little different compared to the others: it shows the quantity of goods demanded as a function of the income.
Price Offer Curve
This is the curve that shows the optimal quantity of goods as a function of the price change of a single good.
Demand Curve
This curve shows the quantity of goods demanded as a function of the price of a single good Viceversa the inverse demand curve plots the price of the good in function of the quantity demanded).
Market Demand
Aggregate Demand
$$ X(p_{1}, p_{2}, m) = \sum_{i} x_{i}(p_{1}, p_{2}, m_{i}) $$Economists usually treat this aggregate demand as if it was from a single person.
Elasticity of Demand
$$ \epsilon = \frac{dX}{dp} \frac{p}{X} $$We add $p$ and $X$ so that we are comparing fractions, which are irrespective on some scaling constants. This indicator is often useful to understand how quickly the quantity demanded can adjust to a change in price.
This value is often related to the presence of substitutes: if there are many substitutes, the elasticity of demand is higher, as the market can quickly adjust to always choose the substitute good.