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Demand curve

Consider three prices $p_x''<p_x'<p_x$ and their corresponding budget lines for income $I$.

This gives 3 equilibrium point in the utility map. Plot $p_x'',p_x',p_x$ with $x'',x',x$ which are the optimal quantity of $X$ purchased for each of the $p_x$ respectively. This is the demand curve. For a normal good, the demand curve is always negatively sloped.

Thus the demand curve displays the relationship between the price and quantity demanded, all else assumed constant.

Every point in the demand curve is an equilibrium point (by definition).

Here we hold constant,

• $p_y$

• $I$

• Consumer preference

If these change, the demand curve shifts.

As the price decreases, demand increases.

If the income increases, the demand curve shifts away from the origin parallely.

If $p_y$ increases, and if $y$ is a perfect substitute, more of $x$ is bought. This results in a shift away from the origin in the demand curve. If on the other hand $y$ is a perfect complement, the demand curve shifts towards the origin.

If the preference changes, so that, say, $x$ is more preferred, the demand increases, and the demand curve of $x$ shifts to the right.

Elasticity

Responsiveness of demand to price changes.

Demand function:

Price elasticity of demand: proportional change in quantitiy demanded of $x$ due to proportional change in the price of x. i,e

It is often negative.

If $e_{xp}=-1$, it means that if price increases by $1\%$, quantity demanded decreases by $1\%$.

This is known as unitary elastic demand.

What if $e_{xp}>-1$?

Sin goods are inelastic. Along with petroleum, rice etc. Their demand change is less sensitive to the price change. This is why governments increase higher taxes on inelastic goods.

Non necessary goods are elastic demand.