NotesAtHKU

Perfect competition market

We assume that the market is perfectly competitive, which means that:

Buyers and sellers have negligible market power, they have to take the price as given.
Demand and supply jointly determine market price.

Curves

Here we study the relationship between price $P$ and quantity $Q$ in the market. Graphs are plotted $P-Q$ .

Demand curve

Demand describes the consumers' desires to purchase a good at different prices.

P_d = f(Q_d)

Where $P_d$ is the price that consumers are willing to pay for a quantity $Q_d$ .

It is a downward-sloping curve because:

$P \uparrow \rightarrow$ buyers no longer than to buy as much.
$P \uparrow \rightarrow$ buyers will switch to alternative.

Market Demand curve

The market demand curve is the horizontal aggregation of individual demand curves of the consumers:

Q_{md} = Q_{d1} + Q_{d2} + \cdots

To assess the $Q_d$ for market plot, we reference the topmost demand curve for each price.

Supply curve

Supply describes the producers' willingness to sell a good at different prices.

P_s = f(Q_s)

Where $P_s$ is the price that producers are willing to sell for a quantity $Q_s$ .

It is an upward-sloping curve because:

$P \uparrow \rightarrow$ producers want to sell more.

The marginal cost of production can be directly intepreted as the supply curve.

Example

If $MC(q) = 2q$ , then the supply curve is $P = 2Q_s$ .

Market Supply curve

The market supply curve is the horizontal aggregation of individual supply curves of the producers:

Q_{ms} = Q_{s1} + Q_{s2} + \cdots

To assess the $Q_s$ for market plot, we reference the bottommost supply curve for each price.

Equilibrium

Here we study the plot of both demand and supply curves.

Market equilibrium

The market equilibrium is the point where the quantity demanded equals the quantity supplied:

P^* = P_s = P_d\\ Q^* = Q_{s} = Q_{d}

Where $P^*$ is the equilibrium price and $Q^*$ is the equilibrium quantity. At this point, the market of which buyers and sellers are satisifed, and the market clears.

Excess

However, prices can be set above or below $P^*$ , leading to excess:

Excess is the $Q$ difference between the quantity demanded and supplied at a given price:

Name	Set price	Quantity difference
Surplus	$P > P^*$	$Q_s > Q_d$
Shortage	$P < P^*$	$Q_s < Q_d$

Trading Locus

The trading locus is the set of all possible prices and quantities that can be traded in the market. The quantity that can be traded is:

Q_\text{traded} = \min(Q_d, Q_s)\quad @P

Surplus of exchange (gain)

Consumer and producer surplus are the gain / loss from trade at a certain price. The total economic surplus is the sum of both.

They can be calculated as:

\begin{align*} \text{Consumer surplus} &= \int_0^{Q^*} P_d - P^* \, dQ\\ \text{Producer surplus} &= \int_0^{Q^*} P^* - P_s \, dQ\\ \text{Total economic surplus TES} &= \int_0^{Q^*} P_d - P_s \, dQ\\ & = \text{Consumer surplus} + \text{Producer surplus} \end{align*}

We can see that the TES is maximized at equilibrium. (Can check by increasing / decreasing quantity traded).

Assuming all benefit of consumption goes to buyers, and all benefit of production goes to sellers, the TES @ $P^*$ is equilivalent to the welfare to the society.

Types of goods

Categorizing goods

We can categorize goods by:

Type categorization
- Normal
- Inferior
- Luxury
Comparative categorization
- Substitute
- Complements

Type characteristics

Type	$Q_d$ when $I \uparrow$	Income elasticity of demand
Normal	$\uparrow$	$>0$
Luxury	$\uparrow$	$>1$
Inferior	$\downarrow$	$<0$

Related: Income elasticity of demand.

Comparative characteristics

Type of good B	$Q_d$ of good A when price of good B $\uparrow$	Cross-price elasticity of demand
Substitute	$\uparrow$	$>0$
Complements	$\downarrow$	$<0$

Comparative Statics

Here we study the $\Delta P^*Q^*$ when the demand or supply curve shifts.

Shifting

If it is said that the demand / supply increases, the curve shifts to the right. This will lead to a higher $P^*$ and $Q^*$ .

Demand shifters

The following factors can shift the demand curve.

Factor (increase)	Demand, Shift	Example
Population	$\uparrow, \rightarrow$	Number of ppl and water demand
Income to normal goods	$\uparrow, \rightarrow$	Income and restaurant demand
Income to inferior goods	$\downarrow, \leftarrow$	Income and instant noodle demand
Price of substitutes	$\uparrow, \rightarrow$	If electric car is expensive, ppl will buy more petrol cars
Price of complements	$\downarrow, \leftarrow$	If petrol is cheap, ppl will buy more petrol cars
Expectation of future price	$\uparrow, \rightarrow$	If ppl expect price of house to rise, they will buy more now
Taste	$\uparrow, \rightarrow$	If apple has recently been found to be healthy, ppl will buy more apples

Original consumers and producers and shifted curves

If the demand / supply changes due to a factor (e.g. country opening supply to another country), the original consumers and producers might be hurt or benefited.

We can calculate the surplus for the original group by the area between original demand / supply curve and new equilibrium price (line).

Supply and Demand