Chapter 5 Market Equilibrium

Equilibrium, Excess Demand, Excess Supply

In previous chapters, we studied the behaviour of individual consumers (demand) and individual firms (supply). This chapter combines these perspectives to understand how buyers and sellers interact in a perfectly competitive market to determine the market price and quantity.

A market is in equilibrium when the plans of all consumers and firms are compatible, and the market "clears".

At the equilibrium price ($p^*$), the total quantity that consumers wish to buy (market demand, $q^D(p^*)$) is exactly equal to the total quantity that firms wish to sell (market supply, $q^S(p^*)$).

Thus, equilibrium is achieved when:

$q^D(p^*) = q^S(p^*)$

The price at which this equality occurs is the equilibrium price ($p^*$), and the corresponding quantity is the equilibrium quantity ($q^*$).

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Out-Of-Equilibrium Behaviour

When the market price is not at the equilibrium level, there is a mismatch between quantity demanded and quantity supplied, leading to either excess demand or excess supply.

• Excess Demand: If the prevailing market price is below the equilibrium price ($p < p^*$), the quantity demanded ($q^D$) will exceed the quantity supplied ($q^S$). Consumers want to buy more than firms are willing to sell at that low price ($q^D > q^S$). This shortage creates upward pressure on the price as buyers compete for the limited available goods.
• Excess Supply: If the prevailing market price is above the equilibrium price ($p > p^*$), the quantity supplied ($q^S$) will exceed the quantity demanded ($q^D$). Firms want to sell more than consumers are willing to buy at that high price ($q^S > q^D$). This surplus of goods creates downward pressure on the price as firms compete to sell their excess inventory.

In a perfectly competitive market, the "Invisible Hand" of the market (driven by buyers and sellers pursuing their self-interest) automatically pushes the price towards the equilibrium level where excess demand and excess supply are both zero.

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Market Equilibrium: Fixed Number Of Firms

We first analyse market equilibrium assuming that the number of firms in the market is fixed in the short run.

The market demand curve (DD) slopes downwards, reflecting the inverse relationship between price and quantity demanded by all consumers collectively.

The market supply curve (SS) slopes upwards (or is horizontal at $\min AVC$ in the short run for prices above $\min AVC$), reflecting the positive relationship between price and quantity supplied by all firms collectively (derived from the horizontal summation of individual firm supply curves above $\min AVC$).

Equilibrium is found graphically at the intersection of the market demand and market supply curves.

At price $p^*$, $q^D = q^S = q^*$.

If the price is $p_1 < p^*$, there is excess demand ($q_1 > q'_1$), causing the price to rise towards $p^*$.

If the price is $p_2 > p^*$, there is excess supply ($q_2 > q'_2$), causing the price to fall towards $p^*$.

Answer:

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Wage Determination In Labour Market

The labour market operates similarly to a goods market but with reversed roles for households and firms.

• Supply of Labour: Comes from households, who supply hours of work. An individual's labour supply decision involves a trade-off between income (from working) and leisure. While individual supply curves might be backward-bending at very high wages, the market supply curve of labour (S$_L$) is typically upward-sloping – higher wages generally attract more people to supply labour.
• Demand for Labour: Comes from firms, who hire labour. A perfectly competitive firm hiring labour aims to maximise profit. It will hire labour up to the point where the additional cost of hiring one more unit of labour equals the additional revenue generated by that unit.
  • Additional cost of one more unit of labour = Wage Rate ($w$).
  • Additional revenue from one more unit of labour = Marginal Revenue Product of Labour ($MRP_L$).
  • $MRP_L = Marginal Revenue (MR) \times Marginal Product of Labour (MP_L)$.
  • For a perfectly competitive firm, $MR$ equals the market price of the output ($p$). So, $MRP_L = p \times MP_L = Value of Marginal Product of Labour (VMP_L)$.

  Firms hire labour until $w = VMP_L$. Due to the law of diminishing marginal product, $VMP_L$ decreases as more labour is hired. This means the firm's demand for labour curve is downward-sloping.

The equilibrium wage rate ($w^*$) and equilibrium level of employment ($L^*$) are determined at the intersection of the market demand for labour ($D_L$) and market supply of labour ($S_L$) curves, where the quantity of labour demanded equals the quantity supplied.

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Shifts In Demand And Supply

Equilibrium price and quantity change when either the demand curve, the supply curve, or both curves shift due to changes in underlying factors (e.g., tastes, income, technology, input prices, number of buyers/sellers).

Impact of a Demand Shift (Supply Unchanged):

• Rightward Shift in Demand (e.g., increase in income for a normal good, increase in the number of consumers): At the initial price, excess demand is created. Price rises, quantity supplied increases along the supply curve, and quantity demanded decreases along the new demand curve. The new equilibrium is at a higher price and higher quantity.
• Leftward Shift in Demand (e.g., decrease in income for a normal good, decrease in the number of consumers): At the initial price, excess supply is created. Price falls, quantity supplied decreases along the supply curve, and quantity demanded increases along the new demand curve. The new equilibrium is at a lower price and lower quantity.

Impact of a Supply Shift (Demand Unchanged):

• Rightward Shift in Supply (e.g., technological progress, decrease in input prices, increase in the number of firms): At the initial price, excess supply is created. Price falls, quantity demanded increases along the demand curve, and quantity supplied decreases along the new supply curve. The new equilibrium is at a lower price and higher quantity.
• Leftward Shift in Supply (e.g., increase in input prices, decrease in the number of firms): At the initial price, excess demand is created. Price rises, quantity demanded decreases along the demand curve, and quantity supplied increases along the new supply curve. The new equilibrium is at a higher price and lower quantity.

Simultaneous Shifts of Demand and Supply:

When both curves shift, the impact on equilibrium price and quantity can be either clear or ambiguous, depending on the direction and magnitude of the shifts.

The table below summarizes the potential outcomes:

Shift in Demand	Shift in Supply	Impact on Equilibrium Quantity	Impact on Equilibrium Price
Rightward	Rightward	Increases	May increase, decrease or remain unchanged
Leftward	Leftward	Decreases	May increase, decrease or remain unchanged
Rightward	Leftward	May increase, decrease or remain unchanged	Increases
Leftward	Rightward	May increase, decrease or remain unchanged	Decreases

When the impact is ambiguous, the final equilibrium depends on which shift is relatively larger. For example, if both demand and supply shift right, quantity *always* increases, but price rises if demand shifts more than supply, falls if supply shifts more than demand, and stays the same if they shift by the same relative amount.

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Market Equilibrium: Free Entry And Exit

When firms can freely enter and exit the market (a characteristic of the long run in perfect competition and assumed for this section), a crucial condition is added to the equilibrium analysis.

With free entry and exit, firms will enter the market if they can earn supernormal profits ($p > AC$), increasing market supply and driving down price. Firms will exit the market if they are incurring losses ($p < AC$), decreasing market supply and driving up price.

This process continues until firms in the market are earning only normal profit (zero economic profit). This occurs when the market price equals the minimum average cost ($p = \min AC$) of the firms.

Assuming all firms are identical, the long-run equilibrium price in a perfectly competitive market with free entry and exit will always be equal to the minimum point of the firms' average cost curves ($p^* = \min AC$).

Graphically, the long-run market supply curve under free entry and exit is a horizontal line at the price level equal to $\min AC$. Equilibrium occurs at the intersection of the market demand curve and this horizontal price line.

The equilibrium quantity ($q^*$) is determined by the market demand at the price $p^* = \min AC$.

The equilibrium number of firms ($n^*$) is determined by dividing the total market quantity ($q^*$) by the output produced by a single firm at $\min AC$ (let's call this $q_f^*$):

$n^* = \frac{q^*}{q_f^*}$

Answer:

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Shifts In Demand (With Free Entry and Exit)

When demand shifts in a market with free entry and exit, the long-run equilibrium price remains fixed at $\min AC$. The adjustment occurs through changes in the quantity supplied by the market, which is achieved by firms entering or exiting.

• Rightward Shift in Demand (e.g., $DD_0$ to $DD_1$): At the initial price ($p^*=\min AC$), there is excess demand. This temporary shortage allows firms to earn supernormal profits, which attracts new firms to enter. Entry shifts the market supply curve to the right, increasing the total quantity supplied until it matches the new higher demand at the price $p^*$. The new equilibrium is at the same price ($p^*$) but a higher quantity ($q_1 > q_0$). The number of firms increases ($n_1 > n_0$).
• Leftward Shift in Demand (e.g., $DD_0$ to $DD_2$): At the initial price ($p^*=\min AC$), there is excess supply. Firms incur losses, which causes some existing firms to exit. Exit shifts the market supply curve to the left, decreasing the total quantity supplied until it matches the new lower demand at the price $p^*$. The new equilibrium is at the same price ($p^*$) but a lower quantity ($q_2 < q_0$). The number of firms decreases ($n_2 < n_0$).

Compared to a market with a fixed number of firms, demand shifts have a larger impact on equilibrium quantity but no impact on equilibrium price when entry and exit are free in the long run.

Applications

Demand and supply analysis is a powerful tool for understanding various market phenomena, including the effects of government policies.

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Price Ceiling

A price ceiling is a government-imposed maximum legal price for a good or service. It is typically set below the market equilibrium price ($p_{ceiling} < p^*$) to make essential goods more affordable for consumers.

When a price ceiling is imposed below the equilibrium price:

• Quantity demanded ($q^D$) is greater than quantity supplied ($q^S$) at the ceiling price, resulting in excess demand (a shortage) ($q_c > q'_c$).
• The market cannot reach equilibrium where $q^D = q^S$.
• Despite the lower price, consumers may not be able to buy as much as they want at that price.

Possible consequences of an effective price ceiling (below $p^*$):

• Shortages: Quantity supplied is less than quantity demanded.
• Rationing: Governments may need to implement rationing systems (e.g., ration coupons, fair price shops) to distribute the limited supply among consumers.
• Black Markets: Goods may be illegally sold at prices above the ceiling due to excess demand, creating a black market.
• Queues: Consumers may have to wait in long lines to purchase the limited supply.

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Price Floor

A price floor is a government-imposed minimum legal price for a good or service. It is typically set above the market equilibrium price ($p_{floor} > p^*$) to support producers' incomes (e.g., farmers) or guarantee a minimum income (e.g., minimum wage).

When a price floor is imposed above the equilibrium price:

• Quantity supplied ($q^S$) is greater than quantity demanded ($q^D$) at the floor price, resulting in excess supply (a surplus) ($q'_f > q_f$).
• The market cannot reach equilibrium where $q^D = q^S$.
• Producers are unable to sell all the output they are willing to supply at the floor price.

Possible consequences of an effective price floor (above $p^*$):

• Surpluses: Quantity supplied exceeds quantity demanded.
• Government Purchases: In agricultural markets, the government may buy the surplus output to maintain the price floor, leading to storage and disposal costs.
• Unemployment (in labour market): If a minimum wage is set above the equilibrium wage, the quantity of labour supplied exceeds the quantity demanded, resulting in unemployment.
• Inefficient Allocation: Resources may be used to produce goods that consumers do not value as highly as the cost of production at the supported price.