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Market Equilibrium Summary
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- ECO204
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- University Of Toronto (U Of T )
Market Equilibrium Summary
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ECO204Y-2022/23Market Equilibrium Summary
In this chapter we explore market equilibrium in a perfectly competitive market. All
demanders and suppliers take prices as given (prices are exogenous to the actors—they
are “price takers”).
Equilibrium is defined by the equality of demand and supply: D( p) = S( p) . This equality
defines the equilibrium price p * and the equilibrium quantity 𝑞∗ .
Note we now know where these market demand and supply curves come from. They are
€
the horizontal sums of the underlying individual or firm demand and supply curves
respectively. They €
are the result of utility maximizing or profit maximizing decisions.
In general, equilibrium price and quantity are determined by both supply and demand. In
the special cases of perfectly inelastic supply (or demand) or perfectly elastic supply (or
demand) the determination of price and quantity is separated. The cases of perfectly
inelastic supply and perfectly elastic supply are explained in the text and were discussed
in class.
Note that we graph the inverse supply and demand curves--𝑝" (𝑞) and 𝑝# (𝑞)
Comparative Statics
The comparative statics of this model involve shifting either the demand or supply
curves, or both. An important thing to remember is that changes in the price of the good
under study imply movements along the supply or demand curve. Changes in the prices
of other goods/inputs or other things initially being held constant (e.g., incomes) imply
shifts of the curves.
Taxes
Taxes drive a wedge between the price that demanders pay and the price that suppliers
receive. We define the legislative or statutory burden or incidence of a tax as falling on
the side of the market which nominally pays the tax (e.g., consumers pay the HST as it’s
added to the purchase price of each good). We define the effective burden or incidence
of the tax as the difference between the demand price (or supply price) and the price in
the pre or no tax equilibrium. The effective burden on demanders (or suppliers) does not
depend on who nominally pays the tax; it depends on the relative shapes of the demand
and supply curves. We derive graphical and algebraic expressions of the effective
incidence of a per unit tax.
, Partial Equilibrium Graphical Analysis
To analyze the impact of a per unit tax graphically, using the inverse supply and demand
curves, you have the choice of either subtracting the tax from the demand curve (i.e.,
drawing a new demand curve that lies below the original demand curve by a distance
equal to the tax per unit) or adding the tax to the supply curve. You should be able to
graphically analyze the impact of a per unit tax and be able to identify the incidence of
the tax on your graph.
In general the more inelastic side of the market bears more of the burden. You can see
this in the special cases of perfectly inelastic supply or perfectly elastic supply.
Partial Equilibrium Algebraic Analysis
When solving algebraically for the impact of a tax we must create two equations in two
unknowns. We can solve for either 𝑝# or 𝑝" . If we solve for 𝑝# then we can solve for 𝑝"
as 𝑝" = 𝑝# − 𝑡, and we can solve for the quantity transacted by substituting 𝑝# back into
the demand curve. If instead we solve for 𝑝" then we can solve for 𝑝# as 𝑝# = 𝑝" + 𝑡
and we can solve for the quantity transacted by substituting 𝑝" back into the supply curve.
Next we derive an expression for the effective burden of a tax. Suppose, for example, the
legislative burden of the tax is on consumers. So 𝑝" is the producer price and 𝑝# =𝑝" +t is
the consumer price.
Let D(p) and S(p) be the demand and supply curves for the good.
In equilibrium we need D(𝑝" +t)= S(𝑝" )
#$!
We next derive an expression for the effective burden of the tax, #%
.
Starting from t=0, and D(p)= S(p), dt leads to a change dp so equilibrium continues to
hold.
𝑆(𝑝 + 𝑑𝑝) = 𝐷(𝑝 + 𝑑𝑝 + 𝑑𝑡) ⟹
𝑆(𝑝) + 𝑆′(𝑝)𝑑𝑝 = 𝐷(𝑝) + 𝐷′(𝑑𝑝 + 𝑑𝑡) ⟹
𝑆′(𝑝)𝑑𝑝 = 𝐷′(𝑝)(𝑑𝑝 + 𝑑𝑡) ⟹
𝑑𝑝" 𝐷′(𝑝)
= &
𝑑𝑡 𝑆 (𝑝) − 𝐷′(𝑝)
$/(
Multiply numerator and denominator by $/( = 1 to get
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