2. What effect does a $1 specific tax have on equilibrium price and quantity, and what is the
incidence on consumers, if a. The demand curve is perfectly inelastic? b. The demand curve is
perfectly elastic? c. The supply curve is perfectly inelastic? d. The supply curve is perfectly elastic?
Use graphs and math to explain your answers.
Impact of a $1 tax on equilibrium price and quantity with
different elasticities:
Here's a breakdown of the effects of a $1 specific tax on equilibrium price and quantity, visualized
with graphs and explanations for each scenario:
a. Perfectly inelastic demand:
• In this case, the demand curve is completely vertical, indicating consumers have no substitutes and
will buy the same quantity regardless of price.
• When a $1 tax is imposed, the entire burden falls on consumers.
• Graph: The demand curve remains unchanged (vertical), while the supply curve shifts upward by
$1. The new equilibrium price increases by $1, and the quantity remains the same.
b. Perfectly elastic demand:
• Here, the demand curve is horizontal, meaning any price increase leads to zero demand.
• With a perfectly elastic demand, the seller cannot pass on the tax expense. They absorb the entire $1
tax to maintain any positive sales.
• Graph: The demand curve remains unchanged (horizontal), while the supply curve shifts upward
by $1. The new equilibrium price remains the same, and the quantity decreases to zero.
c. Perfectly inelastic supply:
• This scenario represents a fixed supply, unaffected by price changes.
• The supplier can fully pass on the $1 tax to consumers, as no alternative supply exists.
• Graph: The supply curve remains unchanged (vertical), while the demand curve shifts downward
by $1. The new equilibrium price increases by $1, and the quantity remains the same.
d. Perfectly elastic supply:
• With a perfectly elastic supply, producers readily adjust their output to match any price change.
• In this case, the tax burden is shared between consumers and producers. The price increase and
quantity decrease depend on the relative elasticities of demand and supply.
• Graph: Both the demand and supply curves shift upward by $1. The new equilibrium price and
quantity depend on the specific slopes of the curves (elasticities).
Mathematical analysis:
• In general, the impact of a specific tax on price (ΔP) and quantity (ΔQ) can be calculated using the
following formulas:
ΔP = T / (1 + 1/Ed + 1/Es)
ΔQ = -T * Ed / (1 + 1/Ed + 1/Es)
• Where:
•
•
•
•
T is the tax amount ($1)
Ed is the price elasticity of demand
Es is the price elasticity of supply
Plugging in the elasticities for each scenario (Ed = 0, Ed = ∞, Es = 0, Es = ∞) will confirm the
results observed in the graphs.
Remember:
• These are idealized scenarios with extreme elasticities. Real-world markets often exhibit varying
degrees of elasticity, leading to more nuanced outcomes.
• The incidence of the tax also depends on market power dynamics and other factors not explicitly
considered here.
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Q3
Suppose there are only two goods (X and Y) and only two individuals (numbered 1 and 2) in an
economy. Let PX be the price of good X and PY be the price of good Y. And finally, let I1 represent
the income of individual 1 and I2 the income of individual 2. Suppose the quantity of good X
demanded by individual 1 is given by X1 = 10 – 2 PX + 0.01 I1 + 0.4 PY and the quantity of X
demanded by individual 2 is X2 = 5 – PX + 0.02 I2 + 0.2 PY . a) Graph the two individual demand
curves (with X on the horizontal axis and PX on the vertical axis) for the case I1 = 1000, I2 = 1000,
and PY = 10. b) Using the individual demand curves obtained in part (a), graph the market demand
curve for total X. What is the algebraic equation for this curve?
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