Microeconomics Problem Set: Elasticity and Tax Incidence Guidance

Q1a. Graph the demand and supply curves and calculate the equilibrium price and quantity which clear the market.

Background

Topic: Market Equilibrium

This question tests your understanding of how to find the equilibrium price and quantity in a competitive market using linear demand and supply equations.

Key Terms and Formulas

• Demand Curve: $Q_D = 110 - 10P$

• Supply Curve: $Q_S = 40 + 4P$

• Equilibrium: Occurs where $Q_D = Q_S$

Step-by-Step Guidance

1. Set the demand and supply equations equal to each other: $110 - 10P = 40 + 4P$

2. Combine like terms to solve for $P$ (price): Move all terms involving $P$ to one side and constants to the other.

3. Once you have $P$, substitute it back into either the demand or supply equation to solve for $Q$ (quantity).

4. To graph, plot both equations on a Price-Quantity axis. The intersection point represents the equilibrium.

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Q1b. Consider that the government decides to collect a $1.00 tax from producers on each unit they sell. Show this tax on your graph, and calculate the effect on the equilibrium price and quantity.

Background

Topic: Taxes and Market Equilibrium

This question examines how a per-unit tax on producers shifts the supply curve and affects equilibrium price and quantity.

Key Terms and Formulas

• Tax on Producers: Shifts the supply curve vertically by the amount of the tax.

• New Supply Curve: For a tax $t$, $Q_S = 40 + 4(P - t)$

Step-by-Step Guidance

1. Adjust the supply equation to account for the $1.00 tax: Replace$P$with$(P - 1)$ in the supply equation.

2. Set the new supply equation equal to the demand equation: $110 - 10P = 40 + 4(P - 1)$

3. Solve for the new equilibrium price $P$ using algebraic steps.

4. Substitute the new $P$ into the demand equation to find the new equilibrium quantity.

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Q1c. What is the total tax collected?

Background

Topic: Tax Revenue

This question tests your ability to calculate the total tax revenue collected by the government from a per-unit tax.

Key Terms and Formulas

• Total Tax Collected: $\text{Tax Revenue} = \text{Tax per unit} \times \text{Quantity sold after tax}$

Step-by-Step Guidance

1. Recall the equilibrium quantity found after the tax was imposed (from part b).

2. Multiply the per-unit tax ($1.00) by the new equilibrium quantity to set up the calculation for total tax revenue.

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Q1d. How is the burden of the tax shared between the buyers and sellers?

Background

Topic: Tax Incidence

This question explores the concept of tax incidence, which is how the burden of a tax is divided between buyers and sellers depending on the elasticities of demand and supply.

Key Terms and Formulas

• Tax Incidence: The division of the tax burden between buyers and sellers.

• Buyers' Burden: Increase in price paid by buyers.

• Sellers' Burden: Decrease in price received by sellers (after tax).

Step-by-Step Guidance

1. Compare the equilibrium price before and after the tax to determine how much more buyers pay and how much less sellers receive.

2. The difference between the price buyers pay and the price sellers receive (after tax) should equal the tax amount.

3. Relate the division of the burden to the elasticities of demand and supply (to be calculated in part e).

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Q1e. Calculate the price elasticity of demand between $5-$6, and the price elasticity of supply between $5-$6. How do these values relate to the incidence of tax in d) above?

Background

Topic: Price Elasticity and Tax Incidence

This question tests your ability to calculate the price elasticity of demand and supply over a price range, and to interpret how elasticity affects tax incidence.

Key Terms and Formulas

• Price Elasticity of Demand: $E_D = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}$

• Price Elasticity of Supply: $E_S = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}}$

• Midpoint Formula: $E = \frac{\Delta Q}{\Delta P} \times \frac{P_{avg}}{Q_{avg}}$

Step-by-Step Guidance

1. Find the quantities demanded and supplied at $P = 5$ and $P = 6$ using the demand and supply equations or the table provided.

2. Calculate $\Delta Q$ (change in quantity) and $\Delta P$ (change in price).

3. Compute the average price and average quantity for each calculation.

4. Plug these values into the midpoint formula for elasticity for both demand and supply.

5. Interpret how the relative elasticities affect the division of the tax burden (from part d).

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