Question

Assume an initial equilibrium price of $5.00 per unit of good Z. Now the government imposes a $2.00 per unit tax on good Z. a. Assume the demand for good Z is perfectly inelastic. Graphically, show the impact of this tax. What will be the new price for the consumer? What will be the new price for the producer? Explain whether there will be any deadweight loss. b. Following the imposition of the tax, the consumer price rises to $5.50. What will be the new producer price? Graphically show the new equilibrium quantity of good Z. Show any area of deadweight loss on your graph. How is this tax burden shared between the consumer and producer?​

Answer 1

Part a: Perfectly Inelastic Demand:

1. Graph:

2. New Price for Consumer: $7.00

3. New Price for Producer: $5.00

4. Deadweight Loss: Yes

Part b: Consumer Price Rises to $5.50:

1. New Producer Price: $5.25

2. Graph is attached.

3. New Equilibrium Quantity: Slightly higher than the original equilibrium quantity.

4. Deadweight Loss: Smaller than in part a.

Impact of Tax on Good Z

Part a: Perfectly Inelastic Demand:

1. Graph:

2. New Price for Consumer: $7.00

3. New Price for Producer: $5.00

4. Deadweight Loss: Yes

Step-by-step explanation:

Due to perfectly inelastic demand, the entire $2.00 tax burden falls on the consumer, who now pays $7.00 per unit.

The producer receives the same price as before ($5.00) as they cannot pass on the tax burden to consumers.

The tax reduces the equilibrium quantity of good Z, resulting in a deadweight loss shown by the shaded triangular area between the initial and post-tax equilibrium points.

Part b: Consumer Price Rises to $5.50:

1. New Producer Price: $5.25

2. Graph:

3. New Equilibrium Quantity: Slightly higher than the original equilibrium quantity.

4. Deadweight Loss: Smaller than in part a.

5. Explanation:

Since the consumer price is now $5.50, the producer receives $5.50 - $2.00 (tax) = $3.50.

This higher price for the producer results in a new equilibrium at a slightly higher quantity compared to the original equilibrium without the tax.

The deadweight loss is still present, but it is smaller than in the case of perfectly inelastic demand due to the shift in demand caused by the higher price.

6. Tax Burden Sharing:

Consumer burden: $7.00 (new price) - $5.00 (original price) = $2.00

Producer burden: $5.25 (new price) - $5.00 (original price) = $0.25

Therefore, the tax burden is shared between the consumer and producer, but the consumer bears a larger portion of the burden.