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Quantity effect of a specific tax. A regulator plans to impose a specific tax on a previously unregulated monopolist. Before imposing the tax, they want to know what the change in quantity produced will be from such a tax. The proposed specific tax is τ = 10 and the following are the inverse demand and total cost functions:

P(Q) = 100 − 1 8 Q

C(Q) = 20 + 10Q + 1 8 Q 2 .

Find the change in quantity from a $10 increase in the tax.

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Nusrat Fatima
Nusrat FatimaLv10
28 Sep 2019

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Related questions

Quantity effect of a specific tax
A regulator plans to impose a specific tax on a previously unregulated monopolist. Before
imposing the tax, they want to know what the change in quantity produced will be from
such a tax. The proposed specific tax is τ = 10 and the following are the inverse demand
and total cost functions:
P(Q) = 100 − (1/8)Q
C(Q) = 20 + 10Q + (1/8)Q2
Find the change in quantity from a $10 increase in the tax.

Politicians concerned with climate change are proposing that a tax on electricity should be implemented with the hope that it will incentivize energy abatement. But they are also want to structure a policy such that it is the producers of electricity that pay the tax, not the consumers. Therefore, they propose a tax of $1/MW h to be paid by the generator of electricity. You have been hired to assess the economic implications of the proposed tax.

After running your econometric modeling, you conclude that the market for electricity is characterized by the following equations:

Demand Curve: P = 40 - 3Qd

Supply Curve: P = Qs

Where P is dollars per MWh and Q is Millions of MWhs.

Part 1: What are the equilibrium price (P) and quantity (Q) with no tax assessed?

Part 2: What will be the equilibrium quantity after the tax is assessed? What is the price that the consumer will pay after the tax is assessed? What is the price that the producer will receive after the tax is assessed?

Part 3: Was the politician successful in reducing electricity usage? If so, by how much?

Part 4: How much tax revenues are raised by the new tax?

Part 5: What is the tax incidence to the consumers?

Part 6: What is the tax incidence to the producers?

Part 7: Was the policymaker successful in assessing the tax on producers, not consumers?

Regulation of monopolies

A monopolist hospital faces the following demand curve for diabetes screening: Pd=100-2Qd where Pd is the price of delivery and Qd is the demand for delivery in a hospital. The hospitals are MC=Q for deliveries and the fixed costs are zero.

Total Revenue = P*Q= (100-2Q) * Q = 100Q - 2Q2

Marginal Revenue = derivative of Total Revenue = 100 - 4Q

Total cost = Integral of Marginal Cost = (1/2)Q2

What is the unregulated price and quantity that the hospital will choose?

Suppose the government wanted to increase access to diabetes screening. What would be the maximum output that could be obtained from the monopoly hospital if the government could regulate its price? Assume the government cannot force the hospital to operate at a loss.

What would be the price and quantity regulated if the government decided that the hospital should use marginal cost pricing (ie suppose the government decided they wanted to simulate the quantity that would be produced in a competitive market)? Please draw all three scenarios.

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