Assignment
1. The US domestic demand for steel is given by the inverse demand equation: P = 2100 - 13.33Q where P is the price of steel measured $ per ton and Q is quantity of steel consumed measured in million tons per year. The inverse supply curve is given by the equation P = 42.86 + 7.79Q where P and Q are in the same units.
a. Solve for the marketing clearing price and quantity if there is no trade (no imports or exports).
b. Now suppose that the world price is $600 per ton of steel. At this price the U.S. can either import as much as it wants or export as much as it wants. Find the following:
• the market clearing price,
• the level of domestic consumption
• the level of domestic production
• the level of imports or exports
• the change in consumer surplus relative to part a
• the change in producer surplus relative to part a
• the gains from trade (the change in total surplus)
c. Calculate the impact of the Trump Administration deciding to impose an import tariff of 25% on steel. With the tariff in place find the following:
• the market clearing price,
• the level of domestic consumption
• the level of domestic production
• the level of imports or exports
• the change in consumer surplus relative to part b
• the change in producer surplus relative to part b
• tariff revenue
• deadweight loss from the tariff
Hint: Graph the domestic supply and demand curves and use the graph to define what you need to calculate before you start your calculations.
2. Yolanda gets utility from income, I, and hours of leisure, L. She earns income by working, getting paid an hourly wage, w, for each hour she works. Her utility function is U = I0.5L0.95. Find the combination of income and hours of leisure that maximize Yolanda's utility if her wage rate is $20 per hour. Assume that hours worked = 24 hours in a day minus L. So I = w(24 - L). Use Solver to find the solution.
3. The production of paint involves the release of volatile organic compounds (VOCs) that combine with other atmospheric chemicals to produce harmful air pollution. The EPA wants to impose a tax on paint as a way to induce a reduction in the production and consumption of paint and consequently on the release of VOCs. You have been asked to analyze the impacts of such a tax on consumers and producers and to estimate the tax revenue that would be generated. You are given the following information:
• Paint demand elasticity = -0.7
• Quantity demanded = 100 million gallons of paint when the price of paint = $10/gal
• Paint supply elasticity = 1.5
• Quantity supplied of paint = 100 million gallons when the price of paint = $10/gal
• Both demand and supply are linear
• The proposed tax is $3 per gallon
a. Calculate the following when the tax is imposed on consumers
• Market-clearing price and quantity
• Price paid by consumers
• Price received by producers
• Tax revenue
• Change in consumer surplus
• Change in producer surplus
b. Calculate the following when the tax is imposed on producers
• Market-clearing price and quantity
• Price paid by consumers
• Price received by producers
• Tax revenue
• Change in consumer surplus
• Change in producer surplus
c. Calculate the tax incidence on consumers and producers in part a and part b.
4. A firm in a perfectly competitive industry has the following cost functions:
• Total Variable Costs: TVC = 300Q - 5.13Q2 + 0.0333Q3
• Marginal Costs: MC = 300 -10.26Q + 0.1Q2
• Total Fixed costs: FC = $4000
For market prices of $250, $130, and $85, calculate the profit-maximizing levels of output for this firm and its level of profit at each price. (Hint: Use Solver unless you want to solve a quadratic formula.)
5. An industry has only one firm in it. The following information characterizes the firm's cost functions and the demand curve it faces.
Total Variable Cost: TVC = 10Q+5.5Q2
Marginal Cost: MC = 10 + 11Q
Total Fixed Cost: TFC = 5,000
Inverse Demand: P = 1,000 - 10Q
a. Find this firm's profit-maximizing output level and profit level.
b. Suppose regulators decide that this firm's price is too high. Calculate the lowest price cap regulators could impose on the firm while still allowing the firm to break-even.
c. Suppose the firm is successful at lobbying the regulator to allow it to earn 10% more than its costs. Calculate the price cap that the regulator would impose to allow this 10% rate of return.
6. Suppose that there are only two tobacco farmers in the United States with marginal costs of production given by
• MC1 = 20 + 0.8Q1
• MC2 = 20 + 0.5Q2
where Q1 and Q1 are the quantities of tobacco produced by each farmer (million pounds) and marginal costs is measured in cents per pound.
The inverse industry demand curve is given by P = 280 - Q, where P is cents per pound of tobacco and Q is million pounds.
a. Assuming perfect competition calculate the following:
• the market-clearing price and quantity
• how much tobacco each farmer produces
• producer surplus for each farmer (expressed in $ million)
b. Now suppose these two farmers are successful in lobbying the federal government to develop a farm program that gives them a higher price for their tobacco. The program is initially set up to give each producer a tobacco quota of 65 million pounds. Each farmer can produce up to their quota and no more. Calculate the following:
• the market-clearing price
• the per-pound quota rent for each farmer
• change in producer surplus for each farmer relative to Part a (expressed in $ million)
c. Farmer 2 offers to buy one million pounds of Farmer 2's quota for a price of 75 cents per pound. Should Farmer 1 accept the offer? Explain.
d. Farmer 1 offers to sell one million pounds of quota to Farmer 2 for 85 cents per pound. Should Farmer 2 accept the offer? Explain.
e. Find the allocation of tobacco quota (130 million pounds) between the two farmers such that neither farmer can benefit from a trade. At this allocation calculate the following:
• the market-clearing price
• the per-pound quota rent for each farmer change in producer surplus for each farmer relative to Part b (expressed in $ million).