Problem Set #4
a.) 90, 75, 60 b.) $675, $540, $405 c.) 4 workers; once you add a fifth worker, the VMP falls below the marginal cost ($700) for that additional worker, thus cutting into profits
3.) Graph: a.) What are the marginal products of the 2nd, 3rd, and 4th workers? b.) Suppose the firm hires each unit of labor for $600 per week, and each unit of output sells for $9. What is the value of the marginal product of the 3rd, 4th & 5th workers? c.) Suppose the firm sells its output for $12 per unit, and it pays each of its workers $700 per week. How many workers will the firm hire to maximize its profit? Why?
a and b.) Table includes answers c.) The firm should employ 4 workers to earn profits of $120.
4.) Table: Droid-making firm. a.) Complete the table's marginal product column. Describe what is happening. b.) Suppose that the firm pays its workers $45 per day. Each unit of output sells for $10. Complete the VMP column. c.) Assuming that $45 wages per worker is the only cost and that droids cost $10 to make, how many droid-making laborers should this firm employ? How much profit will it earn? (table has answers a and b)
a.) P = $1.60; Q = 42 b.) P = $1.80; Q=35 c.) The market equilibrium differs from the socially optimal equilibrium due to negative externalities. Those externalities add social (public) costs, for example pollution & negative health effects to those not producing or consuming the product. As a result, the socially optimal price is higher to pay for those added costs while reducing the quantity from the market equilibrium levels.
5.) Figure: The tobacco industry. a.) Without any government intervention, what is the market equilibrium (price and quantity)? b.) What is the socially optimal equilibrium (price and quantity)? c.) Are the two the same? Why or why not? Explain completely.
a.) 4 units b.) 5 units c.) $7 per unit needed as subsidy to cover the difference between private cost & private value at that level of output
6.) Table: The following table shows the private value, private cost, and social value for a market with a positive externality. a.) What is the market equilibrium quantity of output for this product? b.) What is the socially-optimal level of output in this market? c.) How large would a per unit subsidy need to be in this market to move the market from the equilibrium level of output to the socially-optimal level of output?
a.) $90,000; includes 45 million families b.) $30,000; includes 7.5 million (or 7,500,000) families c.) 60 million families
8.) Table - The following table shows the distribution of income in Marysville. a.) Seventy-five percent of all families have incomes below what level? If the population included 60 million families, how many families would have incomes at those levels? b.) Seventy-five percent of all families have incomes above what level? How many families would that mean if the population included 10 million families? c.) With a population that includes 120 million families, how many families earn incomes $60,000 or more per year?
a.) Plan A b.) Plan A c.) neither Plan A nor Plan B because any plan that forcibly redistributes income is against the philosophy
9.) Scenario - Suppose that a society is made up of five families whose incomes are as follows: $120,000; $90,000; $30,000; $30,000; and $18,000. The federal government is considering two potential income tax plans: Plan A is a negative income tax plan where the taxes owed equal 1/3 of income minus $20,000. Plan B is a two-tiered plan where families earning less than $35,000 pay no income tax and families earning more than $35,000 pay 10% of their income in taxes. The income tax revenue collected from those families earning over $35,000 is then redistributed equally to those families earning less than $35,000. a.) Assuming that utility is directly proportional to the cash value of after-tax income, which government policy would an advocate of utilitarianism prefer? b.) Assuming that utility is directly proportional to the cash value of after-tax income, which government policy would an advocate of liberalism prefer? c.) Assuming that utility is directly proportional to the cash value of after-tax income, which government policy would an advocate of libertarianism prefer?
a.) $6 per gallon for 3 gallons each; profit would be $36 b.) As a perfectly competitive firm, they would sell 12 gallons for $0 per gallon (no profit) c.) The price would fall to $4 because each would try to earn more profit by producing one more item; as a result the total quantity produced would be 8, making the price fall. Thus, each would earn only $16 in profit.
1.) Table - Imagine a small town in which only two residents, Abby and Brad, own wells that produce safe drinking water. Each week Abby and Brad work together to decide how many gallons of water to pump. They bring water to town and sell it at whatever price the market will bear. To keep things simple, suppose that Abby and Brad can pump as much water as they want without cost so that the marginal cost is zero. The weekly town demand schedule and total revenue schedule for water is shown in the table below: a.) Suppose that Abby and Brad work together to operate as a profit-maximizing monopolist. What price will they charge for water? What quantity will each of them sell? For how much profit? b.) If this market for water were perfectly competitive instead of monopolistic, what would be the price for water and how much would they sell? How much profit would they make? c.) Suppose the town enacts new antitrust laws that prohibit Abby and Brad from operating as a monopoly. What will be the price of water once Abby and Brad reach a Nash equilibrium? Why? How much profit will Abby and Brad each earn once they reach a Nash equilibrium?
a.) $90 for 9,000 subscriptions b.) Profit = TR - TC for 2 firms; Thus, 810,000 - 400,000 = 410,000, or $205,000 per company colluding successfully. c.) 12,000 subscriptions sold at $60 each lead to 720,000 - 400,000 = $320,000 in total profits in the market
2.) Table - The information in the table below shows the total demand for premium-channel digital cable TV subscriptions in a small urban market. Assume that each digital cable TV operator pays a fixed cost of $200,000 (per year) to provide premium digital channels in the market area and that the marginal cost of providing the premium channel service to a household is zero. a.) If there is only one digital cable TV company in this market, what price would it charge for a premium digital channel subscription to maximize its profit? How many subscriptions would it sell? b.) Assume there are two digital cable TV companies operating in this market. If they are able to collude on the quantity of subscriptions what would each fim's profit be? c.) Assume there are two profit-maximizing digital cable TV companies operating in this market. Further assume that they are not able to collude on the price and quantity of premium digital channel subscriptions to sell. At what price and quantity of premium digital channel cable TV subscriptions will this market reach a Nash equilibrium? How much total profit will the market achieve?
a.) 3 acres b.) 5 acres c.) 2 acres since 2/3 of the residents are willing to pay at least $8 per acre for a park that large. $8 is a third of $24, the cost per acre.
7.) Table: Consider the town of Springfield with only three residents, Sophia, Amber, and Cedric. The three residents are trying to determine how large, in acres, they should build the public park. The table below shows each resident's willingness to pay for each acre of the park. a.) Suppose the cost to build the park is $24 per acre. How many acres should the park be to maximize total surplus from the park in Springfield? b.) Suppose the cost to build the park is $9 per acre. How large should the park be to maximize total surplus from the park in Springfield? c.) Suppose the cost to build the park is $24 per acre and that the residents have agreed to split the cost of building the park equally. If the residents vote to determine the size of park to build, basing their decision solely on their own willingness to pay (and trying to maximize their own surplus), what is the largest park size for which the majority of residents would vote "yes?"? Why?