Q1. Fallsview Casino offers two gambles: G0(0, 100: 1⁄2, 1⁄2) and G1(0, 100: 3⁄4, 1⁄4). The fee to play either gamble is 1 but no one is playing G1. The Casino wants to make G0 and G1 equally popular for people with preferences u = w1/2 and will vary the payoffs to make this happen. There are two plans being considered.
Plan One: They will increase the payoff in gamble G1 by CV dollars G1(0, 100 + CV: 3⁄4, 1⁄4) so as to make these risk averse customers indifferent between this gamble and G0(0, 100: 1⁄2, 1⁄2).
Plan Two: They will decrease the payoff in gamble G0 by EV dollars G0(0, 100 - EV: 1⁄2, 1⁄2) so as to make these risk averse customers indifferent between this gamble and G1(0, 100: 3⁄4, 1⁄4).
a. Compute the values for CV and EV that would accomplish this task. Which plan would result in higher revenues for the casino? Provide a diagram showing the CV.
b. Explain why CV > EV for risk averse gamblers. Will CV < EV for risk lovers? Will CV = EV for risk neutrals? Why not?
Q2. Christine's cookies are produced using a precisely measured recipe. 1000 grams of flour must be combined in fixed proportion with either 4 small eggs or 2 large eggs. The recipe yields 50 yummy cookies. Shopping at the grocery store you can purchase flour for $1 per 1000-gram bag. Large eggs are 50 cents each; small are 20.
1. Write down the production function for this recipe.
2. Demonstrate that the production function exhibits constant returns to scale.
3. Derive the long run total cost function.
4. Graph AC and MC.
Q3. Adam's mom bakes these amazing delicious chocolate chip cookies combining inputs in fixed proportions. Using 100 grams of butter (B), 200 grams of brown sugar (S), 200 grams of flour (F) and 50 grams of chocolate chips (C) he can produce 50 cookies. At the grocery store butter is $4 per 400 grams, sugar is $8 per 1000 grams, flour is $4 per 2000 grams and chocolate chips are $16 per 200-gram package. Write down the Production Function for this process.
1. Write down the production function for this recipe.
2. Derive the Long-Run Total, Average and Marginal Cost Functions.
3. Graph AC and MC.
4. Demonstrate that this process exhibits CRTS.
Q5. Joel runs a firm that specializes in cutting the lawns for those big houses on Mississauga Road. He purchases gasoline at a price of $1.00 per litre. He hires students from his ECO220 tutorial and pays them $16.00 per hour for labour. Small 12" lawn mowers operate with a production function q = 25L1/3G1/3 while larger 24" lawn mowers have a production function q = 25L2/3G1/3 where output q measures square metres of grass.
a. Working with PL = $16 and PG = $1 derive the long-run total cost functions and long-run marginal cost functions for each type of lawn mower. Calculate the cost of cutting a q = 100 lawn using each type of lawn mower. Which machine is cheapest for this task?
b. Suppose you can use both lawn mowers on this q = 100 property. How would you divide up the task between the machines to minimize the cost of the job? Hint: equalize marginal cost curves from part a.
Q6. Short-run costs for firms "1", "2" and "3" are given by C1 = q12, C2 = 2q22 and C3 = q32 respectively. Assume that these firms behave under the rules of perfect competition and that these are the only firms in the industry. Derive the market supply curve. If demand is given by D = 260 - 2P, solve for equilibrium price, equilibrium quantity, the quantity supplied by each firm and profits earned by each firm.
Q7. A Perfectly Competitive Industry faces market demand Q = 800 - 20P and consists of many identical firms each with total costs C = q2 + 100. Beginning next month, the government will implement a per-unit tax. After entry and exit occurs, revenues from the tax can be calculated as R = t × Q2.
c. Calculate the value of t that will maximize the government's tax revenues.
d. Provide a labelled diagram showing equilibria p0, p1, p2.
e. Would the revenue maximizing tax be bigger if this was a DCI?
Q8. Each firm in a competitive, decreasing-costs industry DCI has costs given by C = q2 - nq + 16. Market demand is D = 20 - P. Your role as a government economist is to implement a per-unit tax on this industry. You should choose the tax rate to maximize the revenues collected R = t × Q2 after firms have had time to enter or exit the industry.
a. Provide the usual pair of diagrams showing The Firm and The Industry and supporting calculations to illustrate the impact of this tax.
b. A policy assistant suggests that the revenue maximizing tax rate would be lower if this was a constant cost industry CCI. Is she correct?
Q9. Country A has utility function U = XAYA, production functions xA = [9LXAKXA]0.25 and yA = [LYAKYA]0.25 and resource constraints KXA + KYA = 4 units and LXA + LYA = 4 hours. Country B has utility function U = XBYB, production functions xB = [LXBKXB]0.25 nd yB = [9LYBKYB]0.25 and resource constraints KXB + KYB = 4 units and LXB + LYB = 4 hours.
Determine the level of utility that each country could enjoy in the absence of free trade.
Find the exchange rate that will occur under free trade. For each country, provide diagrams showing the PPF.
Provide a second set of diagrams showing the Edge worth Box for Production in each country.
Q10. Country A has utility function UA = X1AX2A with production functions X2A = 10L2A and X1A = L1A1/2 and the total labour endowment is 12 persons, L1A + L2A = 12. Country B has utility function Utility is UB = X1BX2B with production functions X2B = L2B and X1B = L1B1/2 and the total labour endowment is 210 persons, L1B + L2B = 210. Demonstrate that Free Trade will increase utility in both countries. Provide fully labelled PPF diagrams for each country that shows the open economy and closed economy results.
Q11. A price discriminating monopolist has total costs C = 2Q2. The firm sells to students, who have elasticity E1 = - 5.00 and to professors who have elasticity E2 = - 2.00. The firm wishes to sell precisely 100 units of output. What prices should be charged? Provide a labelled diagram showing prices, quantities and profit. (February 2007).
Q12. A campus restaurant can act as a monopolist selling meals to students, with demand QS = 100 - 2P and to faculty who have demand QF = 140 - 2P. The firm has total costs given by C = 0.5Q2.
1. Provide diagrams to illustrate and quantify how an ordinary price discrimination (third degree) plan will increase profits over a single-price monopoly plan.
2. Fire regulations only allow them to serve 32 customers. What is the profit maximizing strategy that you would recommend for the restaurant? Should the restaurant just sell to professors?
Q13. Mikey is an 11-year-old kid with a promising future. For the past three summers, he has operated a window washing company in the area around his family cottage. Since Mikey is the only person providing this service he is a monopolist. Mikey hires the other kids in the area to work for him. The little boys have labour supply function LB = wB - 3 while the little girls have labour supply function LG = wG - 5. Since Mikey is the only source of employment he is also a monopsonist. Market demand is Q = 72 - 8P and his production function is Q = 2L.
Provide a fully labelled diagram and supplementary calculations to explain how Mikey has implemented a wage discrimination scheme. Calculate his profit maximizing output level, the price he charges.
Show that the ability to wage discriminate makes his operation more profitable.
Q14. Workers in Niagara Falls USA with labour supply L = w - 60 use production functions Q = 0.1L and sell per demand P = 1800 - 100Q. All firms in this industry are wage-taking price takers. The same services are produced in Niagara Falls Canada by workers with labour supply L = w - 40 using production functions Q = 0.1L with output is sold per demand P = 1200 - 100Q. Canadian firms are also wage-taking price takers. Strict enforcement by the RCMP at the Canadian border makes it impossible to transport this commodity between markets. (September 2010).
a. Compute equilibrium w, L and P in the American market and w, L and P in the Canadian market. No diagram required.
b. If workers can commute by driving across the bridge, there is a single labour market. Aggregate the labour supply and the labour demand curves. Solve for equilibrium w, L. Solve for equilibrium P in each market.
c. Provide a set of 3 diagrams showing the two local labour markets and the aggregated labour market. Show the number of commuters in your diagram.
d. Factor mobility (commuting) eliminates differentials between prices even when a commodity cannot be transported between markets. Explain.
Q15. Firms with costs C = q2 + 36 face demand P = 24 - nq and behave under the rules of Monopolistic Competition. Compute and illustrate the prices and quantities that occur in the short run, with one monopolist, and in the long run, where entry has occurred. Illustrate, calculate and explain how the efficiency loss is affected by this entry.
Q16. For nearly 3 years 16-year old Lynn has had monopoly power over babysitting on her street. Now a new family with a 14-year old girl named Elizabeth has moved in. Suppose that Lynn operates as an incumbent monopolist with total costs CL = QL2 + 16. Elizabeth has total costs CE = QE2 + 54. Market demand for babysitting is QD = 24 - 2P. Demonstrate how Lynn could reduce price in a way that would deter Elizabeth's entry into the market. Briefly explain your answer. What would happen to Lynn's profits because of this plan? Provide a labelled diagram.
Q17. A professional basketball team produces baskets B, by combining forwards F and guards G. The production function is B = f (F, G). Assume that each input exhibits diminishing marginal productivity. A team has 15 players. Suppose the Toronto Raptors trade Jose Calderon, one of the team's four guards, to the Boston Celtics for Kevin Garnett, a forward.
Graph Toronto's marginal product curve for forwards and their marginal product curve for guards. How would this trade affect the two curves?
Under what conditions would this trade increase the number of baskets scored by the team?
Q18. The Cycle of Life Model suggests that life consists of two periods. In Period 1 you are young and able to earn income. In Period 2 you are retired. The model usually assumes that you can borrow and/or save at the bank but sometimes there are no banks. Suppose you find yourself stranded on an island. Your only companion is a five-year-old named Simba. You and Simba both have symmetric Cobb Douglas preferences. Because you are a healthy, strong adult you are able to hunt and collect 8 units of food per day; young Simba can only collect 2. You and Simba are both getting older. Simba is getting stronger every day; but sadly, you are losing your abilities, losing your hair and even losing your teeth. In Period 2 you anticipate that you will only be able to collect 3 units of food per day but a healthy, strong and adult Simba will be able to collect 12. In the absence of a banking sector, but with endowments of (8, 3) and (2, 12) what is the pareto optimal strategy that you and he should follow? Explain why this strategy is pareto optimal. Provide a labelled diagram that illustrates how you and Simba will behave.