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THE A. GEORGE WASHINGTON UNIVERSITY Department of Economics Sixth Problem Set Answers in Econ 11 Fall 2007
1. On Blackboard under the November 19th date, you will find a word file that is an outline of the course. For topics that we will have covered by November 28th , please fill in all the key ideas that we have covered under each topic. Include all the golden rules, important equations, and types of diagrams as well as skills such as maximizing utility given prices. The answer to this question will become the basis for your review efforts before the final examination.
Course Outline To Answer Problem Set #6 Question #1
I. Introduction To The Course & Subject - Basic Concepts A. Thoughts On The Textbook And Learning Economics Lots of key concepts in economics like opportunity cost, scarcity, marginal analysis, etc. B. Scarcity & Choice Using Production Possibility Frontiers Know how production functions for two goods combined with limits on inputs taken together generate a PPF. Be able to do this for linear production as in the "Mr. Chips" case. Know what shifts a PPF in and out. Understand how the slope of a PPF indicates opportunity cost. Understand technical efficiency as a point on the PPF and contrast this with inefficient points inside the PPF and infeasible points outside the PPF. Allocative efficiency requires that the correct mix of products be produced represented by the point where the iso-revenue line is tangent to the PPF. Plot iso-revenue lines given information on product prices. Find the revenue -maximizing output of the two goods. Generate a supply response of the firm in response to a change in product prices that changes the slope of the iso-revenue line. Find the revenue -maximizing output when the PPF is linear. Identify comparative advantage when there are two linear PPF's with different slopes. Solve problems in which you identify where production should take place. C. Introduction to Markets: Supply & Demand Analysis, Exchange The concept of market demand and market supply curves along with market equilibrium price and quantity. Understand what happens if price is above or below equilibrium (inventory change). Solve problems involving the effects on market equilibrium of shifts in demand and supply or on taxes and subsidies on a simple S&D diagram. D. Solving Problems With Supply & Demand, Concept of Elasticity Own price elasticity of demand and the relation between own price elasticity and changes in total revenue. E = %?Q/%?P and %?Revenue = %?Q + %?P Cross price elasticity, income elasticity, and elasticity of supply.
II. What's Behind Demand Curves? Consumer's Demand Theory A. Individual & Market Demand, Marginal & Total Willingness to Pay Total and marginal utility curves. Equal marginal utility principle when two goods have the same price. Golden rule for maximizing utility: MRS = price ratio for all goods consumed. Or for goods A, and B, MU A/MU B = PA/PB Identify consumer surplus on a demand curve. Solve for the consumer surplus in complex transactions involving multi-part pricing such as the "all you care to eat for a fee case" or "club" pricing in which paying a fee entitles the consumer to a reduced price. Develop the ability to add individual demand curves horizontally to form the market demand curve. Go from individual demand to market demand and use price determined on the market diagram to determine consumption by each type of consumer on the individual demand curve. III. Cost and Production - Theory of the Firm - Foundations of Supply A. Technology, Productivity And Production The KLEM production function, Q = F(K,L,E,M). Total, average, and marginal product curves, including the skill of finding the relation between average and marginal product by drawing a ray from the origin to the total product curve to determine average product. B. Short-Run Cost Curves, Output & Profit Maximization Total fixed, and variable cost curves. Short run total, average, average variable and marginal cost curves all drawn correctly using the big stick to find the output levels at which average and average variable costs are minimized. Golden rule for hiring inputs to minimize cost: Marginal Rate of Technical Substitution = MRTS = MP L/MP K = W/r. This can be restated as the requirement that the marginal cost of producing output be equal for all inputs used in the production process or: W/MP L = r/MP K = MC S of producing output. Golden rule for a price-taking firm to maximize profit in the short run: P = MC and P = AVC. Note AVC is the short run shut down point. Develop the ability to add short run marginal cost curves of firms to form the market supply curve of the industry. C. Cost Curves & Supply-Demand Interaction In Competitive Markets Long run cost curves and the supply of output in the long run. Golden rule for long run profit maximization by a price-taking firm is P = MC and P = ACL. Entry and exit of firms in the long run based on economic profit. External economies and diseconomies of scale give rise to long run supply of constant, increasing, and decreasing cost industries. Analyze the short and long run effects of demand and input cost shifts, taxes, and subsidies in constant, increasing, and decreasing cost industries.
IV. Market For Inputs (Factors) Labor, Land, Capital
A. Labor & Land Markets: Determinants Of Wages, Salaries, & Rents Demand for inputs based on marginal revenue product of that input. This follows from the Golden rule for cost minimization above because if W/MPL = r/MP K = MC = P, then P(MP L) = W and PMP K = r. Go from input demand by individual firms to market demand for inputs by adding horizontally. Labor supply based on demand for leisure as shown by consumer demand theory rising wages raise the price of leisure and require consumers to lower leisure by working more. B. Capital And Land Markets: Rent, Interest & Profits Land supply fixed and demand based on MRP of land added horizontally. Capital supply comes from the theory of the firm (like supply of goods) but capital lasts over time so the Golden rule for hiring capital sets PK = Discounted Present Value of MRPK V. Market Efficiency: Why is it Important? When does it Occur? Technical efficiency produce given output at minimum cost requires MRTS = input price ratio or Golden rule for cost minimization above because if W/MP L = r/MP K = MC. This can be stated alternatively that the marginal cost of producing output be equal for all inputs used in the production process. Allocative efficiency produce the "correct" mix of outputs. This requires technical efficiency as a necessary condition and then requires price equal to marginal cost and that consumers can set the marginal rate of substitution in consumption equal to the price ratio or it require s, W/MPL = r/MP K = MC = P and MRS = price ratio for all goods consumed. Or for goods A, and B, MU A/MU B = PA/PB
I did not require that you deal with item IV on the reading list but I am providing the answer below in order to help you prepare for the final.
IV. Economics of Imperfect Competition, Monopoly, Oligopoly, & All That A. The Problem of Monopoly and Antitrust Policy as Solution Monopolists face the market demand curve which means that they do not have a linear total revenue curve like price taking firms. Golden rule for monopolists to maximize profit is that Marginal Revenue = MR = MC . Price is then greater than both MR and MC, and this means that while monopolists are technically efficient they are not allocatively efficient because P > MC so they produce TOO LITTLE. You must be able to draw marginal revenue curves associated with linear demand curves (easy, the MR curve has the same price intercept as demand and twice the negative slope i.e. the intercept on the Q axis is half as large as the demand curve). Identify monopoly profit or rent as the difference between price and average cost multiplied by output = (P AC)Q. Be able to draw diagrams of different types of monopolists, including zero profit monopoly and "natural" monopoly. B. Oligopoly & Monopolistic Competition - Game Theory, Antitrust In this section, you should concentrate on game theory. Learn to write down a payoff matrix for the firms involved and then to identify the cooperative
equilibrium, dominant strategy equilibrium, Nash equilibrium in pure strategies, and lack of Nash equilibrium in pure strategies mixed strategy equilibrium. C. Externalities, Public Goods, & Government Regulation or Provision Understand and apply the concepts of non-rivalry and non-exclusion as they apply to public goods. Understand the effects of taxes and subsidies on markets (you had this earlier, now don't forget it) Understand the welfare loss associated with markets where there are either positive or negative externalities associated with either production or consumption of a good and the way in which market strategies (taxes and subsidies) can deal with these problems. Understand the Coase Theorem and the way in which firms and consumers can bargain and contract over externalities. D. Comparative Advantage, Globalization, and International Trade Don't forget what you learned about comparative advantage with linear PPF's under topic IB above. Also be able to use horizontal addition of domestic supply from a country as well as imports from the rest of the world to determine the fraction of imports to a county and the way tariffs can change the level of imports. 2a. For those of you going home over Thanksgiving, discuss investments (including real estate) owned by your parents. Consider whether they are taking unique risk and if they are well diversified. If they are taking unique risk, consider steps that could be taken to diversify away this risk. I hope that you did this and that you will continue to have such conversations with your parents in the future to let them benefit from your GW education. 2b. Go to the Yahoo Finance website. Enter the symbol for a stock (you may pick one from the newspaper). Note the share price. Click "key statistics" note the "market capitalization" (the market value of all the shares of stock in the firm) and the "Beta" (which measures the specific risk of the stock. A Beta of 1.0 indicates average level of risk compared to other stocks) and the dividend. Go back to the initial page, click on the "five year" chart for the stock. Then click the option that shows the Dow Jones Average over the same time period. Compare the volatility of your stock with the Dow (which has a Beta of 1.0). Which had a greater percentage increase over the past 5 years? If your stock has a Beta > 1.0 (< 1.0) its total return (including dividends) should be larger (smaller) than the Dow is this true? Now repeat the exercise for another stock with a different Beta. What have you learned? The chart below shows stock price movements for the general Dow Jones Industrial Average, Kellogg Company (symbol "K"), and Pappa Johns International (symbol "PZZA"). Note that these charts just reflect the changing price of the stock and fail to include the dividend return (which has been about 2% per year on the Dow Jones Average and on K and 0% per year on PZZA). Movement of the Dow is a reflection of systematic risk of fluctuation in the general economy. K has a Beta of only 0.15 indicating very little systematic risk but PZZA
has a Beta of 1.85 indicating substantial systematic risk (or that PIZZA moves with the Dow and is about twice a volatile). As you may note from the charts below, it appears that K is not very volatile at all and not highly correlated with the Dow and PZZA is more volatile than the Dow and fairly well correlated with it. This is a case in which looking at a single statistic, Beta, gives substantial information about the risk characteristics of individual securities.
3. In each case, consider the source of unique risk that might be involved and how that risk might be diversified away. In each case, identify unique risk by thinking of the bad things that could happen things that could cause financial loss other than general recession (systematic risk). Then think of ways in which one could use financial markets to diversify away the risk (variance) in that loss. 3a. You own a rice farm Sources of unique risk include (1) crop failure, (2) fall in price of rice, (3) fall in price of farm land. Diversify away risk as follows: (1) crop failure we have crop insurance in the US, (2) fall in price of rice, it is possible to sell rice in the commodity futures market run by the Chicago Merchantile Exchange
buy a contract to sell rise at a fixed price in the future when your rice crop will hit the market and, if the price of rice is lower then, you the high value of your futures contract will make up for the lower price of your crop. (3) I'm not sure what you do about the risk of farm land prices falling. 3b. You work for Wallmart Sources of unique risk include (1) you will be fired or laid off, (2) you retain your job but K-Mart cuts wages and benefits relative to other firms. Diversify away unique risk as follows (1) we have a government unemployment insurance program {government insurance can also diversify some of the systematic risk of recession that are associated with higher unemployment}, (2) you could buy shares in other retailers that compete directly with K-Mart or you could buy shares in industries that tend to prosper when retail industries struggle. 3c. You must drive your automobile 100 miles per day in connection with your work. Sources of unique risk (1) include rising gasoline prices (2) automobile wreck (3) automobile suffers mechanical problems. Diversity away unique risk by (1) buy shares in an oil company (refiner and producer of petro leum), buy an energy industry mutual fund, (2) buy insurance against collision for your auto, (3) you can buy automobile repair insurance. 3d. You own a house in Scranton, PA. Sources of unique risk include (1) fire, flood, etc and (2) fall in price of ho using in Scranton. Diversity away unique risk with (1) property insurance against fire, flood, etc and (2) risk of house price fall in Scranton not yet set up as a market yet but coming soon. By maintaining a large mortgage, you limit the amount that you can lose in the event that there is a major decline in housing prices. 3e. You own stock options in Millennium Pharmaceuticals Sources of unique risk include (1) risk that Millenium's drugs will either fail to work or fail to sell and stock price will decline, (2) risk that the general drugs sector of the economy will experience falling stock prices. Note risk that stock price declines because the entire stock market declines is systematic risk not unique and can't be diversified away. Diversify away unique risk of drug failure by holding shares in competing drug companies. Diversify away unique risk of fall in prices of drug stocks generally by holding a mutual fund invested in the general stock market. 4. In Chapter 11 of Hamermesh, answer questions 11.2, 11.4, and 11.8 11.2 Deer in an urban area are a nuisance but a public policy allowing individuals to shoot them would not be Pareto Optimal because it would benefit some residents but make others worse off. Ignoring those with a "bambi" complex, many residents would be disturbed by the shooting (and particularly by the missing) and would rather have the deer with no gunshots than have few deer but hear periodic shooting in a residential area. 11.4 Apparently Hamermesh made a charitable contribution and received 4 concert tickets in return. Giving away 2 tickets was Pareto Optimal because he felt better and so did the recipient. However giving away cash to the frient would not be Pareto Optimal because clearly Hamermesh is not the type of person to give $ to his friends.
11.8 Switching textbooks to a better book makes the instructor, students, and publisher of the better book happy. But the publisher of the old book is not better off and this change is not Pareto Optimal. Some may believe that this reveals a problem with Pareto Optimality because it requires unanimity. It is true that Pareto Optimality is a very conservative criterion and will reject many changes that are overwhelmingly popular. However, in such cases, the majority who benefit might try to find ways to compensate the minority who lose. 5. In Chapter 15 of Hamermesh, answer questions 15.5, 15.7, 15.9, and 15.11. 15.5 Hamermesh notes that some children would rather have one sweet before dinner than 2 sweets after dinner. This implies a VERY high discount rate. But it also may reflect the fact that they are hungry before dinner and not hungry after dinner so the marginal utility of food falls after dinner. In the case of a $ tradeoff, the same child might well prefer $2 after dinner to $1 before dinner. 15.7 The problem notes that the $100 million lottery actually pays either $37.5 million today ($50 million today taxed at 25%) or 25 annual payments of $3 ($4 less 25% tax), with total payments of $75 million. But Hamermesh notes that the 25 payments of $3 discounted to a present value at 5% would only be about $37 million so the two payment alternatives were essentially equivalent. He then asks what would happen if interest rates rose to 20%. At this higher interest rate, the 25 payments of $3 million would be far less than $30 million so take the money and run. 15.9 Hamermesh notes that Enron employees who claim to have lost a fortune when the company failed are basing their losses on the inflated price of the stock that included extraordinary returns generated by the accounting fraud. An employee who put $10,000 in the pension fund would have a paper profit of $33,000 by 2000 when the stock price collapsed. How much did the employee actually lose? Compared to a normal return of perhaps 10% per year over 1997-2000 in which the employee would have had $14,641 by 2000, and this is the loss (much less than the $43,000 loss using an inflated stock price) based on a normal market rate of return. 15.11 Assume that the cost of neutering a dog is $100 and that there is an annual "saving" on dog licenses of $20 for those who neuter their dogs. How long does Fido have to live to make neutering pay? You are comparing $100 today with a string of $20 per year. The present value of the $20 savings in each year can be discounted to a present value until it reaches $100. Let's do it assuming that interest rates are 10%. PV = 20 + 20/1.1 + 20/(1.1)2 + 20(1.1)3 + 20/(1.1)4 + 20(1.1)5 + PV = 20 + 18.2 + 16.5 + 15.0 + 13.7 + 12.4 + 11.3 = 107 > 100, so the PV of the savings is equal to $100 sometime during the 7th year. Without discounting you might think that dog owners would break even in 5 years. 6a. Chrysanthi's Tutoring is a economics tutoring firm. Chrysanthi is confronted with the following relation between the number of lessons that can be taught per day and
the number of tutors hired displayed in the table below. If the wage of tutors is $60 per day, fill in the table below. Number of Lessons/Day 0 6 12 17 21 24 26 27 Number of Workers 0 1 2 3 4 5 6 7 Marginal Product of Workers 0 6 6 5 4 3 2 1 Marginal Cost=60/Marg. Product 10 10 12 15 20 30 60 Marginal Cost=40/Marg. Product 6.6 6.6 8 10 13.3 20 40 6b. Based on your analysis of 6a, if the market price for lessons is $20, how many tutors should Chrysanthi hire to maximize her profits? Explain. If price = $20 and Chrysanthi is a price taker, she should hire 5 tutors and give 24 lessons/day because profit maximization occurs where p = MC = 20. 6c. How would your answer to 6b change if the price for lessons were $30? If the wage of tutors were $40 per day. What does this tell you about the determinants of the demand for tutors? If price = $30, the wage of tutors is $40, and Chrysanthi is a price taker, she should hire 6 tutors and give 26 lessons/day because profit maximization occurs where p = MC and this occurs somewhere between 6 and 7 totors. We learn that a rise in output price and fall in input price causes the price-taking Chrysanthi to hire more tutors and supply more lessons as she maximizes profits. 7a. Assume that the total cost in dollars per month of production at Jahangir's Kayaks is given by TC = 10,000 + 800 K, where K is kayaks per month. What is the total cost of producing 1, 2, 3, 4, 5, 6 kayaks per month. What is the marginal cost of a kayak? What is the average cost per kayak? Find a general expression for Jahangir's average cost. If TC = 10,000 + 800K, then cost of 3 kayaks = TC(3) = 10,000 + 800(3) = 12,400; and TC(4) = 10,000 + 800(4) = 13,200; TC(5) = 10,000 + 800(5) = 14,000; TC(6) = 10,000 + 800(6) = 14,800. Marginal cost is the change in total cost and it equals 800 in all cases. Given that marginal cost is constant, i.e. the marginal cost curve is horizontal and assuming price equals marginal cost, producers' surplus is equal to 0. 7b. Now assume that total cost in dollars per month of production at Jahangir's Kayaks is now given by TC = 10,000 + 800 K + 5K2 . What is the total cost of producing 1, 2, 3, 4, 5, 6 kayaks per month. What is the marginal cost of a kayak? What is the average cost? Find a general expression for average cost. If TC = 10,000 + 800 K + 5K2 , then total cost of 3 kayaks is TC(3) = 10,000 + 800(3) + 5(32 ) = 10,000 + 2,400 + 45 = 12,445. TC(4) = 10,000 + 800(4) + 5(42 ) = 13,280. TC(5) + 10,000 + 800(5) + 5(52 ) = 14,125. TC(6) = 10,000 + 800(6) + 5(62 ) = 14,980. Thus marginal cost of the 4th kayak = MC(4) = change in TC = 13,280 12,445 = 835. MC(5) = 14,125 - 13,280 = 845. MC(6) = 14,980 - 14,125 = 855. Note that marginal cost is rising in this case. Thus if price were equal to MC(6) = 855, then producer's surplus would be $20 = 855 - 835 on the 4th kayak and $10 = 855 845 on the 5th kayak. Note that producers' surplus is based on the difference of price and marginal cost.
8. Assume that the market price of tires is currently $50 each and that the government proposes providing a $10 per tire specific subsidy for tires. 8a. If tire production is a constant cost industry, draw short and long run supply curves. What you expect to happen to price and output in BOTH the short and long run. If you provide a subsidy to a constant cost industry, cost curves are all shifted down by the amount of the subsidy and so is the bottom of the bird's nest (indicating the point where each firm is in zero profit equilibrium). In the short run, price falls along the demand curve because the short run supply curve shifts down by the amount of the subsidy. But price net of subsidy (i.e. the price received by the firm) has risen and this means economic profits at firms in the industry. Firms enter the industry but, because this is a constant cost industry, this has no external effect on the cost curves of the remaining firms. Therefore entry continues, with rising output, and short run supply shifts right along the market demand curve until price gross of subsidy (price paid by the consumer) falls until it is below the original price by the full amount of the subsidy and price net of subsidy (received by the firm) equals the original price. 100% of the amount of the subsidy cost is "received" by consumers. 8b. If tire production is an increasing cost industry, draw short and long run supply curves. What you expect to happen to price and output in BOTH the short and long run. This is the typical case presented earlier in this course. The long run supply curve has a positive slope. In the short run, price falls along the demand curve because the short run supply curve shifts down by the amount of the subsidy. But price net of subsidy (price received by the firm including the subsidy) has risen and this means economic profits at firms in the industry. Firms enter the industry. Because this is an increasing cost industry, this entry has an external effect on the cost curves of the remaining firms, causing costs to fall. Therefore entry continues, with rising output, and short run supply shifts right along the market demand curve but price gross of subsidy only has to fall until price net of subsidy hits the falling level of the bottom of the bird's nest - i.e. price gross of subsidy will fall below the original price by less than the full amount of the subsidy and price net of subsidy will be lower than the original price. Less than 100% of the amount of the subsidy is "received" by consumers because price gross of (including) subsidy has fallen by less than the subsidy and price net of subsidy received by the firms has risen as the bottom of the bird's next rose due to entry. 8c. If tire production is a decreasing cost industry, draw short and long run supply curves. What you expect to happen to price and output in BOTH the short and long run. Be very careful because this is a tricky case - ideal for examination questions. The long run supply curve has a negative slope. In the short run, price falls along the demand curve because the short run supply curve shifts down by the amount of the subsidy as in all cases above. But price net of subsidy (price received by the firm
including subsidy) has risen and this means economic profits at firms in the industry. Firms enter the industry. Because this is an decreasing cost industry, this entry has an external effect on the cost curves of the remaining firms, causing costs to fall. Therefore entry continues, with rising output, falling costs and short run supply shifts right along the market demand curve. Price gross of subsidy (price paid by consumers) has to fall until price net of subsidy hits the falling level of the bottom of the bird's nest - i.e. price gross of subsidy will be below the original price by MORE than the full amount of the subsidy and price net of subsidy will be lower than the original price because entry has caused cost curves to shift down. MORE than 100% of the amount of the subsidy revenue is "paid" by consumers because price gross of (including) subsidy has fallen by MORE than the subsidy and price net of subsidy received by the firms has fallen. 9. Alex's Magic Hands Inc. produces massages. The only variable input is labor which is paid $200 per day. Assume that the marginal product of labor, measured as massages per day, is given by MPL = 20 - 0.2L, where L is labor in days. 9a. What is the marginal product of the 10th worker? MPL = 20 - 0.2(10) = 18 What is the marginal cost per massage produced by the 10th worker? Marginal cost is Wage/Marginal Product so, if MPL = 18, MC = 200/18 = $11. 9b. If the price of a massage is $40, how many workers will Alex hire? Maximize profit by setting W = $200 = MRPL = PM MPL = 40(20 - 0.2L) and solve for L = [(200/40) - 20]/-0.2 = [5 - 20]/-0.2 = -15/-0.2 = 75 workers 9c. If the price of a massage falls to $20, how many workers will Alex hire? Maximize profit by setting W = $200 = MRPL = PM MPL = 20(20 - 0.2L) and solve for L = [(200/20) - 20]/-0.2 = [10 - 20]/-0.2 = -10/-0.2 = 50 workers 9d. If the price of a massage falls to $10, how many workers will Alex hire? Maximize profit by setting W = $200 = MRPL = PM MPL = 10(20 - 0.2L) and solve for L = [(200/10) - 20]/-0.2 = [20 - 20]/-0.2 = -0/-0.2 = 0 workers and Alex does not operate if P = 10.