a.Discussion Questions:
8 – If the price increases by 10 percent, by how much does the quantity of household ( a) natural gas and ( b) electricity change in the short run and in the long run? ( Hint: Use the price- elasticity values in Table 4- 3.)
10 – Agricultural commodities are known to have a price- inelastic demand and to be necessities. How can this information allow us to explain why the income of farmers falls ( a) after a good harvest? ( b) In relation to the incomes in other sectors of the economy?
b.Problems:
3(a) and (b) – Starting with the estimated demand function for Chevrolets given in Problem 2, assume that the average value of the independent variables changes to N = 225 million, I = $ 12,000, P F = $ 10,000, P G = 100 cents, A = $ 250,000, and P I = 0 ( i. e., the incentives are phased out). ( a) Find the equation of the new demand curve for Chevrolets. ( b) Plot this new demand curve, D’ C , and, on the same graph, plot the demand curve for Chevrolets, D C , found in Problem 2( d).
7 – The total operating revenues of a public transportation authority are $ 100 million while its total operating costs are $ 120 million. The price of a ride is $ 1, and the price elasticity of demand for public transportation has been estimated to be – 0.4. By law, the public transportation authority must take steps to eliminate its operating defi cit. ( a) What pricing policy should the transportation authority adopt? Why? ( b) What price per ride must the public transportation authority charge to eliminate the defi cit if it cannot reduce costs?
9 – A researcher estimated that the price elasticity of demand for automobiles in the United States is – 1.2, while the income elasticity of demand is 3.0. Next year, U. S. automakers intend to increase the average price of automobiles by 5 percent, and they expect consumers’ disposable income to rise by 3 percent. ( a) If sales of domestically produced automobiles are 8 million this year, how many automobiles do you expect U. S. automakers to sell next year? ( b) By how much should domestic auto-makers increase the price of automobiles if they wish to increase sales by 5 percent next year?
14 – Suppose that a fi rm maximizes its total profi ts and has a marginal cost ( MC) of production of $ 8 and the price elasticity of demand for the product it sells is (-) 3. Find the price at which the fi rm sells the product.
Note:
1.D8: Calculate the percentage decrease in quantity due to 10% increase in price.
2.P3(a): Substitute the given value of independent variables into the equation in problem 2 and show the new equation as Qc= a – 100Pc, a is a number. See equation (4-5) as the example (p. 128).
3.Revised P3(b). If Pc is $10,000, find the value of Qc.
4.P7(a) is asking should the transportation authority increase or decrease the price per ride based upon the price elasticity of demand.
5.P7(b): Suggestion – increase the price of a ride from $1 to be $1.50, a 50% increase in price. Given the price elasticity of demand of -0.4, calculate the percentage change in the ride and the total new rides (the original rides are 100 million = $100 million/$1) using equation (4-7). Then use the total new rides time the new price of $1.50 to obtain the new total revenue.
6.P14: Use equation (4-12) to find the answer. To maximize the profit, MR=MC=$8.
Froeb et al.’s Chapter 6:
a.Individual problems:
6-1 – George has been selling 5,000 t-shirts per month for 8.50. When he increased the price to 9.50 he sold only 4,000 t-shirts. What is the demand elasticity? If his marginal cost if $4 per shirt, what is his desired markup and what is his initial actual markup? Was raising the price profitable?
6-3 – To conduct an experiment, AMC increased movie ticket prices from $9 to $10 and measured the change in ticket sales. Using the data over the following month, they concluded that the inclrease was proftable. However, over the subsequent months, they changed their minds and discontinued the experiment. How did the timing affect their conclusion about the profitability of increasing prices?
6-5 – An end-of-aisle price promotions changes the price elasticity of a good from -2 to -3. If the normal price is $10, what should the promotional price be?
Note:
1.P6-1: Use price elasticity estimator on page 64. The desired markup is 1/׀e׀=1/the absolute value of the price elasticity. The initial actual markup is (P-MC)/P, P=$8.50.
2.P6-3: What would happen to the elasticity of demand in the long run (p. 67).
3.P6-5: Use (P-MC)/P = 1/׀e׀ to calculate MC and then use the same equation to find out the new price.
Salvatore’s Chapter 5:
a.Problems:
8 – In a study published in 1980, B. B. Gibson estimated the following price and income elasticities of demand for six types of public goods:
State of activityPrice elasticityIncome elasticity
Aid to the needy-.83.26
Pollution control-.99.77
Colleges and universities-.87.92
Elementary school aid-1.161.14
Parks and rec areas-1.021.06
Highway construct and main-1.09.99
( a) Do these public goods conform to the law of demand? For which public goods is demand price elastic? ( b) What types of goods are these public goods? ( c) If the price or cost of college and university education increased by 10 percent and, at the same time, incomes also increased by 10 percent, what would be the change in the demand for college and university education?
15(b) and (c) – Integrating Problem Starting with the data for Problem 6 and the data on the price of a related commodity for the years 1986 to 2005 given below, we estimated the regression for the quantity demanded of a commodity ( which we now relabel Q ˆ X ), on the price of the commodity ( which we now label P X ), consumer income ( which we now label Y), and the price of the related commodity ( P Z ), and we obtained the following results. ( If you can, run this regression yourself; you should get results identical or very similar to those given below.)
Year 1986 1987 1988 1989 1990 P Z ($) 14 15 15 16 17
Year 1991 1992 1993 1994 1995 P Z ($) 18 17 18 19 20
Year 1996 1997 1998 1999 2000 P Z ($) 20 19 21 21 22
Year 2001 2002 2003 2004 2005 P Z ($) 23 23 24 25 25
Q ˆ X = 121.86 – 9.50P X + 0.04Y – 2.21P Z (– 5.12) ( 2.18) (– 0.68) R2 = 0.9633 F = 167.33 D– W = 2.38
( b) Evaluate the above regression results.
( c) What type of commodity is Z? Can you be sure?
appendix problem 2 (p. 215)
Note:
1.P15(b) is to evaluate the above regression results in terms of the signs of the coefficients, the statistical significance of the coefficients, and the explanatory power of the regression (R2). The number in parentheses below the estimated slope coefficients refer to the estimated t values. The rule of thumb for testing the significance of the coefficients is if the absolute t value is greater than 2, the coefficient is significant, which means the coefficient is significantly different from 0. For example, the absolute t value for Px is 5.12, which is greater than 2; therefore, the coefficient of Px, (-9.50) is significant. In order words, Px does affect Qx. If the price of the commodity X increases by $1, the quantity demanded (Qx) will decrease by 9.50 units.
2.P15(c). Are X and Z complements or substitutes?
3.For appendix problem 2, use the table right under the problem on page 215, not Table 5-6, for the regression analysis. Enter the data in columns like table 5-11.
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