Generalidades - MANUAL DE FUNCIONAMIENTO (CE) ROUGH TERRAIN SCISSORS MODELOS SJ8831 RT SJ8841 R

Sección 3: operación

3.1 Generalidades

linear demand function at the market equilibrium is -1.5. Then we know that:

A. demand is inelastic. B. marginal revenue is $8. C. marginal revenue is $20. D. demand is unit elastic.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-04 Explain the relationship between marginal revenue and the own price elasticity of demand. Topic: Own Price Elasticity of Demand

Essay Questions

157. Several years ago the National Association of Broadcasters imposed restrictions on the amount of nonprogram material (commercials) that could be aired during children's television shows, effectively reducing the quantity of advertising allowed during children's viewing hours by 33 percent. Within four months, the price of a minute of advertising on network television increased by roughly 14 percent. What impact do you think this had on the revenues of the networks?

The own price elasticity of demand for advertising time is the percentage change in quantity demanded (-33 percent) divided by the percentage change in price (+14 percent), which is - 2.36. Thus, the demand for advertising minutes by those who sell children's products is elastic. By the total revenue test, we would expect this to decrease network revenues.

AACSB: Reflective Thinking Blooms: Understand Difficulty: 1 Easy Learning Objective: 03-02 Illustrate the relationship between the elasticity of demand and total revenues. Topic: Own Price Elasticity of Demand

158. A study sponsored by the American Medical Association suggests that the absolute value of the own price elasticity for surgical procedures is smaller than that for the own price elasticity for office visits. Explain why this would be expected.

The demand for surgical procedures is generally more inelastic than the demand for office visits, since most surgical procedures do not have close substitutes. In contrast, there are close substitutes for many types of office visits. For example, a patient can purchase over-the-

counter drugs. Another explanation is that surgical procedures are usually needed immediately, while office visits can often wait.

159. Suppose the monthly demand for soda by a consumer is given by .

a. If the price of soda is $1 per can, how many sodas will the consumer purchase in a typical month?

b. What is the elasticity of demand for soda?

a. Sodas purchased by a consumer in a typical month: Q = 10 - 8(1) = 2 (cans). b. EQ,P = -8P/Q = -8 (1/2) = -4.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-05 Show how to determine elasticities from linear and log-linear demand functions. Topic: Obtaining Elasticities From Demand Functions

160. The demand function for DVD players has been estimated to be QPlayer = 134 - 1.07PDVD +

46Pm - 2.1PDVD - 5M, where QPlayer is the quantity of DVD players, PDVD is the price of a

videocassette, Pm is the price of a movie, PPlayer is the price of a DVD player, and M is income.

Based on this information, answer the following questions. a. Are DVD players normal or inferior goods?

b. Are movies substitutes or complements for DVD players?

c. What additional information is needed to calculate the price elasticity of demand for DVD players?

a. Since the coefficient associated with income is negative, an increase in income leads to a reduction in demand for DVD players. Hence, DVD players are inferior goods.

b. Movies are substitutes for DVD players, since the coefficient associated with the price of a movie is positive.

c. The actual values of prices and income are needed to calculate the price elasticity of demand for DVD players.

AACSB: Reflective Thinking Blooms: Understand Difficulty: 1 Easy Learning Objective: 03-05 Show how to determine elasticities from linear and log-linear demand functions. Topic: Obtaining Elasticities From Demand Functions

161. When the price of butter was "low," consumers spent $5 billion annually on its consumption. When the price doubled, consumer expenditures increased to $7 billion. Recently you read that this means that the demand curve for butter is upward sloping. Do you agree? Explain.

Disagree. Let P be the initial price and 2P the new price. Then Q(P) × P = $5 billion

Q(P) × P = $5 billion Q(2P) × P = $7 billion

An increase in price leads to a reduction in quantity demanded. Thus, the demand curve for butter is negatively sloped. The rise in expenditures is due to inelastic demand.

AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-01 Apply various elasticities of demand as a quantitative tool to forecast changes in revenues; prices; and/or units sold. Topic: Own Price Elasticity of Demand

162. The cross-price elasticity for textbooks and copies of old exams is -3.5. If the price of copies of old exams increases by 10 percent, what will happen to the quantity demanded of textbooks?

By definition,

Substitute EQ,P = -3.5 and %ΔP = 10 into the equation to get %ΔQ = -35.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Apply various elasticities of demand as a quantitative tool to forecast changes in revenues; prices; and/or units sold. Topic: Own Price Elasticity of Demand

163. Which of the following goods would you expect to have the most inelastic demand? Why? a. Swiss cheese

b. Cheese c. Dairy products

Dairy products are expected to have the most inelastic demand because it is the most broadly defined group, followed by cheese and then Swiss cheese. A more specifically defined category has more substitutes and, therefore, more elastic demand.

164. The following estimates have been obtained for the market demand for cereal: ln Q = 9.01 - 0.68 ln P + 0.75 ln A - 1.3 ln M, where Q is the quantity of cereal, P is the price of cereal, A is the level of advertising, and M is income. Based on this information, determine the effect on the consumption of cereal of

a. A 5 percent reduction in the price of cereal. b. A 4 percent increase in income.

c. A 20 percent reduction in cereal advertising.

a. Since the own price elasticity is -0.68, we use the elasticity formula to

write Solving for %ΔQ we see that there will be a 3.4 percent increase in the quantity demanded of cereal.

b. There will be a 5.2 percent reduction in the demand for cereal. c. There will be a 15 percent reduction in the demand for cereal.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-05 Show how to determine elasticities from linear and log-linear demand functions. Topic: Obtaining Elasticities From Demand Functions

165. Suppose you are the manager of a home-building company and the government is considering eliminating the tax deductibility of mortgage interest payments. A typical consumer's marginal tax rate is 25 percent, and the elasticity of demand for new homes is -1.5. Your boss wants to know the impact of the proposed government policy on your business. What do you tell him?

The price is no longer reduced by 25 percent, so the new price is 33.33 percent higher than the discounted price with the deduction. Use the elasticity formula to write Solving, we see that the demand for new homes will be reduced by 50 percent.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-01 Apply various elasticities of demand as a quantitative tool to forecast changes in revenues; prices; and/or units sold. Topic: Own Price Elasticity of Demand

166. You work for an unemployment agency that distributes unemployment checks to unemployed workers in your state. Your boss recently learned that the president proposed a 21 percent increase in the minimum wage, and she wants you to provide her with an estimate of the number of additional workers who will file for unemployment compensation claims next year if the bill passes. Based on library research at a nearby university, you learn that about 200,000 workers in your state earn at or below the current minimum wage. Further library research turns up a study that reports the own price elasticity of demand for minimum wage earners to be - 0.30. Based on your findings, how many additional workers do you think will file unemployment claims in your state?

Since the elasticity of demand for minimum wage earners equals - 0.3, the 21 percent increase in the minimum wage would decrease the quantity demanded of minimum wage earners by 6.3 percent. This would translate into .063 × 200,000 = 12,600 lost jobs, and presumably, 12,600 additional workers who file unemployment claims. Your boss may need to hire some additional workers to help process claims if the bill passes.

167. The income elasticity of demand for your firm's product is estimated to be 0.75. A recent report in The Wall Street Journal says that national income is expected to decline by 3 percent this year.

a. What should you do with your stock of inventories? b. What do you expect to happen to your sales?

c. How would you answer parts a and b if you expected a 5 percent increase in income instead of a decrease?

a. or The manager should reduce the stock of inventories by 2.25 percent.

b. Sales are expected to decrease by 2.25 percent.

c. Using the elasticity formula,

The stock of inventories should be increased by 3.75 percent, since sales are expected to rise by 3.75 percent.

168. A consumer spends all of her income on only one good. What is the income elasticity of demand for this good? What is the own price elasticity of demand for this good?

Since PQ = M, we can solve for the demand function as Q = M/P. Taking logarithms, we see that ln Q = ln M - ln P. Thus, the income elasticity is 1, and the own price elasticity is -1.

AACSB: Reflective Thinking Blooms: Understand Difficulty: 3 Hard Learning Objective: 03-01 Apply various elasticities of demand as a quantitative tool to forecast changes in revenues; prices; and/or units sold. Topic: Own Price Elasticity of Demand

169. As the manager of a local hotel chain, you have hired an econometrician to estimate the demand for one of your hotels (H). The estimation has resulted in the following demand function: QH = 2,000 - PH - 1.5PC - 2.25PSE + 0.8POH + 0.01M, where PH is the price of a room

at your hotel, PC is the price of concerts in your area, PSE is the price of sporting events in your

area, POH is the average room price at other hotels in your area, and M is the average income

in the United States. What would be the impact on your firm of: a. A $500 increase in income?

b. A $10 reduction in the price charged by other hotels? c. A $7 increase in the price of tickets to local sporting events?

d. A $5 increase in the price of concert tickets, accompanied by an $8 increase in income?

a. ΔQH = (0.01)ΔM = (0.01)(500) = 5. Thus, the demand for your hotel will increase by five

units.

b. ΔQH = (0.8)ΔPOH = (0.8)(-10) = -8. Thus, the demand for your hotel will decrease by eight

units.

c. ΔQH = (-2.25)ΔPSE = (-2.25)(7) = -15.75. Thus, the demand for your hotel will decrease by

15.75 units.

d. ΔQH = (-1.5)ΔPC + 0.01(ΔM) = -1.5(5) + 0.01(8) = -7.42. Thus, the demand for your hotel will

decrease by 7.42 units.

170. Your firm's research department has estimated the elasticity of demand for toys to be -0.7. As the manager of a local chain of toy stores, determine the impact of an 8 percent increase in toy prices on your total revenues.

Since the elasticity of demand for toys is less than 1 in absolute value, an increase in toy prices will increase your total revenues.

171. The demand for Wanderlust Travel Services (X) is estimated to be Qx = 22,000 - 2.5Px + 4Py -

1M + 1.5Ax, where Ax represents the amount of advertising spent on X and the other variables

have their usual interpretations. Suppose the price of good X is $450, good Y sells for $40, the company utilizes 3,000 units of advertising, and consumer income is $20,000.

a. Calculate the own price elasticity of demand at these values of prices, income, and advertising.

b. Is demand elastic, inelastic, or unitary elastic?

c. How will your answers to parts a and b change if the price of Y increases to $50?

a. Qx = 22,000 - 2.5 (450) + 4(40) - 1(20,000) + 1.5(3,000) = 5,535.

b. Since the elasticity is less than 1 in absolute value, demand is inelastic. c. Qx = 22,000 - 2.5(450) + 4(50) - 1(20,000) + 1.5(3,000) = 5,575, so

The elasticity changes from -0.203 to -0.202 as Py changes from $40 to $50.

172. The demand for company X's product is given by Qx = 12 - 3Px + 4Py. Suppose good X sells for

$3.00 per unit and good Y sells for $1.50 per unit.

a. Calculate the cross-price elasticity of demand between goods X and Y at the given prices. b. Are goods X and Y substitutes or complements?

c. What is the own price elasticity of demand at these prices?

d. How would your answers to parts a and c change if the price of X dropped to $2.50 per unit?

a. Qx = 12 - 3(3) + 4(1.5) = 9, so

b. They are substitutes.

c. d. Qx = 12 - 3(2.5) + 4(1.5) = 10.5, so AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-05 Show how to determine elasticities from linear and log-linear demand functions. Topic: Obtaining Elasticities From Demand Functions

173. Your firm's research department has estimated the income elasticity of demand for Art Deco lawn furniture to be -0.85. You have just learned that due to an upturn in the economy, consumer incomes are expected to rise by 5 percent next year. How will this event affect your ordering decision for PVC pipe, which is the main component in your furniture?

Using the formula for the income elasticity, we see that the demand for your lawn furniture will be reduced by 4.25 percent this year. You may want to order about 4.25 percent less PVC pipe.

174. Suppose the demand for sunscreen (X) has been estimated to be ln Qx = 5 - 1.7 ln Px + 3 ln S -

3 ln Ay, where S denotes the average hours of sunshine per day and Ay represents the level of

advertising for good Y.

a. What would be the impact on demand of a 5 percent increase in the daily amount of sunshine?

b. What would be the impact of a 10 percent reduction in the amount of advertising toward good Y?

c. What might be good Y in this example?

a. A 5 percent increase in the daily amount of sunshine leads to a 15 percent increase in the demand for sunscreen (X).

b. A 10 percent reduction in the amount of advertising toward good Y results in a 30 percent increase in demand for X.

c. Beach umbrellas.

175. An econometrician has estimated the inverse demand relation P = a + bQ + e and found that and = 0.75. Find the approximate 95 percent confidence interval for the true values of a and b.

A 95 percent confidence interval for a is Thus, you can be 95 percent confident that a is within the range of 384 and 416. A 95 percent confidence interval for b

is Thus, you can be 95 percent confident that b is within the range of -4.25 and -1.25.

AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-06 Explain how regression analysis may be used to estimate demand functions; and how to interpret and use the output of a regression. Topic: Regression Analysis

176. A firm is considering raising its price by 9 percent and has hired an econometrician to estimate the elasticity of demand for its product. The econometrician estimates the parameters of a log- liner demand function and reports that the parameter estimate for the elasticity of demand is - 1.5 and the standard error of the estimate is 0.3.

a. If the firm raises its price by 9 percent, what is the expected change in quantity demanded? b. Approximate the upper and lower bounds on the 95 percent confidence interval for the change in quantity demanded.

a. Using the estimated own price elasticity of -1.5, the 9 percent increase in price is expected to reduce quantity demanded by 13.5 percent.

b. The lower bound for the 95 percent confidence interval for the elasticity is -1.5 - 2(.3) = -2.1. Based on this lower bound, the 9 percent increase in price would reduce quantity demanded by 18.9 percent. The upper bound for the 95 percent confidence interval for the elasticity is -1.5 + 2(.3) = -0.9. Based on this upper bound, the 9 percent increase in price would reduce quantity demanded by 8.1 percent. In summary, the manager can be 95 percent confident that the 9 percent price increase will reduce quantity demanded somewhere between 8.1 and 18.9 percent.

AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-06 Explain how regression analysis may be used to estimate demand functions; and how to interpret and use the output of a regression. Topic: Regression Analysis

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