ECN 3030 Chapter 3 Homework

You are the manager of a firm that receives revenues of $20,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is -3, and the cross-price elasticity of demand between product Y and X is -1.3. How much will your firm's total revenues (revenues from both products) change if you increase the price of good X by 1 percent?

$-1,570

You are a division manager at Toyota. If your marketing department estimates that the semiannual demand for the Highlander is Q = 150,000 - 1.5P, what price should you charge in order to maximize revenues from sales of the Highlander?

$50,000

Suppose the cross-price elasticity of demand between goods X and Y is -2. How much would the price of good Y have to change in order to change the consumption of good Xby 20 percent?

-10%

Revenue at a major smartphone manufacturer was $2.4 billion for the nine months ending March 2, up 77 percent over revenues for the same period last year. Management attributes the increase in revenues to a 103 percent increase in shipments, despite a 33 percent drop in the average blended selling price of its line of phones.Given this information, is it surprising that the company's revenue increased when it decreased the average selling price of its phones?

No. Own price elasticity is -3.12, which means demand is elastic and a decrease in price will raise revenues

Recently, Verizon Wireless ran a pricing trial in order to estimate the elasticity of demand for its services. The manager selected three states that were representative of its entire service area and increased prices by 5 percent to customers in those areas. One week later, the number of customers enrolled in Verizon's cellular plans declined 4 percent in those states, while enrollments in states where prices were not increased remained flat. The manager used this information to estimate the own-price elasticity of demand and, based on her findings, immediately increased prices in all market areas by 5 percent in an attempt to boost the company's 2016 annual revenues. One year later, the manager was perplexed because Verizon's 2016 annual revenues were 10 percent lower than those in 2015—the price increase apparently led to a reduction in the company's revenues. Did the manager make an error?

Yes- cell phone elasticity is likely much larger in the long-run than the short-run

Suppose the own price elasticity of demand for good X is -2, its income elasticity is -1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Yis -3. Determine how much the consumption of this good will change if: a. The price of good X decreases by 4 percent. b. The price of good Y increases by 10 percent. c. Advertising decreases by 3 percent. d. Income increases by 2 percent.

a. 8% b. -30% c. -6% d. -2%

For the first time in two years, Big G (the cereal division of General Mills) raised cereal prices by 2 percent. a. If, as a result of this price increase, the volume of all cereal sold by Big G changed by -3 percent, what can you infer about the own price elasticity of demand for Big G cereal? b. Can you predict whether revenues on sales of its Lucky Charms brand increased or decreased?

a. it is elastic b. yes- it decreased (because an elastic demand increasing price will lower revenue)

The demand curve for a product is given by QXd = 1,200 - 3PX - 0.1PZ where Pz = $300. a. What is the own price elasticity of demand when Px = $140? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $140? b. What is the own price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price above $240? c. What is the cross-price elasticity of demand between good X and good Z when Px = $140? Are goods X and Z substitutes or complements?

a. own price elasticity: -0.56 Demand is inelastic If the firm charges below $140, revenue will decrease b. own price elasticity: -1.6 Demand is elastic if the firm charges above $240, revenue will decrease c. cross-price elasticity: -0.04 Goods X and Y are complements

The demand function for good X is QXd = a + bPX + cM + e, where Px is the price of good X and M is income. Least squares regression reveals that: The R-squared is 0.35. a. Compute the t-statistic for each of the estimated coefficients. b. Determine which (if any) of the estimated coefficients are statistically different from zero. c. What does the R-square in this regression indicate?

a. t a-square: 1.55 t b-square: -5.22 t c-square: 1.65 b. The coefficient estimate for b is statistically different from zero c. 35% of the variability in the dependent variable is explained by price and income

With milk sales sagging of late, The Milk Processor Education Program (MPEP) decided to move on from the famous "Got Milk" ad slogan in favor of a new one, "Milk Life." The new tagline emphasizes milk's nutritional benefits, including its protein content. MPEP began collecting data on the number of gallons of milk households consumed weekly (in millions), weekly price per gallon, and weekly expenditures on milk advertising (in hundreds of dollars) for the period following the launch of the new campaign. These data, in forms to estimate both a linear model and log-linear model, are available via the link below. Use these data to perform two regressions: a linear regression and a log-linear regression. a. Which model does a better job fitting the data? b. Suppose that the weekly price of milk is $3.40 per gallon and MPEP decides to ramp up weekly advertising by 35 percent to $150 (in hundreds). Use the best-fitting regression model to estimate the weekly quantity of milk consumed after this advertising increase.

a. the linear model b. 1.730 million gallons per week

Suppose the true inverse demand relation for good X is QXd = a + bPX + cM + e, and you estimated the parameters to be: a-square= 22 b-square= -1.8 derivative of a= 2.5 derivative of b= 0.7 Find the approximate 95 percent confidence interval for the true values of a and b.

confidence interval for a: (17, 27) because a is 22 +- 2(2.5) confidence interval for b: (-3.2, -0.4) because b is -1.8 +- 2(0.7)

If Starbucks's marketing department estimates the income elasticity of demand for its coffee to be 1.75, how will the prospect of an economic bust (expected to decrease consumers' incomes by 4 percent over the next year) impact the quantity of coffee Starbucks expects to sell?

it will change by -7.00%