1. The demand for good X is estimated to be:
1000Q_{x} – 40P_{x} 50P_{y} 2M 10A_{x}
where
P_{x} = price of X in dollars
M= personal disposable income in trillions of dollars per year
P_{y} =price of a competitive in dollars
A_{x} = advertising expenditures in dollars $ per year
Q_{x} = sales per year in the U.S.
Suppose P_{X }= $5, P_{Y} = $10, M = $2500, and A_{X} = $100.
a. What is the demand curve and quantity demanded for good X?
b. At the present price, would total revenue rise or fall if the price of the good is lowered? Why?
c. From the conditions in part a, what is the point income elasticity of demand?
d. What is the cross-price elasticity between goods X and Y? Are goods X and Y substitutes or complements? Why? Will the cross-price elasticity between Y and X be the same?
e. From the conditions in part a, what is the point advertising elasticity of demand?
f. Is the demand facing this company more sensitive to a one percent increase in income or a one percent increase in advertising expenditures?
g. Find the algebraic expressions for the company’s total and marginal revenue functions. (Remember, TR = f(Q) and MR = f(Q).)
h. Produce a graph of total revenue and marginal revenue. Graph total revenue for quantities up to 7,500 and put the marginal revenue graph on separate axes, and graph marginal revenue for quantities up to 7,500 also.
i. What level of sales would maximize the company’s total revenues? What price does the company have to charge for X for that level of sales result?
2. Joe is evaluating the marketing strategy at his restaurant and inn. Assume that in response to a $2.00 off sales promotion for spaghetti dinners, Joe finds that nightly dinner sales increase from 20 per night to 40. Usually the dinners sell for $6.00.
a. What is the arc price elasticity of demand for Joe’s spaghetti dinners?
b. Will Joe increase revenues by further reducing the price? What about profits? Describe.
3. For some time, two firms have charged $0.90 per standard unit of crating materials for shipping a particular type of machine tool and each has been selling about 20,000 units per month. Last month, U-Pak-It reduced its price to $0.80 per unit and its volume increased to 25,000 units. At that month, Boxit (the other company) maintained its price at $0.90 but saw its volume decline to 17,000 units.
a. What is the price elasticity of demand facing U-Pak-It?
b. What is Boxit’s cross-price elasticity of demand for U-Pak-It price changes?
c. If the price elasticity of demand for Boxit is the similar as that for U-Pak-It, what price reduction for Boxit will be needed to increase its monthly volume back to 20,000 units per month?
4. Assume that the price elasticity of demand for cereal is −0.75 and the cross-price elasticity of demand between cereal and the price of milk is −0.9. If the price of milk rises by 10%, what would have to happen to the price of cereal to exactly offset the rise in the price of milk so as to leave the quantity of cereal demanded unchanged?
5. Assume you have find outd the following demand function for the product you sell:
Q = 5-0.2P
At what price will the demand for your product be unitary elastic? (Hint: Begin by recalling the relationship between MR and elasticity.)
6. Using the macro model:
a. Show what would happen to national income (GDP) if the administration implements another $100 (billion) stimulus spending package.
b. Show what will happen if instead of a government spending package, the administration implemented a $100 tax cut.
c. From your results, find outs the numerical values of the derivatives dY/dG and dY/dT. (Hint: Numerically, dY is just the new value of Y less the old value and dG is the new value of government spending less the old one. Find the ratios of those numbers and you have found the value of the derivative.) Which policy has the largest effect and why?
7. You’re standing at three light switches at the bottom of stairs to the attic. Each one corresponds to one of three lights in the attic, but you can’t see the lights from where you stand. You could turn the switches on and off and leave them in any position. How can you recognize which switch corresponds to which light bulb if you are only allowed one trip upstairs?