The demand for good X is estimated to be:
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 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 current price, will 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? Would 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 will maximize the company's total revenues? What price does the company have to charge for X for that level of sales result?