Quarterly demand for your product has been estimated as ln Qd= 1 - 1.5 ln P + 0.5 ln Px - 0.5 ln Py + 0.1 ln M + 0.3 ln A, where Qd represents quantity demanded, P, Px, Py represents your unit price and the unit prices of two other products (X and Y), M represents per-capita income, and A denotes your advertising spending.
A. All else equal, would a price cut raise or lower your revenue? Why?
B. Is your product normal or inferior? A "luxury" (income-elastic) or "necessity" (income inelastic)?
C. Is good X a substitute or complement for your product, and how do you know?
D. What about good Y? Substitute or complement?
E. Suppose you increase your advertising by 10%. What is the estimated impact on sales?
F. If you have competitors selling similar products, but you can change your prices & advertising without worrying about reactions of competitors, what type of market are you in?
G. If your marginal costs of production are constant at $4 per unit, find the profit minimizing price.
H. Further analysis reveals that your market consists of 2 distinct groups of consumers: (1) group A, who have a price elasticity of -1.8, and (2) group B, who have a price elasticity of -1.2. Assuming that the marginal cost of production is the same for each group, what is the profit-maximizing price for each group?
I. What type of price discrimination is practiced in (H) above? What conditions are necessary for it to work?
J. Ignoring the 2 separate groups of demanders, what can you say about the effect of advertising on revenue at the price you determined in (G) above? If advertising increases by 10%, what is the increase in revenue?