A business might worry that pricing of one product might impact demand for another product that is also sold by the same business.
Here we€™ll explore conditions under which such worries are more or less important before turning to some specific examples.
A: Suppose first that we label the two goods that a firm sells as simply x1 and x2. The firm considers putting a discount of δ on the price of x1€”a discount that lowers the price from p1 to (1ˆ’δ)p1.
(a) For a consumer who budgets I for consumption of x1 and x2, illustrate the budget before and after the discount is put in place.
(b) Assuming that tastes are homothetic, derive the relationship between δ on the vertical axis and x1 on the horizontal axis.
(c) Now derive the relationship between δ and x2 €“ can you tell if it slopes up or down? What does your answer depend on?
(d) Suppose that x1 is printers and x2 is printer cartridges produced by the same company. Compare this to the case where x1 is Diet Coke and x2 is Zero Coke. In which case is there a more compelling case for discounts on x1?
B: Suppose that tastes are defined by u(x1, x2) = xα1 x2(1ˆ’α).
(a) Derive the demand functions for x1 and x2 as a function of prices, I and δ.
(b) Are these upward or downward sloping in δ?
(c) Under the general specification of tastes as

how would your answer change as ρ changes?

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