Question

Suppose that Coffee East (CE) and Coffee West (CW) are located on opposite ends of College Ave. (e.g. College & University and College & Atherton, respectively) and that the street is one mile long. CE’s marginal cost of brewing a cup of coffee is $6, and CW’s marginal cost is $3. N = 108 students along the street needing coffee walk to one of the two shops and buy at most one cup. They face a travel cost of t = 1.5 for every unit of distance they walk. Each student values a cup of coffee at V = 65 and receives a utility from a cup of coffee that is linear in prices and transport costs. A student located at an arbitrary point 0 ≤ x ≤ 1 along the street has utility

ux, CW =V −pCW −tx

ux,CE =V −pCE −t(1−x)

1. What is each shop’s demand?

2. Write down each shop’s maximization problem and best response function.

3. Are prices strategic complements or substitutes? Explain.

4. What are the equilibrium prices and quantities of coffee sold? What are each shop’s respective profits?

Answer 1