Suppose that ELM Corporation sells two products, A and B. Suppose further that ?A = -1.5 and ?B = -2
Question: Suppose that ELM Corporation sells two products, A and B. Suppose further that ?A = -1.5 and ?B = -2, where ?i denotes the own-price elasticity of product i. Suppose further that the ?AB, cross-price elasticity between the quantity demanded of A and the price of B, is 1/3, and that ?BA = 0.5. Finally, suppose that MCA = $200 and MCB = $300.
a. Based on this information, what prices would maximize profits if A and B were produced by two separate firms?
b. Are A and B complements or substitutes?
c. Does your answer to part b suggest that prices will be higher or lower when sold by a single firm than they would be if produced by two separate firms?
d. Fill in the following table. The first row contains the current values for PA, QA, PB, and QB.
| PA | QA | PB | QB | %ΔPA | %ΔQA | %ΔPB | %ΔQB | TR |
| 2147 | 2500 | 1500 | 4000 | -- | -- | -- | -- | |
| 2100 | 1492 | 4000 | -2.19% | -0.53% | 0% | |||
| 2053 | 1343 | -2.24% | 0% | -9.99% |
e. Would you recommend changing the price of PA from $2147? If not, why not? If so, what type of change would tend to raise profit and why?
f. Would you recommend changing the price of PB from $1500? If not, why not? If so, what type of change would tend to raise profit and why?
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