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In Lumstown, there are only two bookshops, A and B. The demand function for books in this market is P=10-Q. The marginal cost is constant at $2. The owners of the stores have majored in Economics from LUMS and know that the maximum profit in the market is when the price is set at $6.
a. If the bookstores consult with each other and jointly determine their P and Q, what maximum profit will each store earn?
b. Store B deviates from the plan one day and announces its new price of $4. What is the profit of store B? What is the profit of store A?
c. Store A comes up with a new plan and changes its price to $4. What is each company's profit?
d. Store B approaches store A and offers a side payment of x to encourage A to leave Lumstown. What could be the maximum x store B would offer?
e. Explain the intuition for your answer in part (d).
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