The publishing firm AWL sellts its cowboy novels in two regions of the country,
ID: 3346916 • Letter: T
Question
The publishing firm AWL sellts its cowboy novels in two regions of the country, Texas and Massachusetts. The demand for these books in Texas is given by the inverse demand function Pt = alpha - beta Qt, while the inverse demand function in Massachusetts is Pm = gamma - theta Qm, where Q refers to quantity, P refers to price, and the subscripts t and m refer to Texas or Massachusetts. We also assume that beta > theta and alpha > gamma. a) Find the optimal quantities to sell in Massachusetts and in Texas under the assumption that the total cost function for AWL is linear and TC = psi + c(Qm + qt), where c is a parameter and psi represents fixed costs. Determine the profits earned by AWL. b) Find the optimal quantities to sell in Massachusetts and in Texas under the assumption that the total cost function for AWL is quadratic and TC = psi + c(Qm + Qt)^2, where c is a parameter and psi represents fixed costs. c) Now suppose some residents of Texas and Massachusetts begin transporting books such that Pt = Pm, and then AWL faces the overall inverse demand function P = [(alpha theta + gamma beta) / (beta + theta)] - [(beta theta) / (beta + theta)]Q, where P is the common price in Texas and Massachusetts and Q = Qm + Qt. Determine the profits AWL would have earned in this case.
Explanation / Answer
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