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Multimarket Monopoly

A monopolist operates in two separated markets. The inverse demand functions ofthose markets are given by      and      where   arethe quantities supplied to these markets, respectively. The total cost function facedby the monopolist is    . In addition, there is a sales cost of £c perunit sold in market 1. There is no such additional sales cost in market 2.a. Solve for the optimal quantities   in terms of c. What is theneeded condition for the firm to serve both the markets in equilibrium?b. What effects does an increase in c have on the (i) profits in each marketand (ii) overall consumer surplus? Provide both mathematical and intuitiveexplanations of your result.c. Suppose the quantities are fixed at the levels derived at (b), but the firm isnow allowed to charge two part tariffs in both markets. What would be theoptimal unit price (not the fixed fee) in each market? 

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