a) Assume that a firm is considering entering a market. Its estimated inverse demand function in that market is given by p = 180 – 3q. To enter the market, the firm must invest $500 in machines and tools. The variable cost of production is given by 15q2. What are the profit-maximizing quantity and price of the firm? Will this firm enter the market? (Note that the firm is making the decision before entering the market)?
b) Now suppose the firm has already invested $500 in machines and tools. Also assume that the machines and tools once invested cannot be resold and for that reason that cost is sunk. Should the firm continue production or should it shut down? Next, suppose that the capital cost (machines and tools) is not fully sunk but can be sold at some price M. What should be the minimum value of M for which the firm will decide to shut down?