Problem 1 - The Melitz model and technology adoption This problem is based on a paper by Paula Bustos (2011). Consider the monopolistic competition model with productivity differences studied in class. To simplify it further, assume that the variable profit of a firm with marginal cost c is given by A, where A is some positive constant. Thus, the total profit of the firm is A - F (and remember that the fixed cost F must be paid before the firm learns its marginal cost c). 1. Is there a marginal cost draw c that is so bad that firms exit the market? Does the fixed cost matter for this decision, and why? 2. Now, assume that for all firms in the market, a new technology becomes available (say, they can buy a computer to speed up their production). Buying a computer reduces a firm's marginal cost from c to , and has a cost Fo. Will all firms choose to buy computers? If not, which firms will and which firms will not? 3. Next, assume that all firms are allowed to export without any additional costs. They export to a market which is exactly identical to their home one, and therefore now make variable profits 24. How does this export possibility affect the decision to buy a computer? 4. Comment on your results: does this exercise highlight new channels for gains from trade