Now, consider the model of the previous problem with the following small changes. There are initially no semiconductor chip producers in Home, but two firms in Home would be willing to invest in chip production if they thought it would be profitable. The cost of building a plant is negligible, but since this industry is new to the country, a foreign consultant will need to be hired to train plant managers. The consultant's fee is $150. It is impossible to set up shop in this industry without acquiring the knowledge of the consultant. The important thing about the consultant is that once he or she has trained the managers in one firm, the other firm can pick up on that advice for free just by observing the actions of the first firm. Thus, if only one firm pays the $150 fee, the entire domestic industry can get started. (Assume that the two domestic firms do not trust each other, so that a joint venture is impractical.)
Suppose that there are two periods. In period 1, a new producer can set up a plant and begin production. The marginal cost for a new producer is $10 per unit. If a new producer produces up to capacity in period 1, then he or she becomes an experienced producer, and his or her marginal cost will drop to 0 in period 2. However, even for experienced producers, the capacity constraint of 10 units still holds.
(a) Assume free trade. Show that if one firm hires the consultant and sets up shop, then it will be profitable for the other firm to set up shop.
(b) Continue assuming free trade. Now show that the firm that actually hires the consultant will lose money.
(c) Summarizing (a) and (b), what will be the outcome under free trade?
(d) Calculate PSTOT (for both firms), CSTOT, and social welfare under free trade.
(e) Now suppose the government follows a policy of infant industry-protection. Specifically, suppose that it imposes a tariff of $2 per unit on imported chips in period 1 and then returns to free trade in period 2. Now repeat (a), (b), and (c).
(f) Under the policy described in (e), repeat the calculation in (d).