Consider a country, called Hom

Consider a country, called Home, that is thinking about starting up a semiconductor chip industry. There are already many producers of the chips in other countries, and there are initially no producers in Home. Suppose that to produce semiconductor chips one must first construct a plant, at a cost of $150. The capacity of such a plant is 10 units per period. 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.
Home country consumers demand semiconductor chips according to the demand curve:
Q = 36 – P,
Where Q is the quantity they consume in a given period and P is the price they face in that period. Home is small in the world market for chips, so it takes the world price as given. That price is $12 in both periods.
Finally, assume for simplicity that the interest rate is zero, so the present value of a firm’s profits (producer surplus) is just the profits (net of fixed cost, if any) in period 1 (PS1) plus the profits in period 2 (PS2). We will write PSTOT = PS1 + PS2. Similarly, we calculate total consumer surplus by adding together consumer surplus in each of the two periods: CSTOT = CS1 + CS2, and similarly with government revenue when there is any:
GRTOT = GR1 + GR2.
(a) Will any Home firm invest in chip production under free trade?
(b) Calculate PSTOT, CSTOT, and social welfare under free trade. (Note: For simplicity, assume that there is at most only one firm in Home. It will, of course, be a price-taker on world markets.)
(c) 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. This policy is made public at the beginning of period 1 and is intended to give Home chip makers a chance to become competitive on world markets. Now answer (a) again.
(d) Under the policy described in (c), repeat the calculation in (b). Be sure to include the surplus to the government in the calculation of social welfare.
(e) Is the policy of infant-industry protection successful? Is it beneficial? Explain.

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