Tari , Subsidy, and the Direction of Trade
Country A is a small country when it comes to trade in fish- they can import or export fish at a fixed world price, but their trade flows cannot affect the equilibrium price in the world market. Currently, fish is trading at $500 per ton in the world market.
The demand and supply functions in country A are:
D = 8000 P;
where D is the quantity demanded, S is the quantity supplied, and P is the price per ton of fish.
- How many tons of sh will country A import in a free trade equilibrium?
- What is the change in total social welfare between autarky and trade?
- The fish farmers in country A are unhappy about the in ow of cheap foreign fish. They have successfully convinced the government of country A that the imports are threatening the survival of the fishing industry, and the government has agreed to impose an import tariff of $100 per ton of fish to safeguard the fishing industry. After the tariff is imposed, what is the new equilibrium quantity of fish produced in country A? How much is the deadweight loss? How much tariff revenue will the government collect?
- The fish farmers further argue that if the government completely bans the import of sh and subsidizes each ton of fish export by s dollars, in the long run, they could be the leaders in fish production. Do you think it is possible to transform country A into an exporter of sh by using export subsidies? If you think it is possible, compute the value of s that will allow country A to export 1000 tons of fish. If you think it is not possible, clearly state your reasons, and support your arguments with calculations if necessary.
An Asymmetric Helpman-Melitz-Yeaple Model
Assume that there are two countries in the world, North and South. Firms in both countries compete in a monopolistically competitive market: each rm only produces one brand (variety) of goods, sets its own price, and faces the following demand curve: Dij = Hj Pij 3; where Dij is the quantity demanded the product of rm i in country j, Pij is the price set by rm i in country j, and Hj is a variable describing the active market size” in country j in equilibrium, which depends on the number of competitors, the average price level in the market, and the income of the consumers. Hj for the same country might change between autarky and trade equilibrium. In autarky equilibrium, the active market sizes in both countries are the same: HN = HS = 1350.
The cost function for an rm with productivity z producing in-country j is:
Cj(Q; z) = wzj Q + Fj;
where Q is the output, z 2 (0; +1) measures the productivity of the rm, wj is the wage rate in country j and Fj is the xed cost of production in country j. Suppose that both wj and Fj are exogenously given and xed throughout this question.
Exporting to a foreign country incurs both variable and xed costs. Variable trade costs take the form of iceberg cost = 0:5: in order for one unit of goods to reach the market in the other country, a rm must ship out 1 + = 1:5 units of goods out of its factory. In order to set up the exporting network, the rm also needs to pay a xed cost that equals to Fx = 4 before it can start exporting.
Alternatively, rms can also choose to engage in FDI: they can build a new factory in a foreign country. If they choose to do so, they need to pay the wage rate, as well as the xed costs of production in a foreign country. Assume that the outputs from the foreign subsidiary can only be sold to the foreign market as in the standard Helpman-Melitz-Yeaple model.
The North is richer, so the wage there is higher than in the South. However, as the institution in the South is weaker, the entry barriers in the South are signi cantly higher than in the North:
wN = 3; FN = 2;
wS = 1; FS = 40:
- Based on equation (1), derive the marginal revenue of the rm as a function of its price, Pij.
- Derive the price P (z) that optimizes a Northern rm’s pro t in the North Market in the autarky equilibrium. Express P (z) as a function of z and wN .
- Find the value of z^N such that rms located in the North with productivity z^N earn zero total pro t in autarky equilibrium.
- Now countries open up to trade, and the changes in prices and number of rms have lead HN to drop to 600, and HS to drop to 300. Find out the cut-o value of z~ in the North such that rms with productivity z > z~ will choose to build a subsidiary in the SouthF. (Hint: This question is harder than it seems. Think twice.)
- How will z~ change if the wage gap, wN wS, is smaller? What is intuition? Please provide a concise and qualitative answer, and note that you do not need the exact solution of z~ to answer this question.
- The rapid economic growth in the South begins to push up the wage rate in the South to wS0 > wS. Assume that the Northern wage rate is not a ected by this. Facing with the higher wage rates in the South, the Northern rms with subsidiaries in the South is pondering if they shall switch back to exporting instead of FDI. Find out the minimum value of wS0 to ensure that no Northern rm chooses FDI over exporting.
(Hint: there is no restriction on whether wS0 is lower than wN or not. The only restriction is wS0 > wS.)