For each question below, please show all working. Marks will be deducted for incomplete working. Where relevant, calculate solutions to 2 decimal places.
1. The United States (US) and China export cars to, and import cars from, each other. Which of the international trade models discussed in class can be used to at least partly explain this trade pattern? In each case, explain carefully how.
2. New Zealand’s trade deficit with the rest of the world is large. Should the New Zealand (NZ) Government implement restrictive trade policies to help the NZ economy? Explain carefully, referring to what you have learned in this unit.
3. US Milk Co. and EU Milk Co. are milk producers. US Milk Co. produces in the United States while EU Milk Co. produces in Europe. Both firms sell very similar products (milk) to consumers around the world.
Say that the demand curve for a tank (i.e. 50 litres) of milk is given by:
𝑄𝑄 = 700 − 2𝑝𝑝
where Q qA qB is the total number of 50-litre tanks of milk produced by US Milk Co. and EU Milk Co.; p is the price of each 50-litre of milk measured in $. Assume that the marginal cost of producing each tank of milk is $10 for US Milk Co. and $5 for EU Milk Co.
The US is thinking of subsidising US Milk Co.’s production so that it can better compete with its European rival.
i. Initially neither firm receives a subsidy. If both firms seek to maximise profit, how many 50-litre tanks of milk will each produce and what will their profits be? Illustrate the solution on a diagram.
ii. The US Government pays US Milk Co. a subsidy of $5 for each 50-litre tank of milk it produces. Assume that the European Union does not retaliate. How many
50-litre tanks of milk will each firm produce now and what will their profits be? Draw the new solution on the same diagram.
i. Which firm gains and which firm loses from the subsidy? With the aid of diagrams, explain why.
ii. Calculate the optimal subsidy that the US Government could provide to US Milk Co. That is, assuming Europe does not retaliate, calculate the subsidy that will maximise US Milk Co.’s profit.
2. Assume a monopolistically competitive car industry. The demand facing any firm i is given by:
𝑞𝑞𝑖𝑖 = 𝑄𝑄 ��𝑁𝑁� − �
� (𝑝𝑝𝑖𝑖 − 𝑝𝑝̅)�
where qi is firm i’s sales, Q signifies total industry sales (i.e. the size of the
market), N is the number of firms in the industry,
pi is the price charged by
firm i itself and p is the average price charged by firm i's competitors.
Assume that the production function for cars is such that: (i) 10,000,000 hours of labour are required even if no cars are produced and (ii) 500 hours of labour are required to produce each additional car. The wage rate is $50/hour.
Now, suppose that there are two countries: Home and Foreign. Home has annual sales of 1,000,000 cars and Foreign has annual sales of 2,000,000. Both firms face the same production function.
i. Assuming a symmetric autarky equilibrium, use the zero profit condition to derive the equation for the price of cars in Home as a function of N. Do the same for Foreign.
ii. Assuming a symmetric autarky equilibrium, use the profit maximising profit condition to derive the equation for the price of cars in Home as a function of N. Do the same for Foreign.
iii. Using your answers from (i) and (ii), solve for the autarky equilibrium number of firms, the price of cars and the output of each firm in Home and Foreign. (solve to 2 decimal places if required)
iv. (4 marks) Assume no transportation cost and that Home and Foreign freely trade cars with one another. For this integrated market, solve for the equilibrium price, the number of firms in Home and Foreign, and the output per firm. (solve to 2 decimal places if required).
v. Explain how and why the integrated equilibrium calculated in part (iv) differs to the autarky equilibria calculated in part (iii).