Consider a world composed of two countries, Home (H) and Foreign (F). Individuals living in each country == H, F have preferences over two goods x and y. In each country there is only one factor of production, labour, which is perfectly mobile between industries but immobile between countries. The total labour endowment at Home is LH 10 and the total labour endowment in Foreign is LF 10. The marginal product of labour in each industry is constant. At Home, one worker can produce 2 units o good x or 1 unit of good y per unit of time; at Foreign one worker can produce 1 unit of good x or 2 units of good y per unit of time. Assume that consumers in Home and Foreign always consume goods x and y in the same quantity regardless =

"Only answer c-d ones"

(a) Calculate the opportunity cost of producing one additional unit of good x in terms of units of good y in Home and Foreign.

The opportunity cost of producing one additional unit of good x in Home or foreign is the amount of good y that must be given up to produce it.

At Home, one worker can produce 2 units of good x or 1 unit of good y. Thus, to produce one additional unit of good x, half a unit of good y must be given up. The opportunity cost in Home is 0.5 units of good y. In Foreign, one worker can produce 1 unit of good x or 2 units of good y. To produce one additional unit of good x, two units of good y must be given up. The opportunity cost in Foreign is 2 units of good y.

(b) Derive the production possibilities frontier (PPF) for Home and Foreign and plot it in a graph with good x in the horizontal axis and good y in the vertical axis.

To derive the production possibilities frontier (PPF) for Home and Foreign, we use the labor market clearing condition in each country.

For Home, the total labor endowment is LH = 10. In Home, 1 worker produces 2 units of good x (xH) and 1 unit of good y (yH). The labor market clearing condition in Home is: LH = (xH / 2) + yH. Rearrange this equation to get yH in terms of xH: yH = 10 - (xH / 2).

For Foreign, the total labor endowment is LF = 10. In Foreign, 1 worker produces 1 unit of good x (xF) and 2 units of good y (yF). The labor market clearing condition in Foreign is: LF = xF + (yF / 2). Rearrange this equation to get yF in terms of xF: yF = 20 - 2 * xF.

Both PPFs are linear, with negative slopes. We Plot the Home PPF using the equation yH = 10 - (xH / 2) and the Foreign PPF using the equation yF = 20 - 2 * xF  to get the following graph below:

(c) Determine the equilibrium price of good x (setting the price of good y as 1) that prevails at Home and Foreign under autarky - that is, when they do not trade with each other. Explain why any other price could not be the equilibrium price in autarky. (USE profit maximising in each industruy at home and the relative price of x in autarky in a given country has to be equal to the slope of the PPF - the opportunity cost of producing one additional unit of good x, expressed in units of good y.)

(d) Determine the optimal consumption and production at Home and Foreign under autarky. Depict this situation in a graph that includes each country's PPF and indifference curves for the representative consumer. (To find the optimal consumption at Home simply maximise the representative consumer's utility subject to the PPF, noting that in autarky, consumption of each good has to be equal to domestic production. + The Lagrangian  and The F.O.C + Taking the ratio of the two)

(e) Assume that Home and Foreign open to trade with each other. Explain how is the pattern of trade (which good will each country export and import) determined (Use the the Ricardian model, the pattern of trade is determined by comparative advantage)

(f) Suppose that the equilibrium price of good x (keeping the price of good y as 1) is equal to 1. Determine the optimal production and consumption both at Home and Foreign when they open up to trade. Depict this in graph.