Please see attached file.
1. This question is intended to further your understanding of the basic Ricardian model by having you work through a problem on your own. There are two countries, Canada and the U.S, and two goods X and Y . The preferences of agents in each country are represented by the following utility functions:
Canada: UC(XC, Y C) = (XC)1/2(Y C)1/2
U.S.: UUS(XUS, Y US) = (XUS)1/2(Y US)1/2
Each country is endowed with 200 units of labor, which may be transformed into the two goods according to a fixed coefficient technology specific to each country. The technology is as follows: acLX = 2, acLY = 3, ausLX = 1 and ausLY = 4.
(a) [1 pt] Solve for the autarky (no trade) production and consumption allocations in each country. Show your answer on a graph (separately for each country draw the PPF, and mark the production and consumption point).
(b) [1 pt] Calculate the opportunity costs for both goods in Canada and the U.S. Which country should export good X? Which country should export good Y? In what interval must the terms of trade lie?
(c) [1 pt] Solve for the equilibrium with trade. On your graph for part (a), show the equilibrium after trade in
(d) [1 pt] Are both countries better off after trade (be sure to explicitly explain how you know this to be true
2. This question is intended to refresh your memory with regards to the relationship between factor prices and the input choice of a profit maximizing firm.
(a) [0.5 pt] A firms production function is given by X = 2(LX)(1/3)(KX)(2/3). Name three input combinations that would allow the firm to produce 100 units of output. (Hint: Set X = 100, pick a value for LX and
then solve for KX.) In each case, what is the firm's capital-labor ratio? If the wage rate (w) is 10 per unit
and the rental rate on capital (r) is 20 per unit, what are the firm's costs for each of the three input combinations?
(b) [0.5 pt] Solve the cost minimization problem for a firm using the values given in part (a). What is the
optimal capital-labor ratio?
(c) [0.5 pt] Suppose that the wage rate increases, and the rental rate of capital remains unchanged. Does the capital-labor ratio increase, decrease or remain unchanged?
Please find the solutions attached.
1 With 200 units of Labor
X 1 2
Y 4 3
X 200 100
Y 50 66.67
X 40 40
Y 40 40
Graphing the PPF
US X Y
X Axis 200 0
Y Axis 0 50
Consumption 40 40
US X Y
X Axis 100 0
Full solution in excel file.