01 May Question: Due Date: Tuesaay, January zy at tne start or tne lecture Model S
Due Date: Tuesaay, January zy at tne start or tne lecture Model Setup Let’s model an economy that produces and consumes only two goods, croissants (C) and espresso (E), between two cities, Toronto (T) and Paris (P). In Paris, each unit of labour produces 5 croissants or 2 shots of espresso. In Toronto, unit of labour produces 4 croissants or 10 shots of espresso. There are 200 units of labour in Toronto and 400 units of labour in Paris. Let Dj stand for the consumption level of good j in city i. Let Qj stand for the production level of good j in city i. Assume that consumer preferences in both cities are described by the same utility function: Please answer all of the questions below. Questions 1. What does it mean for a city to have an absolute advantage in the produc
5. What is the autarky relative price of espresso in terms of croissants in the two cities? Draw the relative supply curve of espresso to croissants for both cities in autarky. 6. Assuming consumers are maximizing their utility subject to a budget con- straint, we can derive the following optimality condition: Pc MUc PE MUE where MUj is the marginal utility of good j. Please do the following (a) Write down the consumer’s maximization problem for city i, given consumer preferences. Assume income is given and denote it by I (b) Derive the relative price equal relative marginal utility condition above from the first-order conditions of the consumer’s problem. Do these conditions guarantee a solution that is optimal? Why or Why not? (c) Solve for the relative demand functions, (#) (ie, the ratio of demand as a function of prices). 7. Draw the relative demand and supply curves you derived in questions 5 and 6 for each city. Clearly label and solve for the equilibrium relative demands under autarky. What is the relative production in each country under autarky? 8. Solve for the equilibrium consumption and production levels of espresso and croissants in both cities in autarky (Hint: Substitute the equilibrium relative demands into the PPF equations from question 3).
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