Assignment
1. Opportunity Costs and Gains from Trade.
Suppose that the world consists of only two countries, the UK and France, and only two goods are being produced, wine (W) and cheese (C). The amount of labour units required to produce one unit of either good are as follows:
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Unit Labour Requirements
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Wine
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Cheese
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UK
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4
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2
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France
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2
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4
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Also assume that in each country (under autarky, i.e., no trade takes place), the price of either good reflects the production costs. E.g., in the UK, a unit of wine costs 4£, while it costs 2£ in France.
The UK's total labour force is LUK = 240, while France's labour force is LF = 120. Labour is the resource either country has.
Consumers in both countries have identical preferences. In both the UK and in France, consumers' preferences are given by
U (W, C) = min {W, ½ C} (1)
Where W are the units of wine consumed, and C denotes the units of cheese consumed.
(a) Illustrate some indifference curves for this type of utility function (with wine on the vertical axis). Discuss the main properties of the preferences, and explain their rationale.
(b) Derive and illustrate the PPF for each country under autarky (with wine on the vertical axis). Given the prices of goods under autarky, illustrate and solve for the optimal output combination of wine and cheese in each country.
(c) Determine the world PPF and illustrate it. [Hint: The maximum amount of each good produced should be the quantity of both countries' production added together.] Discuss your reasoning. Comment.
(d) Given your result in (c), and the preferences, determine the free trade equilibrium.
Explain the pattern of trade and who gains from trade and why.
2. In the market for apples, quantity demanded is given by QD = 100 - 8P + 0.5Y and quantity supplied by QS = -10 + 4P - 4W, where P is the price of apples, Y is total consumers' income and W is the wage rate. Suppose also that initially Y = 300 and W = 10.
(a) Derive the equilibrium price and quantity and illustrate the equilibrium in a diagram.
(b) Suppose now that Y goes up to 420 and the wage rises to 16. Find the new equilib- rium price and quantity and illustrate it.
(c) You are in the equilibrium of part (b). The government is concerned that the price of apples is too high and wants to maintain a price of P = 30. Suppose the government achieves this through rationing. What would the economic implications of this be?
(d) How would your answer to (c) change if the government achieved a price of P = 30 through manipulation of the wage rate?
3. Cigarette taxation and elasticities
The World Heath Organization (WHO) has a Tobacco Free Initiative (TFI) in place. Studies have shown that demand for tobacco products is sensitive to price changes, which is why the initiative suggests taxation policies for tobacco products to affect demand.
You have been provided with the following estimated demand elasticities for cigarettes in a given country. Here, education is measured in years of schooling, and regulations are measured as an index variable (such that a higher index value corresponds to more stringent regulations on where/when one can smoke).
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Elasticities of Demand
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Own price elasticity, adults
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Own price elasticity, teenagers
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Income elasticity
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Education elasticity
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Regulatory elasticity
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1980 0.0
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-0.8
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0.05
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-0.3
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-0.2
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2010 -0.3
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-1.2
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-0.5
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-0.6
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-0.3
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You can assume that demand for cigarettes is linear.
(a) How do you interpret the change in the price elasticity of demand for adults between 1980 and 2000? Why do you think that the price elasticity for teenagers is larger in absolute value than that for adults?
(b) How do you interpret the fact that the income elasticity has changed sign from 1980 to 2000?
(c) Interpret the sign and magnitude of the education and the regulatory elasticities of demand.
(d) The TFI aims to reduce the levels of smoking. Faced with the values of 2010, should the WHO advise governments to increase taxes on cigarettes, or rather increase regulations? Why?