What does vector refer to? What does it mean if the th element, , is positive
For answering this question, you are supposed to study lecture notes as well as the paper entitled “An Empirical Assessment of the Comparative Advantage Gains from Trade: Evidence from Japan” by Bernhofen and Brown. The authors’ goal is to measure a nation’s welfare gains from free trade compared to autarky.
You do not have to read this paper in its entirety. You are required to study only the parts related to the following questions.
Suppose the economy consists of goods. Let be the vector of prices in autarky, and be the vector of prices under free trade. Let be the vector of production quantities in autarky, and be the vector of consumption quantities in autarky. Similarly, define and as production and consumption vectors under free trade.
The change to welfare between autarky and free trade evaluated at autarky prices, is given by
where • is the inner product. (Note: The authors of the above paper drop • as the inner product with the understanding that they always use inner product.)
a) Show that
b) What does vector refer to? What does it mean if the th element, , is positive?
c) Why did the authors use the more complicated equation (2) instead of the simpler equation (1)?
d) Our equation (2) here is the same as equation (4) in the paper “An Empirical Assessment …” in page 212. In the same page, the authors claim is non-negative. Explain why their claim is correct.
e) Why do the authors measure only an upper bound on instead of itself? What upper bound do they use?
f) The authors report 9% as the change to income from autarky to trade relative to GDP for Japan in the nineteenth century. U.S. GDP is roughly 18 trillion dollars, and U.S. population is roughly 320 million people. Suppose the change to U.S. GDP from a hypothetical move to autarky is 9% of its current GDP. How many dollars would on average an American lose from a move to autarky?
New Trade Theory
Consider the Krugman model whose equilibrium could be described by the intersection of PP (pricing rule) and ZZ (zero profit condition) schedules. How would the closed-economy equilibrium change if fixed costs were larger? Use the graph with PP and ZZ schedules, and explain how in the new equilibrium, consumption per capita of a product, supply quantity of a product, price of a product relative to wage, and number of product varieties change. Provide intuition for your results.
Again, consider the Krugman model. Suppose two identical countries that were in autarky (initial equilibrium) move to free trade (new equilibrium). Use the graph with PP and ZZ schedules, and explain how in the new equilibrium compared to the initial equilibrium, consumption per capita of a product, supply quantity of a product, price of a product relative to wage, and number of product varieties available to consumers change. Provide intuition for your results.
a) Home’s demand and supply curves for sugar are
What would the price of sugar be in the absence of trade in Home? Derive Home’s import demand schedule.
Now add Foreign whose demand and supply curves are: What does vector refer to? What does it mean if the th element, , is positive
Derive Foreign’s export supply schedule, and find the price of sugar that would prevail in Foreign in the absence of trade.
Now allow Home and Foreign to trade with each other at zero trade costs. Find the equilibrium price and volume of trade under free trade.
Home imposes a specific tariff of 0.5 on sugar imports. Determine the effects of the tariff on the following: (i) price of sugar in each country, (ii) quantity of sugar supplied and demanded in in each country, and (iii) volume of trade.
Determine the effect of the tariff on (i) Home’s consumer surplus, (ii) Home’s producer surplus, and (iii) Home’s government revenues. Show graphically and calculate the total effect of the tariff on Home’s welfare. What does vector refer to? What does it mean if the th element, , is positive