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Unformatted text preview: Welfare of Trade Joel R. Landry AEM 2300—International Trade and Finance, Spring 2011 Prof. David Lee Spring 2011 March 3, 2011 This handout is intended as a complement to the graphical analysis presented in class and section, not as a substitute. If you think that you can simply memorize these equations and apply them without thinking you will find yourself ill-prepared both in the exam and with regards to a deeper understanding of the material. What this document is intended to do is to gently walk you through the various stages of thinking about both trade and its welfare implications. These equations, as such, all flow logically with a graphical understanding and analysis of the issues. You will typically find it easier to think through the graphs as a way to get your answer, rather than simply plugging in these equations without thinking. These caveats in mind, we now proceed. 1 Getting the Autarky Equilibrium 1.1 Set-up Our first objective is to generate the autarky (no trade) equilibrium for each country. Consider two countries A and B . We consider trade between A and B in a single good. For simplicity we will specify the inverse 1 demand functions as: P = m A D × Q + b A D (1) P = m B D × Q + b B D For countries A and B , respectively. Here the parameters m A D and b A D are the slope and intercept terms for the demand function for country A . Likewise, m B D and b B D , are the slope and intercept terms for the demand function for country B . 1 We call this the ‘inverse’ demand equation, since the solution to the utility maximization problem yields the demand function, Q D = f ( P ) . In this case we say the consumer (here, country) decides the quantity they demand, Q D , having observed some price p , where f ( · ) is any arbitrary function. The ‘inverse’ demand function simply reverse solves the ordinary demand equation, with P on the left-hand-side, or, P = f- 1 ( Q D ) , where we call f- 1 ( · ) the ‘inverse’ function of f ( · ) . 1 Joel R. Landry, Welfare of Trade We can also specify the supply functions as: P = m A S × Q + b A S (2) P = m B S × Q + b B S For countries A and B , respectively. Here the parameters m A S and b A S are the slope and intercept terms for the supply function for country B . Likewise, m B S and b B S , are the slope and intercept terms for the supply function for country B . 1.2 Solve for Equilibrium To obtain the autarky equilibrium, ( P i ,Q i ) , for each country i = { A,B } , we simply set (1) equal to (2), and solve (in this case) for Q . To distinguish the fact this will yield a different result for each country, note that we have added the superscripts to P and Q from above. Finally, we have: m i D × Q i + b i D = P i = m i S × Q i + b i S ⇔ (3) m i D × Q i = m i S × Q i + b i S- b i D ⇔ m i D × Q i- m i S × Q i = b i S- b i D ⇔ ( m i D- m i S ) × Q i = b i S- b i D ⇔ Q i = ( b i S- b i D ) ( m i D- m i S ) This is the quantity supplied and demanded in country i . We can plug....
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