Linear regression
QUESTION
We solve the 2 × 2 Ricardian model with a constant elasticity of substitution (CES) demand.
Assume that the demand in country n of the goods i, yni, is the result of the utility maximization:
max h
(yn1)
σ−1
σ + (yn2)
σ−1
σ
i σ
σ−1
s.t. pn1yn1 + pn2yn2 = Xn,
where n = N, S indexes the country, and Xn is the total expenditure of the country. σ > 1
denotes the elasticity of substitution across goods.
(a) Write down the Lagrangian function and solve for the optimal consumption bundle for
country n.
(b) The ideal price index is defined as the cost of one unit of utility. Show that with CES
utility function, the price index takes the form:
Pn =
(pn1)
1−σ + (pn2)
1−σ
1
1−σ
(c) Under the assumption of free trade, law of one price holds so we have pN1 = pS1 = p1,
and pS1 = pS2 = p2. Solve for the world relative demand of the two goods.
(d) Same as in the lecture, we assume the North has comparative advantage in goods 1, so:
aN1
aN2
<
aS1
aS2
.
Derive the world relative supply of the two goods.
(e) Derive the autarky real wage in the North.
(f) Derive the real wage in the North under trade, and compute its gains from trade.
1
Created in Master PDF Editor
Sample Solutions
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Phasellus hendrerit. Pellentesque aliquet nibh nec urna. In nisi neque, aliquet vel, dapibus id, mattis vel, nisi. Sed pretium, ligula sollicitudin laoreet viverra, tortor libero sodales leo, eget blandit nunc tortor eu nibh. Nullam mollis. Ut justo. Suspendisse potenti.
Get sample solution
Sed egestas, ante et vulputate volutpat, eros pede semper est, vitae luctus metus libero eu augue. Morbi purus libero, faucibus adipiscing, commodo quis, gravida id, est. Sed lectus. Praesent elementum hendrerit tortor. Sed semper lorem at felis. Vestibulum volutpat, lacus a ultrices sagittis, mi neque euismod dui, eu pulvinar nunc sapien ornare nisl. Phasellus pede arcu, dapibus eu, fermentum et, dapibus sed, urna.
Morbi interdum mollis sapien. Sed ac risus. Phasellus lacinia, magna a ullamcorper laoreet, lectus arcu pulvinar risus, vitae facilisis libero dolor a purus. Sed vel lacus. Mauris nibh felis, adipiscing varius, adipiscing in, lacinia vel, tellus. Suspendisse ac urna. Etiam pellentesque mauris ut lectus. Nunc tellus ante, mattis eget, gravida vitae, ultricies ac, leo. Integer leo pede, ornare a, lacinia eu, vulputate vel, nisl.
Suspendisse mauris. Fusce accumsan mollis eros. Pellentesque a diam sit amet mi ullamcorper vehicula. Integer adipiscing risus a sem. Nullam quis massa sit amet nibh viverra malesuada. Nunc sem lacus, accumsan quis, faucibus non, congue vel, arcu. Ut scelerisque hendrerit tellus. Integer sagittis. Vivamus a mauris eget arcu gravida tristique. Nunc iaculis mi in ante. Vivamus imperdiet nibh feugiat est.
Ut convallis, sem sit amet interdum consectetuer, odio augue aliquam leo, nec dapibus tortor nibh sed augue. Integer eu magna sit amet metus fermentum posuere. Morbi sit amet nulla sed dolor elementum imperdiet. Quisque fermentum. Cum sociis natoque penatibus et magnis xdis parturient montes, nascetur ridiculus mus. Pellentesque adipiscing eros ut libero. Ut condimentum mi vel tellus. Suspendisse laoreet. Fusce ut est sed dolor gravida convallis. Morbi vitae ante. Vivamus ultrices luctus nunc. Suspendisse et dolor. Etiam dignissim. Proin malesuada adipiscing lacus. Donec metus. Curabitur gravida