Intertemporal Trade: Global Equilibrium in an Endowment Model Answer all parts (a)-(f) of this question. Consider a model with two periods t = 1, 2 and two countries, Home and Foreign. Home re- ceives an endowment of Y1 at date 1 and an endowment of Y2 at date 2. Foreigns endowments at dates 1 and 2 are denoted Yb1 and Yb2 respectively. The two countries can borrow and lend from/to each other at (gross) interest rate 1 + r. Representative households in both countries maximize lifetime utility U(C1) + U(C2) with U(Ct) = C 1 t 1 , = 2 and (0, 1) where Ct denotes consumption at date t. (a) [6 marks] Write down the intertemporal budget constraint of the representative household in the Home country. (b) [10 marks] Derive optimal consumption at date 1 of the representative household in the Home country. (c) [10 marks] Use the world market clearing condition at date 1 and your answer from part (b) to derive the world interest rate 1 + r as a function of the world growth rate. [Hint: To simplify notation it may be helpful to denote Y W t = Yt + Ybt as world output at date t.] (d) [8 marks] Derive the autarky interest rate in the Home country. (e) [10 marks] Show that the Home country runs a trade deficit at date 1 if and only if Homes autarky rate is higher than the world interest rate. (f) [6 marks] Explain intuitively how an increase in the Foreign growth rate Yb2 Yb1 affects Homes trade balance at date 1. (No derivations needed.)