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structure in the model is relatively standard in the literature. Home and foreign agents can trade in one non-contingent bond, B t that pays out one unit of home-produced intermediate goods in period t + 1. I denote by B t the quantity and by R t the price of the bond purchased by home agents at the end of period t:The representative consumer faces the following budget constraint in each period t: P t C t + P H;t R t B t = P H;t B t 1 + P t w t h t + t (4) where P t is the price index of the consumption bundle, de…ned below, P H;t is the price of home produced intermediate goods and w t is the real wage. In addition to the wage, the representative household receives dividends, t , from holding a share in the equity of domestic …rms. All domestic …rms are wholly owned by domestic agents and equity holding within these …rms is evenly divided between domestic households. When optimising, the representative household takes the ‡ow of dividends as given. The maximization problem of the Home representative agent consists of maximizing (1) subject to (4), along with the usual transversality condition: lim T !1 E t TY R s B t+T = 0 (5) s=1 in determining the optimal pro…le of consumption and bond holding and the labour supply schedule. The corresponding Lagrange multiplier is: max C t;h t;B t; t L = E t 1 X s=t s U(C s ; (1 PH;s h s )) + s B s 1 + w s h s + s P H;s C s R s B s P s P s Using …rst order conditions for optimal consumption, labour e¤ort and bond holdings one can derive the static e¢ ciency condition for the consumption-labour choice as well as the consumption Euler equation: U C (C t ; (1 h t )) P H;t P t P s (6) U h (C t ; (1 h t )) U C (C t ; (1 h t )) = w t (7) = ( ~ C t ; ~ h t ) 1 R t E t U C (C t+1 ; (1 h t+1 )) P H;t+1 P t+1 In equilibrium, the household and average per capita levels of consumption and e¤ort are (8) 6
the same, such that C t = ~ C t (9) h t = ~ h t (10) 2.2 Final consumption goods sector Home …nal consumption goods (C) are produced with the aid of home and foreign-produced intermediate goods (c H and c F ) in the following manner: C t = hv 1 c 1 H;t + (1 v) 1 1 c F;t i 1 (11) where is the elasticity of intratemporal substitution between home and foreign-produced intermediate goods. Final goods in the home and the foreign country di¤er in terms of their composition of home and foreign-produced intermediate goods (v > v ). Final goods producers maximize (12) subject to (11). max P t C t P H;t c H;t P F;t c F;t (12) c H; c F This maximization yields the following input demand functions for the home economy (similar conditions hold for Foreign producers) PH;t PF;t c H;t = v C t , c t;F = (1 v) C t (13) P t P t The price index that corresponds to the previous demand function is de…ned as: Pt 1 = [vP 1 H;t + (1 v)P 1 F;t ] (14) An analogous production structure exists for the production of foreign …nal consumption goods. 7
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Page 3 and 4: sume …nancial autarky. They show
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