TAILIEUCHUNG - International Macroeconomics and Finance: Theory and Empirical Methods Phần 4

KINH TẾ trao đổi Một số người thích suy nghĩ của những Þrms như cây ăn quả. Bạn cũng có thể bình thường hóa số lượng Þrms ở mỗi nước 1. xt là sản lượng trong nước, ngoại sinh và yt là đầu ra nước ngoài ngoại sinh. | . THE BARTER ECONOMY 107 capital inputs. Some people like to think of these firms as fruit trees. You can also normalize the number of firms in each country to 1. xt is the exogenous domestic output and yt is the exogenous foreign output. The evolution of output is given by xt gtxt-1 at home and by yt gt yt-1 abroad where gt and gtt are random gross rates of change that evolve according to a stochastic process that is known by agents. Each firm issues one perfectly divisible share of common stock which is traded in a competitive stock market. The firms pay out all of their output as dividends to shareholders. Dividends form the sole source of support for individuals. We will let xt be the numeraire good and qt be the price of yt in terms of xt. et is the ex-dividend market value of the domestic firm and et is the ex-dividend market value of the foreign firm. The domestic agent consumes cxt units of the home good cyt units of the foreign good and holds Vxt shares of the domestic firm and Vyt shares of the foreign firm. Similarly the foreign agent consumes cXt units of the home good cyt units of the foreign good and holds Ỵtt shares of the domestic firm and yt shares of the foreign firm. The domestic agent brings into period t wealth valued at Wt Yrt-1 xt et yt-1 qtyt et where xt et and qtyt et are the with-dividend value of the home and foreign firms. The individual then allocates current wealth towards new share purchases et Vxt et x yt and consumption cxt qtcyt Wt et xt etuyt cxt qtcyt Equating to gives the consolidated budget constraint cxt qtcyt et xt etuyt Yrt-1 xt et Myt-1 qtyt et . Let u cxt cyt be current period utility and 0 p 1 be the subjective discount factor. The domestic agent s problem then is to choose sequences of consumption and stock purchases cxt j cyt j Vxt j yt j j 0 to maximize expected lifetime utility m X ju cxt j cyt j j 0 108 CHAPTER 4. THE LUCAS MODEL subject to . You can transform the constrained optimum .

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