2. Imagine the following goal of Lenin/Stalin at the beginning of the Soviet regime in Russia: to overtake (i.e. equal) and surpass the world's industrialized economies in terms of GDP per capita. To achieve this goal, the main instrument of control is the fraction of national production that is devoted to building the nation's productive capacity: new machines, factories, transportation equipment, and roads (i.e. investment as a share of GDP). The rest of national production is used for consumer items like clothing and food. The country begins with relatively little capital, being mostly rural and non-industrialized. Assume each of the following:

- GDP per capita starts in Russia at $300/year.

- The world's industrialized economies start with GDP per capita of $5000/year.

- Population growth rates are 2% everywhere in the world.

- All capital depreciates at 8% per year.

Assume the basic growth framework of Solow. Further assume y = 400k1/3 in Russia.

a. Solve for Soviet long-run GDP per capita (y*), as a function of its savings rate. (That is, your expression for y* should include the variable s in it, and no other variables.) For parts b.-d., assume long-run GDP per capita equals $10,000 in the industrialized countries, and that they are saving 10% of income. b. What fraction of national output should be devoted by the Soviet Union to building new capital goods in order to overtake, i.e. equal, the industrialized nations' GDP per capita in the long-run? What fraction is left for consumer items? c. What fraction of national output should be devoted by the Soviet Union to building new capital goods in order to surpass, i.e. double, the industrialized nations' GDP per capita in the long-run? What fraction is left for consumer items? d. In the long run, what is the ratio of Soviet GDP per capita to GDP per capita in the industrialized countries, and what is the ratio of Soviet consumption per capita to consumption per capita in industrialized countries if the Soviet Union achieves the goal of part b? of part c? (That is, find four ratios.)

e. Comparing the outcomes of part d. of this question to the same question answered using the Harrod-Domar model (5e. from problem set 1), which model produces a more optimistic outlook for achieving, by saving and investing at high rates, the Soviet goals of overtaking and surpassing industrialized countries' living standards? Remember that living standards are best measured by consumption here.