C,D 1- Complementaritiesand IndustrializationConsider the following variation of the model of industrialization and coordinationfailures by Murphy, Shleifer and Vishny (1989) discussed in lectures 8.Consumers: The economy is populated by N consumers, each of them demanding Ndifferent goods. Individuals expend a constant fraction, 1/N, of their income in eachof the N goods.Traditional Firms: In each sector, there are a large number of firms that can produceusing a traditional technology. Using the traditional technology, 1 unit of labor can beused to produce 1 unit of the good, qold-1. Notice that the price of the good could neverexceed the wage w (why?). Therefore, traditional firms will earn zero profits.Modern Firms: In each sector, there is a potential firm that must decide whether to use amodern technology. To use the modern technology a firm must purchase yF/N units ofthe goods produced by each of the N industries (including itself) and hire (1-y)F units oflabor, so that the total fixed cost is equal to F. If the modern technology is adopted by agiven firms in a sector, this firm produces using a superior technology that transform 1unit of labor into a units of the good, qmodern=a*1, where a>1.Labor Market: Traditional and modern firms compete in the same labor market, andtherefore, they must pay the same wage. Wages paid by traditional and modern firms isnormalized to 1, wold- wmodern =1.a. Suppose that the expected sales in each industry are equal to q. Derive an expressionforTT, the expected profits of using the new technology as a function of F, q, a.b. The income per capita in this economy, y, is the sum of per capita labor income as wellas the profit income from the firms adopting the modern technology. Derive anexpression for y in terms of n, à and where n is the fraction of sectors using the moderntechnology.c. The expected sales of each industry, q, are the sum of the demand from consumers andthe demand from modern firms. The demand from modern firms is equal to nyF, the totalpurchases by firms adopting the new technology. Therefore, the expected sales of anindustry areq=y+nyFUsing this equation and your answer to a-b, derive an equation relating y with n, a, y andF. Solve for y in terms of n, a, y and F.d. Combining a-c, derive an expression for a in terms of n, a, y and F.

Outcomes from point (a) and (b) π = (a-1)l - F(1-γ) - γFN(N-1) y = l + n((a-1)l - F(1-γ) -…

c. The expected sales of each industry, q, are the sum of the demand from consumers and the demand from modern firms. The demand from modern firms is equal to nyF, the total purchases by firms adopting the new technology. Therefore, the expected sales of an industry are q=y+nyF Using this equation and your answer to a-b, derive an equation relating y with n, a, y and F. Solve for y in terms of n, a, y and F. d. Combining a-c, derive an expression for in terms of n, a, y and F.

c. The expected sales of each industry, q, are the sum of the demand from consumers and the demand from modern firms. The demand from modern firms is equal to nyF, the total purchases by firms adopting the new technology. Therefore, the expected sales of an industry are q=y+nyF Using this equation and your answer to a-b, derive an equation relating y with n, a, y and F. Solve for y in terms of n, a, y and F. d. Combining a-c, derive an expression for in terms of n, a, y and F.

Economics For Today

10th Edition

ISBN:9781337613040

Author:Tucker

Publisher:Tucker

Chapter2: Productions Possibilities, Opportunity Costs, And Economic Growth

Section2.7: Present Investment And The Future Production Possibilities Curve

Problem 1GE

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