A, B 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.

Given: Consumers: The economy is populated by N consumers, each of them demanding N different goods.…

a. Suppose that the expected sales in each industry are equal to q. Derive an expression for л, 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 well as the profit income from the firms adopting the modern technology. Derive an expression for y in terms of n, and where n is the fraction of sectors using the modern technology.

a. Suppose that the expected sales in each industry are equal to q. Derive an expression for л, 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 well as the profit income from the firms adopting the modern technology. Derive an expression for y in terms of n, and where n is the fraction of sectors using the modern technology.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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