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TAMU ECON 652 - Quality Ladders Handout

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Quality Ladders and Product CyclesGene M. Grossman and Elhanan HelpmanQuarterly Journal of Economics 106 (1991): 557-586Product Cycle & Quality Improvement Product differentiation can take two forms: horizontal (variety) and vertical (quality). GH had product cycle model where innovations introduced new varieties. Also had model of endogenous quality upgrading. Put together to get product cycle model where innovations introduce higher quality levels of existing products. Following innovation, Northern firm earns profits until a Southern firm imitates, who earns profits until another innovation occurs.Product Quality Each product can be improved repeatedly. Increments to quality are common across all products and exogenously given by the parameter λ > 1. Initial lowest quality level of a good is normalized to q0(j) = 1 [j is ω in article]. After m [j in article] improvements in product j, its highest available quality is qm(j) = λm.Consumers Problem Maximize additively separable intertemporalutility function: Instantaneous utility Subject to intertemporal budget constraint∫∞−0i)(loge=U dttuitρ()()()dttYeAdttEeitRiitR∫∫∞−∞−≤00)(0)(()djtjximm,log=(t)u log10mi∫∑λConsumers Solution Choose the highest quality level available of each product at each point in time as offers lowest quality-adjusted price. Evenly spread expenditure across continuum of products and across time Aggregate expenditure E = EN+ ESiiiEtEtjE==)(),(11>(j,t)=λ(j,t)/ppm-m()()djtjxtjpEmmmi,,10∫∑=Innovation Follows a Poisson process. At each time interval dt, the probability of success is ιNdt. The intensity of innovation ιNindicates a firm’s effort. The cost of innovation is wNaNkιNdt. When innovation occurs with finite positive intensity, its value vNkhas to equal to wNaNk.Leaders and Followers  Distinguish between innovation undertaken by firms who successfully developed the current generation of the product (called leaders), and all other firms (called followers). Innovation is easier for leaders than followers aNL< aNFdue to product-specific knowledge acquired. Outsiders observe only the product and not the process that led to its discovery.Imitation Follows a Poisson process. At each time interval dt, the probability of success is μSdt. The intensity of imitation μSindicates a firm’s effort. The cost of imitation is wSaSμSdt. When imitation occurs with finite positive intensity, its value vShas to equal to wSaS.Three Types of Market Structures NN: Northern firm who innovated over another Northern firm and so has a Northern firm one quality level down as closest rival. NS: Northern firm who innovated over a Southern firm and so has a Southern firm one quality level down as closest rival. S: Southern firm who imitated the product of a Northern firm producing same quality level.Production Costs Normalize unit labor requirement in production to one in each country. Normalize prices by the Southern wage (set wS= 1). Define w = wN/ wS= wNas the Northern relative wage, the wage in the North relative to the wage in the South. Producing one unit of output in the North costs w > 1 and in the South costs one.Limit Pricing NN: Set price equal to quality increment times Northern wage (Northern wage is cost of closest rival). NS: Set price equal to quality increment (closest rival has cost of one). S: Set price equal to Northern wage (cost of closest rival). Same quality level so no quality premium.wpS=wpNNλ=λ=NSpProfits()()()EwwEwxpSSS/11/11−=−=−=π()()()EwEwwxwpNNNNNNλλλπ/11/−=−=−=()()()EwEwxwpNSNSNSλλλπ/1/−=−=−=Valuations Northern firms of both types face risk of innovation and imitation. Southern firms face risk of only innovation.SNNNSNSSNNNNNNvvμιρπμιρπ++=++= ,NSSSvιρπ+=Valuation Conditions Northern followers (compete against Northern rival)  Northern leaders (compete against Southern rival) Southern firms()()NSSawEιρ+=− /11()()SNNNLwawEμιρδ++=−1()()SNNNFwaEμιρδ++=−1Aggregation Measures of production sum to one:nNN+nNS+nS= 1 Aggregate rate of innovation equals:ι= ιNS nS+ ιNN (nNN+nNS) Aggregate rate of imitation equals:η = μS(nNN+nNS) Flows in must equal flows out of each type of market structure. Resource Constraints Northern labor constraint requires labor demand for innovation and production to not exceed Northern labor supply: Southern labor constraint requires labor demand for production to not exceed Southern labor supply:NNSNNSNSNSNNNNNLEnwnnana =⎟⎠⎞⎜⎝⎛+++διιSSNSSLwEnna =+μComparative Statics The main equations are the innovation and imitation valuation conditions and the Northern and Southern labor constraints. Consider separately case with efficient followers (innovation targets all products) and with inefficient followers (innovation targets only products where latest quality level has been imitated).Results For inefficient followers, aggregate rate of innovation equals that of imitation. Both increase with increases in either labor supply or increases in subsidies to either innovation or imitation. For efficient followers, aggregate rate of innovation increases with increases in the Northern labor supply or innovation subsidy, decreases with imitation subsidy, and unclear result for Southern labor supply. Aggregate rate of imitation increases with increases in either labor supply or imitation subsidy and decreases with increases in innovation subsidy.++++Rate of innovation& imitationInefficient followers+-++Rate of imitation-+?+Rate of innovationEfficient followerssSsNLSLNConclusion Effects of parameters on rates of innovation and imitation depend on whether: Innovation enhances variety or quality Innovation by leaders or followers Imitation endogenous or


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