1Endogenous Product CyclesGene M. Grossman and Elhanan HelpmanEconomic Journal 101 (September 1991): 1214-1229Product Cycles (Vernon 1966) Innovation and initial production occurs the North (developed countries), close to large, high-income markets. After production methods become standardized, technology transfer or imitation shifts production to the South (developing countries) due to lower wages there. The North exports the latest, innovative goods in exchange for older, more established goods from the South.2Product Cycle Model (Krugman 1979) Exogenous Technological Change  New products are introduced in the North at an exogenous rate. Southern firms become able to produce goods at an exogenous rate. Finds that relative wage paid to Northern labor (compared to Southern labor): Increases in the rate of innovation relative to imitation, Decreases in the relative size of the Northern labor supply.Endogenous Technological Change Innovation: To be able to produce a new product, Northern entrepreneurs must expend resources. Design good and perfect production techniques. Imitation: To be able to produce an existing product, Southern entrepreneurs must expend resources. Engage in reverse engineering to learn about production processes developed in the North.3Reward to Innovation Since innovation involves costs, there must be enough reward to innovation success for innovation to occur, and similarly for imitation. The expected, present discounted value of profits earned acts as the reward to R&D. Successful innovators earn profits until imitation occurs. Successful imitators earn profits forever but magnitude shrinks over time.Structural Parameters Since innovation and imitation endogenous, can look at effects on them of changing parameters: Northern and Southern labor supplies, Productivity of labor in innovation and imitation, Policies such as tariffs and R&D subsidies.4Consumers (Households) Demand side is standard CES setup with symmetric differentiated products. Preferences for differentiated products identical across countries. Consumers seek to maximize time-separable intertemporalutility function. ρ is subjective discount rate.()()[]τττρdueUttilog∫∞−−=Consumers (Households) Instantaneous sub-utility function x(j) is consumption of product j (j is ω in the article) n is measure of varieties available at time τ.() ()αατ/10⎥⎦⎤⎢⎣⎡=∫ndjjxu5Consumers (Households) Intertemporal budget constraint: present discounted value of expenditure cannot exceed that of income (plus initial assets). R(t) is cumulative interest rate from time 0 to t, E(τ) is spending and Y(τ) factor income at time τ, A(t) is value of initial asset holdings at time t.() ()[]() ()() ()[]()ττττττdYetAdEettRRttRR∫∫∞−∞−+≤Consumers (Households) Intertemporal utility maximization requires Instantaneous utility maximization generates instantaneous demand for variety j p(j) is price of variety j ε = 1 / (1 - α) > 1 is the constant elasticity of substitution between everypair of products.()()()Edjjpjpjxn∫−−=01''εερ−= REE&&/6Production Single primary input is labor. Production of any variety requires axunits of labor for each unit of output. Marginal cost is wiaxin county i. wiis wage in country i. Producers behave as Bertrand competitors. Take prices of other firms’ products as given.Monopoly and Duopoly Two Northern firms will never invent the same variety. Would price at cost and earn no profits. Must earn profits to offset innovation costs. Similarly, two Southern firms will never imitate the same variety. Each new variety starts as a monopoly. Becomes a duopoly following imitation.7Profit Maximization, Northern Firms Consider a Northern firm that is the only firm able to produce a variety. Faces demand curve with constant elasticity -ε. Profit-maximizing price is fixed markup over marginal cost.αxNNawp =Profit Maximization, Southern Firms Consider a Southern firm that is only firm that has imitated a variety. Competes against Northern innovator of that variety. Two possible outcomes depending on the size of the gap between Northern and Southern wages. Based on whether Northern innovator constrains price of Southern imitator.8Pricing by Southern Firms Wide gap case: If wS< αwN, Southern firm can charge its monopoly price (markup over its costs) without fear of competition from Northern rival. Narrow gap case: Otherwise, Southern firm sets price equal to the cost of the Northern innovator.αxSSawp =xNSawp =R&D Learning Activities When entrepreneur hires labor for innovation or imitation, derives appropriable blueprint for producing a variety. Non-appropriable additions to general knowledge. These knowledge spillovers enhance productivity of subsequent learning efforts within the country.9Southern Imitation Southern entrepreneurs chooses at random an existing product that not yet imitated. Must devote aS/KSunits of labor to mastering the production process. aSis productivity parameter for imitation (aIin article). KS = nSis knowledge stock in the South, and is proportional to cumulative imitation experience. nSis measure of imitated varieties.Northern Innovation Northern entrepreneurs must devote aN/KNunits of labor to mastering the production process. aNis productivity parameter for innovation (aDin article). KN = n is knowledge stock in the North, and is proportional to cumulative innovation experience. n is measure of existing (innovated) varieties.10R&D Valuation Conditions When imitation occurs in equilibrium, present-discounted value of Southern profits must equal the cost of imitation. When innovation occurs in equilibrium, present-discounted value of Northern profits must equal the cost of innovation.() ()[]( ) () ()tnatwdeSSSSttRR/=∫∞−−ττπτLabor Constraints Labor demand for innovation and production in the North cannot exceed Northern labor supply. Labor demand for imitation and production in the South cannot exceed Southern labor supply.NNNxNLxnanna=+/&SSSxSSSLxnanna=+/&11Results for Wide Gap Expansion in Northern labor supply or improvement in productivity of innovation does not affect innovation and imitation! Northern relative wage rises. Expansion in Southern labor supply or improvement in