Modeling Technological Change

Transcription

1 Modeling Technological Change Yin-Chi Wang The Chinese University of Hong Kong November, 202

2 References: Acemoglu (2009) ch2

3 Concepts of Innovation Innovation by type. Process innovation: reduce cost, or introduce higher quality versions of existing products In growth models, quality improvements = cost reductions E.x. Assume that the utility takes the form of U (qc (q), yjq), where c (q) is the amount consumed of the "vintage" of quality q, y is all other goods, budget constraint p (q) c (q) + y m Alternatively, we can write the problem as max x (q),y s.t. U (x (q), y jq) p(q) q x (q) + y m where x (q) qc (q) is the e ective unit of consumption of good c, i.e., q and c (q) are perfect substitutes 2. Product innovation: Introduce new product

4 Concepts of Innovation 2 Innovation by signi cance. Macro innovations: radical innovations (e.x. electricity, computer,...etc.) that change the organization of product in many di erent product lines (general-purpose technology) 2. Micro innovations: common innovations that introduce newer models of existing products, improve quality, or reduce costs

5 Modeling of Technological Change Model technological change Existence of the meta production function A production function over production functions that determines how new technologies are generated as a function of inputs Also termed as innovation possibilities frontier or R&D production function Usually non-deterministic (uncertainty, stochastic) and allow e orts to a ect the probability of success On the consumer side: usually start with homogenous consumers (though not the case in the real world)

6 Modeling of Technological Change 2 Nonrivalry of ideas Romer (986a): The use of an idea by one producer to increase e ciency does not preclude its use by others F (K, L, A) is CRTS in (K, L) but IRTS in (K, L, A): when ideas are nonrival, the new production facility does not need to re-create or replicate A Spillover e ects: underinvest in R&D Market size e ect: the size of its potential market will be a crucial determinant of whether it is pro table to implement it & whether to research it in the rst place ( xed cost associated with R&D is usually very high) Nonrival v.s. nonexcludabe: could be nonrival but excludable, e.g. patents Is tech. change be driven by scienti c breakthrough or pro ts? Historians: exogenous growth of scienti c breakthrough Economists: pro ts (e.g. horseshoe making, air-conditioniers, cars...etc.)

7 Partial Equilibrium Analysis Start with partial equilibrium model: usually see this approach in IO literature Focus on a single industry Supply Existing technology: produce goods with a xed marginal cost ψ > 0 Demand: Q = D (p) Strictly decreasing, di erentiable, D (ψ) > 0 and PD 0 (p) ε D (p) = 2 (, ) < 0 (elasticity of demand > ) D (p) Ensure a well-de ned monopoly price

8 Pure Competition Research technology: No uncertainty Fixed cost: µ > 0 ψ Marginal cost: λ, λ >, nonexcludable, nonrival Assume N competitive rms, and focus on rm Pro ts of rm : π N p = N ψ q N Since competitive market, p N = ψ, π N = 0 If innovate, when technology is nonexcludable & nonrival: Competitive market, p I = ψ λ < pn, D p I > D p N π I = p I ψ λ q I µ = µ < 0 No incentives to innovate! Schumpeter: pure competition will not generate innovation

9 Social value of innovation Pure Competition 2 S I = 4consumer suplus + 4savings in costs cost of innovation Z ψ ψ = [D (p) D (ψ)] dp + D (ψ) ψ µ ψ λ = λ Z ψ ψ λ [D (p) D (ψ)] (+) if µ is relatively small and λ large Solution dp + D (ψ) λ ψ µ > 0 λ (+). Ex-post monopoly power of innovation (ex-ante perfect competition, ex-post monopoly) Boldrin & Levine are against this view 2. Trade secrecy 3. Innovations that are only appropriate for the rm (de facto excludable)

10 Ex-post Monopoly Suppose that rm can fully enforce the patent if it undertakes a sucessful innovation. Two cases to consider: drastic innovation and limit pricing. Consider the case of drastic innovation rst Drastic innovation: rm becomes an e ective monopolist after the innovation and takes over the entire market (when λ is large enough) Which values of λ leads to this? Suppose taht rm acts like a monopolist max π I p p = D (p) ψ λ µ

11 Ex-post Monopoly 2 Following the standard way to solve the monopolist s pricing: deal with the inverse demand function max π I ψ q = p (q) q λ q µ FOC =) p 0 (q) q + p (q) = ψ {z } λ MR MC p (q) + p0 (q) q = ψ p (q) λ =) pm = ψ/λ ε D (p M ) The innovation is drastic if p M ψ. This happens when λ λ = ε D (p M ). When the innovation is drastic, rm can set its unconstrained monopoly price p M and capture the entire market.

12 Ex-post Monopoly 3 Limit pricing: when the innovation is not drastic so that p M > ψ, or λ < λ, rm has to set the price at p = ψ so as to make sure that it still captures the intire market. Proposition 2. Consider the above-described industry. Suppose that rm undertakes an innovation reducing the marginal cost of production from ψ to ψ λ. If pm ψ (or if λ λ ), then it sets the unconstrained monopoly price p = p M and makes pro ts ˆπ I = D p M p M If p M > ψ (or if λ < λ ), then it sets the limit price p = ψ and makes pro tsψ ψ λ µ. π I = D (ψ) λ λ ψ µ < ˆπI.

13 Ex-post Monopoly 3 Compare the social surplus under drastic innovation and limit pricing: Drastic innovation: Ŝ I = D pm p M ψ λ + R ψ D (p) dp µ p M Limit pricing: S I = D (ψ) λ λ ψ µ Proposition 2.2 We have that π I < ˆπ I < S I and S I < Ŝ I < S I. That is, a social planner interested in maximized consumer and producer suplus is always more willing to adopt an innovation (appropriability e ect). On the contrary, an ex post monopoly rm can only appropriate a portion of the gain in consumer surplus. In addition, the social surplus under ex-post monopoly is always less than that achieved by a social planner.

14 Arrow s Replacement E ect Ex-post Monopoly 4 Assume that rm is an existing monopolist with ˆp M ψ =, ε D (p M ) ˆπ N ˆp ˆp = D M M ψ. If rm undertakes innovation MC = ψ λ, rm still remains as a monopolist p M ψ/λ =, ε D (p M ) ˆπ I = D p M p M 4π I = ˆπI ˆπ N = D p M p M ψ λ ψ λ µ D µ ˆp M ˆp M ψ

15 Ex-post Monopoly 5 Proposition 2.3 We have 4π I < πi < ˆπI, so that a monopolist always has lower innovation incentives than does a competitive rm. Corollary 2. A potential entrant has stronger incentives to undertake an innovation than does an incumbent monopolist. Why? Innovation will replace a monopolist s already existing pro ts.

16 Ex-post Monopoly 6 Creative destruction (Joseph Schumpeter) A process in which economic growth is driven by the prospect of monopoly pro ts and is accompanied by the destruction of existing productive units The essece of the capitalist economic system Create winners and losers Political economy interaction: Because of the replacement e ect, innovations displace incumbents and destroy their rents. To prevent this to happen, current incumbents (usually politically powerful) may use their power to create strong barriers against the process of economic growth Business stealing e ect: the entrant steals the pro ts/business of the incumbent Business stealing e ect helps to close the gap between the private and social values of innovation Possible to lead to excess innovations

17 The Dixit-Stiglitz Model: Finite Number of Products Developed by Dixit and Stiglitz (977) and Spence (976) Feature: constant monopoly markups Representative household s preferences: U (c,..., c N, y) = u (C, y) N where C i= c ε ε i ε ε u (, ) strictly increasing & di erentiable in both arguments, jointly strictly concave C N i = c ε ε ε ε i is called the Dixit-Stiglitz aggregator or the CES aggregator ε : the elasticity of substitution between the di erentiated varieties, assume ε > Budget constraint: N i= p i c i + y m

18 The Dixit-Stiglitz Model: Finite Number of Products 2 Love-for-variety: consider c =... = c N = C N 0 U (c,..., c N, y) = N C i= N = u N ε C, y ε ε! ε ε, ya As N increases, U also increases (love-for-variety, even if total consumption C is xed) Representative household s problem from FOC max u (C, y) fc i g N i=,y s.t. ci ε c i 0 N i= p i c i + y m = p i, for any i, i 0 p i 0

19 The Dixit-Stiglitz Model: Finite Number of Products 3 The ideal price index P: the price index corresponding to the consumption index C ci ε C = p i, for i =,..., N P Use the de nition of C together with the above condition, the ideal price index P is derived as P = N p i i= ε ε. In many circumstances, it is convenient to choose the ideal price index as the numeraire, but not here. The original maximization problem can be boiled down as max C,y u (C, y) subject to constraint PC + y m The budget constraint can be written as: PC + y m

20 The Dixit-Stiglitz Model: Finite Number of Products 4 The maximization yields the FOC u (C, y) / y u (C, y) / C = P Combined with the budget constraint y = g (P, m) and C = m g (P, m) P Pro t maximization problem of rms pi ε max C (p i ψ) p i 0 P FOC: p i = p = ε ε ψ for each i =,..., N

21 The Dixit-Stiglitz Model: Finite Number of Products 5 Hence, the ideal price index and pro ts can be derived as P = N ε ε ε ψ, π i = π = N ε ε C ψ for each i =,..., N. ε Pro ts are decreasing in ε and N, increasing in C The total impact of N on π could be positive: depends on the utility function C = N ε ε m g N ε ε εψ ε ψ, m, π = m g N ε ε εn ε ψ, m. Aggregate demand externality: higher N raises the utility from consuming each of the varieties bks of the love-for-variety e ect

22 The Dixit-Stiglitz Model: In nite Number of Products The Dixit-Stiglitz model with a continuum of products is more widely used in IO and growth literature and more tractable. Also, the supplier of each variety is in nitesimal and their price has no e ect on P and C Representative household s preferences: U [c i ] i2[o,n ], y = u (C, y) Z N where C Budget constraint: R N 0 p i c i di + y m 0 c ε ε i di ε ε

23 The Dixit-Stiglitz Model: In nite Number of Products 2 R N The ideal price index: P = 0 p i ε ε di Pro t: π = εn m g N ε ε ε ψ, m Ex-ante competitive: assume the entry cost is µ, and the free-entry condition is thus εn m g N ε ε ε ψ, m = µ

24 Limitations The most important limitation of the Dixit-Stiglitz model is the feature that makes it tractable: the constant markup Most IO models imply that markups over MC decline in the number of competing products In growth models: if markup declines toward zero, the process of innovation will cease Impossible to have sustainable growth if allowing for decreasing markup Could allow other factors simultaneously increase the potential markups that rms can charge, but not easy to deal with Hence, the growth literature typically focuses on the Dixit-Stiglitz framework