Chapter 5. The Engine of Growth. Instructor: Dmytro Hryshko

Transcription

1 Chapter 5. The Engine of Growth Instructor: Dmytro Hryshko

2 Endogenous growth theory. The Romer model Where does the technological progress come from? Is there limit to economic growth and technological progress? The theory focuses on understanding the economic forces underlying technological progress (the possibility to earn a prot is important). Better thought of as a model for developed economies, where technological progress is driven by R&D in advanced economies.

3 The basic elements of the model The nal good is produced as: = F (K; L ) = K (L ) 1 ; 0 < < 1; where L is the amount of labor used to produce the nal good. F (K; L ) is increasing returns to scale in, K and L : F (K; L ) = K (L ) 1 = 2 >. s before, _K = s K, and _ L L = n. Want to model _ creation of new ideas (the ow of ideas).

4 Production function of new ideas Intuitively, _ should depend on: the amount of labor devoted to creation of ideas, L : e.g., _ = dl each unit of labor involved in R&D produces d new ideas; maybe, more people searching for ideas will tend to duplicate ideas: _ = dl, < 1; the available stock of ideas, : e.g., larger stock, harder to produce ideas _ = L, < 0; larger stock, easier to produce ideas _ = L, > 0. Summing up, _ = dl : llocation of labor L + L = L, where L = s R L, and L = (1 s R )L.

5 Growth in the Romer model In the model, g = g y = g k, where g, g y and g k are growth rates of ideas, output per worker and capital per worker, respectively. Use _ = dl, to obtain _ = dl 1 = d L 1. For _ to be constant, L should grow at the same rate as 1. Thus, L _ L = (1 ) _ = (1 )g L. Note that _ L L = _ = n, otherwise, L labor engaged in research will either exceed the total population (if _L L > _ L L ), or cease to exist (if _ L L Thus, n = (1 )g, and g = n 1. < _ L L ). Suppose = 1, = 0, so that _ = dl. Exponential growth is possible only if population grows (more population means more researchers, which means more ideas, which means sustained economic growth).

6 Some notes Romer (1990) assumes = 1 and = 1: _ = dl, or _ = dl. This gives a prediction that runs against the data: g and the growth rate in output per worker should have been accelerating after 1960 since L was accelerating during that period. Thus, should be less than one. Even if we model evolution of, the long-run growth cannot be manipulated by policymakers, for example, by subsidizing R&D.

7 Growth eects versus level eects n increase in the share of population doing research (e.g., a subsidy for R&D) to s 0 R > s R. 1 nalyze the eects on technological growth and the stock of ideas. 2 Follow the steps of transitional dynamics in the Solow model. ssume = 0 and = 1: _ = dl, and _ = d L Since _ = g in steady state, L = g d. = d s RL. The level of technological progress increases permanently, the growth rate reverts to its previous level, g.

8

9

10

11 Output per worker in steady state with = 1 and = 0 In the steady state, L = L = (1 s R )L, L (t) = steady state, _ 1 s 1 n+g (t). Since + 1 s 1 (1 s R )(t). In the n+g + = g = d s RL, and so (t) = d s RL(t) g. Thus, output per worker in the economy is 1 L (t) = s 1 n+g (1 s + R )d s R g L(t). L(t) in the formula stands for the scale eect: a larger world economy is a richer economy (more labor, more demand for ideas (demand eect), and more ideas created (supply eect)). s R enters positively to reect the idea that more researchers create more ideas and increase productivity and negatively (through the term 1 s R) to reect the idea that more researchers means less labor producing output.

12 Micro-foundations of the Romer model There are 3 sectors in the economy. 1 research sector (produces ideas). 2 n intermediate-goods sector (manufactures a capital good developed by the research sector and has an exclusive right to selling this capital good). 3 nal-goods sector (purchases the capital good and produces the nal good).

13 The nal-goods sector The number of capital goods/ideas is. competitive rm producing the nal good utilizes all capital goods: = L 1 (x 1 + x 2 + : : : + x ) = L 1 X j=1 x j : Easier to think in terms of integration, where the number of intermediate goods is innite and they are labeled on the real-line interval [0; ]. = L 1 Z j=0 x j dj: P 10 R For example, j=1 xj and 10 xj dj j=0 when xj = 100 for all j are the same, and equal to 1,000.

14 The objective of the nal-goods rm max L ;fx j g j=1 X L 1 x j j=1 {z } X wl p j x j ; j=1 where p j is the price of the j-th capital good. t the optimum, the following + 1 equations should hold: w = (1 )L p j = L 1 x 1 j : X j=1 x j = (1 ) L The second equation species the demand curve for capital good j.

15 The intermediate-goods sector Monopolists produce the capital goods used by the nal-goods sector. Patent enables each rm to produce only one capital good. The objective is: max x j j = p j (x j )x j rx j ; where r is the marginal cost of producing one unit of x j. Dropping subscript j, at the optimum, for each rm the following should be satised: Note that p = 1 1+ p0 (x)x p p 0 (x)x + p(x) r = 0: is priced at a mark-up over marginal cost. r. Since p 0 (x) = ( 1) p x, p = r a good

16 Production function consistent with micro-foundations P P Note that j=1 j = j=1 L1 X X x j j=1 {z } L 1 x j j=1 {z } 2 L 1 x 1 j P x j j=1 p jx j = = (1 ). If prots of each rm are equal so that j =, then = (1 ) and = (1 ) P. Market-cleating for the intermediate-goods sector: K = j=1 x j = x, or x = K if x j = x. Output in the nal-goods sector is: = L 1 (x + x + : : : + x ) = L 1 x = L 1 K = {z } times K (L ) 1 the aggregate production function we started with in the beginning of our analysis of this chapter.

17 The research sector The inventor sells his patent to the intermediate-goods rm. What is the fair price of the patent/idea, P? Price the patent using the arbitrage method. Consider 2 options: 1 Invest the patent money at the interest rate r. One-period return is rp. 2 Purchase the patent. One-period return is + _ P. In equilibrium, rp = + P_, or r = P P + _ P. In steady state, r is constant and so and P should grow at the same rate; since = (1 ), grows at the rate n, and so does P. Thus, P = r n.

18 Wages in the model In the nal-goods sector, w = (1 ) L. The productivity of research labor in the economy overall is dened from _ = dl. If a researcher ignores the economy-wide eects of his own eort, so that _ = dl, w R = dp. In the equilibrium, w R = w, and s R = r n g The interest rate r is obtained from r = p = L 1 ( x ) = 2 1 L 1 K = 2 K K. {z} K=

19 Optimal R&D Distortions to research that cause s R to dier from its optimal level. 1 Ideas rewarded by the stream of prots but increases in future productivity for the overall economy are not internalized into the price too little research from a social standpoint. 2 Researchers do not \pay" for reducing productivity of others via potential duplication (if < 1) too much research. 3 The \consumer-surplus eect": the gain to society is larger than the prot+consumer surplus extracted at the monopoly price too little research.

20