Economic Geography, Monopolistic Competition and Trade

Transcription

1 Economic Geography, Monopolistic Competition and Trade Klaus Desmet November Economic () Geography, Monopolistic Competition and Trade November / 35

2 Outline 1 The seminal model of economic geography: Krugman (1991). 2 Different ways of modeling monopolistic competition: Ottaviano, Tabuchi and Thisse (2002), Melitz and Ottaviano (2008) and Desmet and Parente (2010) 3 Market size effects in international trade: Desmet and Parente (2010) and Melitz and Ottaviano (2008). Economic () Geography, Monopolistic Competition and Trade November / 35

3 1. THE SEMINAL MODEL IN ECONOMIC GEOGRAPHY: KRUGMAN (1991). Economic () Geography, Monopolistic Competition and Trade November / 35

4 Endowments and Preferences Endowments Two regions, denoted by 1 and 2. 1 µ Agricultural workers: 2 in each regions and geographically immobile. Manufacturing workers: geographically mobile, with L 1 + L 2 = µ. Preferences U = ([ N i=1 c σ 1 σ i ] σ 1 σ ) µ C 1 µ A (1) where N is a large number and σ is the elasticity of substitution between any two varieties of manufactured goods.. Economic () Geography, Monopolistic Competition and Trade November / 35

5 Technologies Agriculture CRS, perfect competition. Unit labor requirement of 1. Normalize price of agricultural good (and agricultural wage) to 1. Manufacturing IRS, monopolistic competition. Production function L Mi = α + βx i (2) where x i is the output of good i and L Mi the labor input.. Economic () Geography, Monopolistic Competition and Trade November / 35

6 Transport Costs Agricultural goods: zero transport costs. Manufactured goods: positive transport costs of the iceberg type. If one unit is shipped to the other country, a fraction τ < 1 arrives. τ is the inverse of the transport cost.. Economic () Geography, Monopolistic Competition and Trade November / 35

7 Utility Maximization An agent of region 1 with income y 1 solves the following maximization problem: max c 11i,c 12j s.t. ([ N i i=1 c σ 1 σ 11i + N j j=1 c σ 1 σ 12j ] σ σ 1 ) µ c 1 µ N i i=1 p 11ic 11i + N j j=1 p 12jc 12j + c A = y 1 A Taking the first order condition with respect to any two varieties c k and c l and dividing one through the other gives: c k c l = ( p k p l ) σ (3). Economic () Geography, Monopolistic Competition and Trade November / 35

8 Utility Maximization Given the Cobb-Douglas utility structure in the upper-tier we know that µw = N i i=1 p 11ic 11i + N j j=1 p 12jc 12j. Substituting (3) into the above equation gives c 11i = A similar expression holds for c 12i. µy 1 p11i σ N i i=1 p1 σ 11i + N j j=1 p1 σ 12j Aggregate demand for a good i produced in region 1 is then C 1i = C 11i + C 21i = µ(w 1L µ 2 )p σ 11i N i i=1 p1 σ 11i + N j j=1 p1 σ 12j + µ(w 2L µ 2 )p σ 21i N i i=1 p1 σ 21i + N j j=1 p1 σ 22j. Economic () Geography, Monopolistic Competition and Trade November / 35

9 Profit Maximization A representative firm in region 1 solves the profit maximization problem max p 11 C 11 (p 11 ) + p 21 C 21 (p 21 ) (α + βc 11 (p 11 ) + β C 21 p 11,p 21 τ (p 21))w 1 where the first subscript refers to the region where the good is sold and the second subscript refers to the region where the good is produced. Given that the marginal cost is constant, we can split up the maximization problem in two parts. This gives us two first order conditions C 11 C 11 C 11 + p 11 βw 1 = 0 p 11 p 11 C 21 C 21 + p 21 β w 1 C 21 = 0 p 21 τ p 21. Economic () Geography, Monopolistic Competition and Trade November / 35

10 Profit Maximization These expressions can be rewritten as 1 + p 11 C 11 C 11 p 11 = βw 1 p 11 p 11 C 11 C 11 p 11 Hence, so that 1 + p 21 C 21 C 21 p 21 = βw 1 τp 21 p 21 C 21 C 21 p 21 p 11 = ε ε 1 βw 1 p 21 = ε ε 1 βw 1 τ p 21 = p 11 τ. Economic () Geography, Monopolistic Competition and TradeNovember / 35

11 Profit Maximization If one does not take into account that a change in a firm s price affect the overall price level of the economy, then it is easy to see that ε = p 11 C 11 C 11 p 11 = σ ε = p 21 C 21 C 21 p 21 = σ In reality one can only ignore the effect of a change in a firm s price on the overall price level if there is a continuum of firms. We will return to this point later on.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

12 Zero Profit Condition From the results above it is obvious that p 11 = w 1 p 22 w 2 The notation in the paper calls p 11 = p 1 and p 22 = p 2. Free entry and exit implies that in equilibrium firms make zero profits, so that so that p 11 C 11 + p 21 C 21 (α + βc 11 + β C 21 τ )w 1 = 0 σ σ 1 β(c 11 + C 21 τ ) α β(c C 21 τ ) = 0 X 1 = C 11 + C 21 τ = α(σ 1) β. Economic () Geography, Monopolistic Competition and TradeNovember / 35

13 Number of Firms The last equation, together with the production function, implies that L Mi = ασ so that all firms have the same size in terms of workers. As a result, the number of firms will be proportional to the labor force in manufacturing: N 1 = L 1 N 2 L 2. Economic () Geography, Monopolistic Competition and TradeNovember / 35

14 Short-Run Equilibrium For now suppose that the allocation of workers between regions is given. From our demand expression, we can write down the demand in region 1 for goods of region 1 relative to goods of region 2: C 11 C 12 = ( p 1 p 2 /τ ) σ Now define the ratio of region 1 spending on region 1 goods relative to region 1 spending on region 2 goods: z 11 = N 1C 11 p 1 N 2 C 12 p 2 /τ = L 1 L 2 ( w 1 w 2 /τ )1 σ (4). Economic () Geography, Monopolistic Competition and TradeNovember / 35

15 Short-Run Equilibrium Similarly, the ratio of region 2 spending on region 1 goods relative to region 2 spending on region 2 goods: z 12 = L 1 L 2 ( w 1/τ w 2 ) 1 σ (5) Total income in region 1 (or 2) industrial workers must be equal to total spending on industrial goods produced in region 1 (or 2) z 11 z 12 w 1 L 1 = µ[( )Y 1 + ( )Y 2 ] (6) 1 + z z w 2 L 2 = µ[( )Y 1 + ( )Y 2 ] (7) 1 + z z 12. Economic () Geography, Monopolistic Competition and TradeNovember / 35

16 Short-Run Equilibrium The incomes of the two regions can be defined as Y 1 = 1 µ 2 Y 2 = 1 µ 2 + w 1 L 1 (8) + w 2 L 2 (9) Equations (4)-(9) give us six equations in six unknowns (taking L 1 and L 2 as given). This defines the short-run equilibrium. By symmetry, it is obvious that if L 1 = L 2, then w 1 = w 2.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

17 Long-Run Equilibrium If labor is shifts from region 2 to region 1, w 1 /w 2 could increase or decrease. Two forces at work: Force #1: Home market effect: If production costs were the same, firms would always prefer to locate in the larger market. This pushes up the wages in the larger market. Divergence force. Force #2: Proximity to agricultural workers: Manufacturing workers face less competition in the local market. This pushes up the wages in the smaller market. Convergence force. Force #3: Real wages: Because more goods do not pay transport costs, larger markets will have higher real wages. Divergence force.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

18 Long-Run Equilibrium Plug consumption of manufactured goods into the subutility function of manufactured goods: µw 1 (N 1 p 1 σ 1 + N 2 (p 2 /τ) 1 σ ) 1 σ 1 Substituting N 1 = L 1 /(ασ) and p 1 = σ/(σ 1)βw 1 into the above expression gives us a price index in region 1 (upto a constant) of and by analogy P 1 = (L 1 w 1 σ 1 + L 2 ( w 2 τ )1 σ ) 1 σ 1 P 1 = (L 1 ( w 1 τ )1 σ + L 2 w2 1 σ ) σ 1 1 If nominal wages are the same, shifting workers from region 2 to region 1 increase the real wage in region 1.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

19 Rest of Paper Two forces pull towards divergence (home market and price index) and one force towards convergence (local agricultural market). Paper analyzes numerically when we will get divergence (all of the manufacturing sector located in one region) or when we will get convergence (half of the manufacturing sector located in each region). This amounts to determining whether the convergence equilibrium is stable or not.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

20 Analysis If v is above one, divergence (concentration) is unstable, if v is below one, divergence (concentration) is stable. High transport cost favor convergence (dispersion).. Economic () Geography, Monopolistic Competition and TradeNovember / 35

21 Analysis Area below curves: divergence (concentration) unstable. High substitutability across goods, high transport costs, and low share of manufactured goods lead to convergence (dispersion).. Economic () Geography, Monopolistic Competition and TradeNovember / 35

22 Other Papers: Krugman and Venables (1995) Brief look at Krugman and Venables (2005) No labor mobility across regions, but labor mobility across sectors. Agglomeration force happens through linkages: cost or forward linkage (manufacturing firms use manufacturing goods as inputs, the more varieties, the more productive they become) and a demand or backward linkage (more firms increases the demand for manufactured intermediates). Analyzes how a drop in trade costs affects inequality across countries.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

23 Other Papers: Krugman and Venables (1995) Zero trade costs (location does not matter), Low trade costs (concentration but everyone has access to same goods), Intermediate trade costs (concentration but real wages higher in industrialized region), High trade costs (dispersion). Economic () Geography, Monopolistic Competition and TradeNovember / 35

24 2. MODELLING MONOPOLISTIC COMPETITION. Economic () Geography, Monopolistic Competition and TradeNovember / 35

25 Standard Model of Monopolistic Competition Take a one-sector one-country version of the Krugman (1991). Analyze the effect of doubling the number of workers, L: The elasticity remains the same, σ. Therefore mark-ups remain the βσ same, σ 1. Constant mark-ups, together with the zero profit conditions, implies constant firm size: output per firm is α(σ 1) β and workers per firm ασ. Constant firm size, together with a doubling of L, implies a doubling of the number of firms N. If one interprets trade as an increase in market size, then the gains from trade come from an increase in the number of varieties (rather than from a reduction in prices).. Economic () Geography, Monopolistic Competition and TradeNovember / 35

26 Standard Model Inconsistent with Empirical Evidence Price elasticity increases with market size: Barron et al. (2003) compute price elasticities in U.S. gasoline markets and find that larger markets are associated with more elastic demand. Hummels and Lugovskyy (2006) document that import demand in larger markets is more responsive to changes in trade costs. Mark-ups decrease with market size: Tybout (2003) finds that mark-ups fall with import competition. Firm size positive related to market size: Campbell and Hopenhayn (2005) report a positive relationship between market size and firm size for a number of retail industries across U.S. cities. Hummels and Lugovskyy (2006) find that the number of plants increases less-than-proportionally with the size of the market across a wide variety of industries and countries.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

27 Need a Model Consistent with Empirical Evidence Easy to fix: suppose firm takes into account that a change in its own price affects the economy overall price level. Recall the demand expression coming out of the monopolistic competition model: C j = wlp σ j N i i=1 p1 σ i. Economic () Geography, Monopolistic Competition and TradeNovember / 35

28 Need a Model Consistent with Empirical Evidence Take the derivative with respect to p i, but take into account that p i influences the summation in the denominator. C j p j = σp σ 1 j wl pj σ 1 wlp σ j (1 σ)pj σ ( pi 1 σ ) 2 Now write down the elasticity expression C j p j = σ p1 σ j (σ 1) p j C j pi σ 1 Because of symmetry the above expression simplifies to ε = C j p j = σ σ 1 p j C j N. Economic () Geography, Monopolistic Competition and TradeNovember / 35

29 Implications of Alternative Model The number of varieties is where ε depends on N. In particular, N = N = L αε L α(σ (σ 1)/N) = Solving out for N gives L + α(σ 1) N = ασ If L goes up, N increases less than proportionately. NL α(nσ σ + 1). Economic () Geography, Monopolistic Competition and TradeNovember / 35

30 Implications of Alternative Model The price elasticity of demand, ε = σ σ 1 N is increasing in N, and because N is increasing in L, it is also increasing in L. Mark-ups, ε ε 1 are decreasing in ε and therefore decreasing in L. Output per firm, α(ε 1) β, and workers per firm, αε, are increasing in ε, and therefore increasing in L. The wage level divided by the price of a variety, w p = ε 1 ε increasing in ε, and therefore increasing in L. 1 β is Therefore, an increase in the size of the market (trade liberalization) leads to a greater price elasticity of demand (tougher competition), smaller mark-ups, larger firms (to break even), and a higher w/p.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

31 Implications of Alternative Model Compared to the standard monopolistic competition model, where the gains from trade come only from an increase in the number of varieties, here there is a second channel: real wages increase. If one is only interested in showing gains from trade, the difference between the two approaches does not matter. But in other contexts it may. See part 3. Other preference structures with endogenous markets and procompetitive effects from market size: Linear demand system with horizontal product differentiation: see Ottaviano, Tabuchi and Thisse (2002) and Melitz and Ottaviano (2008) Hotelling-Lancaster preferences: for an application, see Desmet and Parente (2010). Economic () Geography, Monopolistic Competition and TradeNovember / 35

32 3. MARKET SIZE EFFECTS AND PRODUCTIVITY. Economic () Geography, Monopolistic Competition and TradeNovember / 35

33 Market Size, Trade and Innovation (Desmet and Parente, 2010) Start off with a model in which larger markets lead to larger firms because of tougher competition. Suppose firms can improve their technology by paying a fixed cost of innovation. Larger firms find it easier to pay the fixed cost of innovation because they can spread it over a larger number of units. As a result, larger markets lead to larger firms, and larger firms lead to more innovation. Trade liberalization leads to more innovation. This implies that trade liberalization may not just lead to a level effect but also to a growth effect.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

34 Empirical Evidence on Market Size, Firm Size and Innovation Competition and productivity Nickel (1996) finds that U.K. manufacturing firms facing a larger number of competitors experienced higher productivity growth. Galdon-Sanchez and Schmitz (2002) show that increased competitive pressure in the iron ore industry during the 1980s can explain productivity increases of up to 100 percent in some countries. Market size and productivity Syverson (2004) documents in a study of the U.S. cement industry that firms in larger cities are more productive. Luzio and Greenstein (1995) and Lewis (2006) document substantial increases in productivity following a reduction in trade barriers in the Brazilian computer and automobile industries. Firm size and innovation Atack et al. (2008): larger firms were more likely to use steam power in the 19th century. Hannan and McDowell (1984): larger banks more likely to adopt ATMs in the 1970s.. Economic () Geography, Monopolistic Competition and TradeNovember / 35

35 More on the Effect of Market Size on Productivity There are three channels in the literature: Channel #1: Agglomeration economies The economic geography literature. Channel #2: Competition and innovation Desmet and Parente (2010) emphasize the positive effect of trade liberalization on productivity and innovation within establishments. Channel #3: Selection effect Melitz and Ottaviano (2008) Larger markets lead to more competition. The smaller (least productive) firms do not survive whereas the larger (more productive firms) do and become even larger. This literature does not emphasize innovation within establishments. Instead, the economy s productivity improves through a composition effect.. Economic () Geography, Monopolistic Competition and TradeNovember / 35