A New Ricardian Model of Trade, Growth and Inequality - PowerPoint Presentation

1. A New Ricardian Model of Trade, Growth and InequalitySugata MarjitIIFT, KolkataCTRPFP (CSSSC)CES-Ifo, Munich, Germany

2. MotivationThis is essentially a paper on History of Economic Thought highlighting the Classical interpretation of the Neoclassical system through the lens of the Ricardian Trade Model. But it contains host of results of contemporary relevance and broadly consistence with stylized empirical evidence. Noting that Credit Market is generally missing in conventional Trade Models, we focus on how to introduce this to the basic textbook Ricardian Model. We introduce the classical Wage Fund or Working Capital as K and thus allow the Ricardian model to have both K and L. Then we compare this with the major workhorse of the profession, the Neoclassical model with K and L. Our New Ricardian model surprisingly generates results very similar to neoclassical models without any neoclassical tools such as smooth production functions, cost functions, MP theory, CRS and all that. The Model points towards an independent way to learn microeconomic theory of Production( where K is only used as Finance and not as a Factor of Production) and use it for analyzing Trade, Growth etc.

3. Motivation Contd.The usual way we treat K is to take it Inside the production process, as an input that can be substituted by other factors, though in reality factor substitution can be very rare , once a specific technology is chosen.In this approach we deliberately eliminate that role of K and use it purely as Credit , a Loan from the Bank, which is used to finance production by employing ONLY L. Thus, we have a New Ricardian Model with K and L both and K is completely Outside the production process. This is consciously done to see what K just as a source of finance does to the simplest General Eqm. System.

4. Motivation and ResultsThis replicates the Solow model of Growth including modified golden rule of accumulation.The K/L and W/r relationship is the same as one derives with Marginal Productivity Theory. There is no need of Production Function, Cost Function, Diminishing Returns or CRS. Yields results of contemporary relevance such asTrade always increases income gap between K and L and Labour share of income declines independent of what you trade. Trade increases growth temporarily, but that is not sustainable.

5. ResultsW cannot increase without accumulation of K. Technological progress does not help labor but helps capital. It is R and D which can continuously sustain growth.Tendency of a Capitalist process is to undermine accumulation for production vis a vis R and D , as W tends to grow with the former but mot with the latter. Finance can flow only to the R and D sector eliminating production completely. Financial Crisis may not hurt capital but labor. With sectors employing different skills, rising wage gap and rising r/W both can go hand in hand. Echoes the concern of Picketti (2013)

6. LiteratureFinance and Trade have been discussed in a few papers , but not systematically and largely ignored and scattered in the context of pattern of trade , factor price movements, inequality and development in open economies. For a quick look one may refer to Jones and Marjit (2001, AER) Matsuyama (2005, JEEA), Antras and Caballero (2009,JPE) Manova(2013,RES),Bandopadhyaya, Marjit and Yang ( 2014,CJE)Marjit and Mishra (2020, WP CES-Ifo) etc. However, from the perspective of History of Economic Thought , Ricardo (1817),Mill (1848) Solow (1956,QJE), Kaldor (1957,EJ) Phelps (1965,AER),Caves and Jones (1973 or any Edition), CUP) Hicks and Hollander (1977,QJE) Findlay (1995, Ohlin Lectures), Jones (1965, JPE, 2018,CUP), Jones and Marjit (2009, ET) Maneschi (1983,OEP), etc. are predecessors of this paper.

7. History of Thought (Contd)But none has cared to explore what would happen if the Wage Fund Model ( I think it is due to J.S. Mill 1848) was applied to an ideal distortion free full employment model instead of the fixed wage unlimited supplies of labor model of the classical thinkers, as a natural experiment with capital in Ricardo’s comparative cost model.Our New Ricardian Model preempts most of the results of the Neoclassical Production Theory and replicate many iconic results, including that of Solow (1956) without any reference to smooth production function, cost function, CRS etc. It is as if one does not need to know these for the results such assumptions generate and highlight.

8. The New Ricardo Model (NRM)W = K/L (1) (1) relates W positively to K/L . Note that the relationship qualitatively is the same for a CRS production function with diminishing marginal productivity, most commonly used in neo classical production theory.Competitive price conditions will yieldW al1 (1+r) = P (2)W al2 (1 +r) = 1 (3)

9. NRM Contd.We assume homothetic demand function which leads to the following market clearing condition D (P) = X1/X2 (4)Full Employment condition al1X1 + al2X2 = L (5)(1)-(5)determine W, P, r, X1 and X2

10. NRMK/W = L is the key equation of the model.It tells us many things.It is a demand function for labor. As W goes up , with the same amount of credit or wage fud K , you can employ fewer workers. It is downward sloping. This is exactly like demand for labor derived from diminishing MP of labor as we do in a standard classroom model.Given Labor supply L, eqm. W is determined to clear the market.

11. NRMIf K/L does not change W will not change. K/L has to increase for W to increase. That is accumulation of K relative to L is necessary for W to increase. Higher W means lower r given price. Thus K/L is positively related to W/r This is exactly the property of a CRS production function. This is a full employment model. K does not determine Output, L does as in a Ricardian model. But with Unemployment and fixed wage Employment will be determined by Credit K and hence Output will also be determined. Thus Credit fluctuations impact W in a Full Employment model and Output in a model with unemployment.

12. TradePropositionInternational Trade must reduce the real income of the workers and inequality between labour and capital income rises independent of the pattern of trade, assuming that the workers do not own capital and earn less than the capitalists to start with.If workers own a part of the capital stock their real income can still go down and inequality will surely rise even if their real income goes up.

13. GrowthReplicating Solow Growth ModelLet Kt be the capital stock at t , then Kt+1 = Kt ( 1+r) and similarly Lt+1 = Lt (1+n)Therefore, K/L grows at a rate (1+r)/(1+n). Proposition - A unique and stable steady state growth path exists with r = n

14. Proof- Start from any K/L and we have a unique closed economy equilibrium values of P and r, given K/L=W, and assumptions of the model. First, we show that if there is a steady state it must give us a unique set of values of the variables.Steady state implies r=n. K/L is a constant, so is W and given W all other variables have same values over time. Hence, it is unique.Given n>0, we can solve for r = n, if there is a solution for the system at initial K/L, the same solution will persist for r = n. Hence, a steady state exists.Suppose r>n, K/L is rising, so is W (P is frozen by technology) and r will fall up to n. Once it reaches n, it will remain there as K/L will reach its steady state value. Suppose r< n. K/L is falling, so is W and r will be rising until it hits n and steady state will be reached. Thus the steady state equilibrium is stable. This completes the proof. QED

15. Proposition 4 – Trade can only temporarily boost up growth in per capita income but in the long run per capita income will depend only on steady state K/L = (K/L)*Optimal Growth under Free TradePhelps (1965) – Golden Rule , Later Modified Golden Rule with Discounting. AlsoKaldor, Pasinetti etc. Euler’s FOC in Optimal Growth Model, from the NRMMUt. = MUt+1[1+(r-n)]/ (1 +ρ) r=n+ρ ( The same condition) with ρ as the pure rate of time preference (0,1)

16. Some points need to be made clear.Our assumption of K owners save and invest all their income and Workers only consume, is done to recall Classical economists. Constant saving rate for both groups, optimal dynamic saving investment process etc. nothing changes the essence of the results. The key is that as in any neoclassical model with concave and CRS production function W/r rises with K/L , it also always happens in this model without concavity and hence the critical result that more accumulation means less incentive for further accumulation or the well-known unconditional convergence hypothesis holds.

17. Technological ProgressProposition -Technological Progress will increase return to K while W does not change.Proposition -Both trade and technological progress contribute unambiguously to rising inequality.One could show that in this model capitalists will try to do as much R and D as possible if P does not change much as diverting K from production towards R and D will benefit r from better technology, though W does not change.

18. In the standard Solow model continuing growth can happen iff technological progress takes place at a constant rate, since without it K/L remains the same in a steady state, so is per capital income. Here , the same thing happens , without R and D it is bound to be zero growth for per capita income. But the capitalists have explicit incentive to go for technological progress to boost r and W is insulated as K/L remains the same. So an eqm. is possible that the capitalists stop production, only invest for better technology and sell those to other countries who produce the output.

19. A result in Ricardian Trade model is there that even after complete specialization, a country can sell off the technology that gives absolute advantage but that good it does not produce as it does not have comparative advantage in that. Thus technology is there for sale beyond Trade in Goods [Beladi, Jones and Marjit (2002, PER)]In this model, Finance will not like production but technology. Since without RandD they would get a stagnant return from investment.

20. The Specific Factor Model (SF)With Skilled and Unskilled Sector Specific Labor, K finances both , earning a common r. Like Solow (1956) , I replicate Jones (1971) and Samuelson (1971) Ws ( Skilled wage ) = PK/ PAS + L , W ( Unskilled wage ) = K/AS+LP is the relative price of the skilled good. A is the ratio of unit labor coefficients of unskilled and skilled.Those who are familiar with SF structure will notice the similarity. K, S and L affect Ws, W and r similarly. All results flow without cumbersome elasticity of factor substitutions, factor shares, CRS or DMP.

21. The Heckscher-Ohlin-Samuelson counterpartSuppose at beginning of any period we inherit M number of Machines and L number of people. L has to be employed and M machines need to be sold. Finance will come from K amount of saved funds i.e. Credit. M and L are used in fixed proportions in X and Y.K =WL + PmM = f ( P, 1+r) This follows from below. ( WAlx +Pm Amx) = P/1+r, ( WAly +PmAmy) =1/1+r, , Y as the numeriare. Competitive Price Conditions. As r goes up both W and Pm drop. Demand for K falls. Given K, this determines 1+r. Then given P, W and Pm are determined. X and Y are solved from below. AlxX + AlyY = L, AmxX + AmyY=M – Full Employment conditions

22. HOS contd.Thus X/Y is determined by L/M and P determines W/Pm, given 1+rHomothetic demand will determine P.If X is M intensive , a rise in P will increase Pm/W. Stolper Samuelson. But effect on r will be ambiguous. As Pm rises and W falls, if share of wage bill in total K is greater(smaller) demand for K will tend to decline(increase) and 1+r will fall(rise). Note that movement in 1+r , given P will not change Pm/Wm , only absolute levels will change. Thus the magnification effect of Jones (1965) remains unaffected. Factor endowments will determine pattern of trade, Rybczynski and SS will hold. Greater K wont affect output but only 1+r.

23. HOS Contd.So , think of at a given P and the same L and M, if one country has larger K, only 1+r will be smaller, W and Pm both will be higher but W/Pm will be same. X/Y will be same, P will be same and no commodity trade will be there. But as 1+r is smaller , given a chance K will flow out to get higher return squeezing both W and Pm.Capital export and Import will take place and Factor prices will tend to get equalized. Though Labor and machines are not directly traded. On the other hand if K is different and all others are the same still there will be factor price differences.

24. Imperfect Credit Market in Ricardian ModelSuppose K is owned by workers, but L is such that all of them can't be sustained by K and they need to borrow B from the banks or lenders. For their internal K the opportunity cost is r. Banks charge R > r. But B is rationed. Banks worry about default and have to lend satisfying a No Default constraint , say for X PX – K (1+r) – qF( B +K) <= PX – B (1+R) – K (1+r)or B = qFK/1+R–qF So , WAx[(K/B+K) (1+r) + (B/B+K) (1+R)]=P, and WAy[ … ] = 1P = Ax/Ay

25. [B (R) + K ]/L= W , Note that as R goes up B falls and hence W must down , so W (R) , W’(R) <0. Then from price equation you can solve for R given r. As we trade and specialize in X , P rises , that should increase R and hence reduce W. Note that with perfect credit market B = 0, R =r etc. and K/L = W. Then W remains the same as we trade but r goes up, now there is a possibility that R may go up and B goes down leading to lower credit and a lower W. Higher R increases the possibility of default.