These assumptions ensure that in our model not only the growth rate of the economy, but also the growth rate of real per capita income is strictly positive in the long run. For this to happen, the population growth rate in both countries must be the same (n1 =n2 =n). As stated above, the rate of capital accumulation equals the rate of profit.
Fordiri is constant along the BGP, the rate of capital accumulation along the BGP leads to. 1−α−β > 0, (19) which shows that the rate of capital accumulation is proportional to population growth.
Case 2: Home produces only manufactured goods while Foreign produces only agricultural goods
That is, if the expenditure share for manufactured goods is less than or equal to half, then agricultural output is strictly positive, meaning that both countries always diversify. However, if a combination of k1 and k2 is outside the cone, one country's agricultural output becomes zero and the country specializes entirely in manufacturing while the other country diversifies. From this the rate of capital accumulation and the growth rate of the exchange rate result.
Case 3: Home diversifies while Foreign produces only agricultural goods
The dynamics in this case are stable: if both countries start with this production model, then the situation is stable. These dynamics are stable: if both countries start with this production pattern, such a situation is stable given γ <1/2.
Case 4: Home produces only manufactured goods while Foreign diversifies
Equation (50) shows that the GDP growth rate of capital accumulation in Home is given by g∗K1 = φn. The BGP growth rate of capital accumulation abroad and terms of trade can be calculated as follows. The BGP capital stock growth rate in both countries is the same as in cases 1-3.
We use real income per capita and real consumption per capita as a measure of economic well-being. Let yi,A and yi,M denote the real income per capita when the economy is fully efficient. However, we use pc=pγ because the constant terms do not affect our results. cializes in agriculture and real income per capita when the economy is completely specialized in production or
Using these growth rates, we can obtain the following growth rates for real income per inhabitant: g∗yi,A =g∗yi,M =γεn>0. Therefore, the growth rate ofyi,Di is equal to the growth rates ofyi,Aandyi,M. 61) Based on the above analysis, we find that the BGP growth for real income per inhabitant is the same in all cases.15). Because both π and ki are constant in the long-run equilibrium, BGP is the growth rate of real consumption per per capita equal to the absolute value of the rate of change in the consumer price index and is therefore equal to the growth rate of real income Per capita:.
In his model, the price of high-growth investment goods relative to low-growth consumer goods continues to fall along the BGP.
Transition to an industrial or a non-industrial country
These loci correspond to a dynamic in which the foreign is fully specialized in production while the foreign is diversifying, which is case 4. These loci correspond to a dynamic in which the foreign is fully specialized in production while the domestic is diversifying. E02 is the long-run equilibrium in which the home country is fully specialized in manufacturing while the foreign country is asymptotically fully specialized in agriculture, corresponding to Case 2.
E03 is the long-run equilibrium in which the foreign fully specializes in manufacturing while the domestic asymptotically fully specializes in agriculture. This means that in the long run one country fully specializes in manufacturing while the other country asymptotically fully specializes in agriculture. This means that a country whose initial capital stock is greater than that of its trading partner diversifies or fully specializes in production in the long run.
In contrast, a country whose initial capital stock is smaller than that of its trading partner asymptotically specializes entirely in agriculture in the long run, regardless of its size. For the behavior of the system at the boundary, see Honkapohja and Ito (1983) and Marrewijk and Verbeek (1993). . In equilibrium, one country diversifies while the other asymptotically specializes entirely in agriculture. In contrast, if the share of employment in industry is more than half, then in the long-run equilibrium one country specializes entirely in manufacturing, while the other country asymptotically specializes entirely in agriculture.
Suppose that the initial capital in the home country is greater than that abroad without loss of generality.
Different paths converging to equilibrium
When both countries diversify at the initial time point, the domestic wage and relative price are the same as foreign, respectively. Because there are increasing returns to scale in production, the domestic rate of profit is higher than the foreign rate.22) The rate of capital accumulation is equal to the rate of profit, which means that the domestic capital stock increases. faster than the stock of foreign capital. . Then, at the next point in time, the domestic capital stock is still greater than the foreign one, from which the domestic rate of profit is still higher than the foreign one, which implies that the domestic capital stock grows faster than the stock of foreign capital. .
In Figure 6, we place dynamic paths starting at different initial conditions on the phase diagram for the case where the share of production costs is greater than 1/2.25). As stated above, in E02, Home fully specializes in manufacturing, while Foreign asymptotically fully specializes in agriculture. Starting in S01, Home always fully specializes in manufacturing, while Foreign is industrialized at first, but gradually becomes an agricultural country.
From S02, S03, and S04, both countries initially remain diversified, but eventually cross the boundary of the diversification cone, and as a result, the home country becomes fully specialized in manufacturing, while the foreign country gradually becomes an agricultural country.
Uneven development in terms of income and consumption
For a while, Home experiences lower consumption under free trade than under autarky, but this situation reverses at some point. The relative price of manufactured goods under free trade necessarily lies between Home's and Foreign's prices under autarky, and therefore the consumer price index for Home rises and Foreign falls under free trade. Because the real consumption per capita is given by the inverse of the consumer price index, Home's real consumption per per capita under free trade less than under autarky, and Foreign's real consumption per per capita under free trade is greater than under autarky.
However, before the countries reach the BGP, the rate of decline in the consumer price index under free trade is greater than that under autarky. The time paths under free trade bend around=60, because after that Home specializes completely in manufacturing, and so the conversion of the system of the differential equations takes place. From figure 10, we find that under free trade, real income per capita in Home increases, while that in Foreign decreases compared to under autarky, which is similar to the case where γ≤ 1/2.
For a while, Home's real consumption under free trade is less than that under autarky, but the former becomes greater than the latter over time. Real foreign consumption under free trade is greater than under autarky, but the former becomes smaller than the latter over time. Under free trade, relative income rises to a certain value, and thus the income gap widens.
Up to approx.
Static and dynamic gains from trade
In contrast, although free trade is better for the economy than autarky in the short run, a situation exists where the economy is worse off under free trade in the long run. If the share of expenditure on manufactured goods is more than 1/2, then the trailing country cannot catch up with the leading country. Nevertheless, a situation exists where free trade is better for the follower country than autarky.
Depending on the share of spending for manufactured goods, we get the following two situations: (1) if the share of spending is less than or equal to 1/2, then one country diversifies (produces both goods) while the other country specializes asymptotically completely in agriculture and (2) if the expenditure share is more than 1/2, then one country specializes completely in manufacturing while the other country asymptotically specializes completely in agriculture. In our model, regardless of the situation to which the economy belongs (autarchy or free trade) and regardless of the sector in which the economy specializes (manufacturing or agriculture), the long-term growth rates of real income per capita and real consumption per capita in both countries are equal. Under free trade, on the other hand, whether or not the follower country can catch up with the leader depends on two factors: the production patterns of the two countries and the measure of economic prosperity used.
We must keep in mind that even though the follower country cannot catch up with the leader country, it is possible that free trade is better for the follower country than autarky. American Economic Review, Papers and Proceedings, 89 (2), p. 1993) “The Theory of Disequilibrium Growth in International Perspective,” Oxford Economic Papers, 45 (2), p. 1999) “Dynamic Comparative Advantage and the Welfare Effects of Trade,”. 2001) “Technical Progress and the North-South Terms of Trade,” Review of Development Economics, 5 (3), p. 1999) “Industrialization, Economic Growth, and International Trade,” Review of International Economics, 7 (3 ), p.
Furthermore, the growth rates of real per capita income and real per capita consumption in autarky are the same as those under free trade. If (k1,k2) lies below the 45◦ line in the phase diagram at the time when both countries move from autarky to free trade, the domestic has a comparative advantage in manufacturing, while the foreign has a comparative advantage in agriculture, and vice versa. Substituting the equations ˙k1 and ˙k2 into the right-hand side of the above equation, we can express ˙π as a function of k1, k2 and π, which is the differential equation for π.
