Every nation's economy is significantly impacted by international trade. It makes it possible to meet the requirements of the populace and promotes the nation's internal growth. The exchange of commodities and services between nations is known as international trade. The study looks into the conditions under which technological leapfrogging between areas will take place. Businesses in imperfectly competitive industries are driven to aggregate in specific areas due to input-output links between them. Since a new technology cannot work with an old technology, it will not benefit from these connections and will therefore be developed in areas with minimal industry already in place and, as a result, cheaper factor prices.

There are many examples from history where a leader in technology loses its position of dominance following a technological advance. One instance is the Norwegian maritime sector in the nineteenth century. A significant hub for the sail-based shipping industry was the port of Risor. Although sail was rendered technologically obsolete by the introduction of steam technology, this did not mean that the technology was abandoned in Risor. Prior to going out of business, sail technology was practiced in Risor for several decades, while steam-based maritime industry became concentrated in Bergen. After sail eventually went extinct, Risor never became a hub for shipping activity again. Additional instances demonstrate hubs of activity that were surpassed by novel technology yet were able to transition to the new. By 1850 It was believed that Britain was the only industrial economy in the globe. However, industrialization had reached other nations by the time of the First World War. Harley (1974) provides instances of British companies that were sluggish to adopt new, internationally adopted processes. For example, in the metalworking and textile industries, Britain was a little delayed to adopt labor-saving innovations like assembly line procedures and ring spindles.

In what situations will a newly developed technology that is both superior to and incompatible with an existing technology be adopted? Will the new technology be taken up by the current industry leader or will it be taken up somewhere else—in a different nation or region? Will the new and old technologies coexist if the new technology is accepted somewhere else, or will the new technology push the old out? Numerous articles have provided justifications for the technological leapfrogging phenomenon. 1 Non-pecuniary externalities form the basis of Brezis, Krugman, and Tsiddon's (1993) theory of technological leapfrogging among nations. They believe that when a significant technological advancement occurs, productivity increases relative to the previous technology with the same amount of experience, and that production is susceptible to national-specific external learning effects. Thus, the new technology is initially less advanced than the old for the leading nation, which has more expertise with the old technology and thus pays a higher wage. On the other hand, the nation that is falling behind can leverage its wage advantage to embrace the new technology because it has less experience with the outdated technology and pays less for it.

As the trailing nation gets more proficiency with the new technology, it overtakes the leading nation. This chapter's mechanism, which is based on financial externalities from transactions in the setting of imperfect competition, is very different. I offer a model with two regions, two industries that are vertically integrated, and labor that is immobile between the two locations. The downstream industry receives homogenous components from the upstream business, which operates as a Cournot oligopoly. The downstream sector produces uniform end products that are exported to the rest of the globe in a perfectly competitive environment. The two industries' vertical links exert pressure on each other to aggregate in one place, as seen in Krugman and Venables (1995).

Demand is correlated because upstream companies profit when the downstream business expands its operational scope. Due to greater competition among upstream firms, the price of upstream goods is declining, which has a positive feedback impact on downstream enterprises through cost linkages. Pecuniary externalities are produced when these forces interact, promoting regional specialization.

Why wasn't it possible for one upstream company to enter the other area at a low cost and benefit from the lower wages there? Demand and cost links would be created if one upstream company pledged to act in a non-monopolistic manner. This would encourage downstream companies to enter, which would then encourage more upstream companies to enter. If the game were set up so that upstream firms decided on quantity before downstream firms decided on entrance, then an upstream firm could decide to commit to a low price; in that scenario, regional specialization would never reach equilibrium. On the other hand, assuming that judgments about admission are made before those about quantity seems more plausible. With the game being staged this way, a possible an upstream entrant cannot swear out acting in a monopolistic manner.

Therefore, until the monopoly price is low enough to cover their fixed costs, downstream firms will not enter the market. In this model of regional specialization, the interactions between the firms are critical to game theory.

Since it is considered that the two technologies are incompatible—like steam and sails—the aggregation of businesses utilizing the older technology does not gain from the introduction of new technology. Therefore, it seems most likely that the new technology, which I expect to be labor augmenting, will be implemented in the "lagging" area with reduced pay. I demonstrate that, as steam and sails did in Norway, there is an equilibrium where the two technologies coexist. In light of this, the model suggests that Risor's failure to adopt the new technology was caused by the advantages of the agglomeration of activities related to sail technology, rather than the fact that the existing agglomeration drove up the costs of immobile factors (labor and port space) in Risor relative to Bergen.

The model's development establishes the prerequisites for regional specialization, examines the environments and conditions in which new technology adoption will occur, draws conclusions, and briefly discusses potential policy ramifications.

The Model

In a model I create, businesses can locate in either of two regions and there are two vertically linked industries. Businesses have to decide on their technology and location. There is just one technology available at first, but then an unexpected technical advance occurs, allowing for the development of a new, superior technology that is incompatible with the previous one. Labor is needed by upstream businesses to make the components they sell to downstream businesses in their own area. Additionally, downstream companies employ labor and componentry to create a final, uniform product that they market to the rest of the globe. There is no movement of labor between the two areas. Thus, the rivalry between the two regions for global demand for their ultimate products binds them together.

For this paper many books, research papers, newspapers and online websites has been reviewed and mentioned in the complete paper.

The study methodology comprises three main methods: system analysis, comparative macroeconomic analysis, and theoretical analysis based on modeling.

Premises of the Framework :

Assumption 1: Firms play a four stage game as follows: In stage 1, upstream firms choose whether to enter and in which region. To enter each upstream firm must pay a fixed cost, F, and choose its technology, θ^k. There are two technologies available, indexed k=A ,B. I set out the general model where both technologies are available. When solving for equilibrium, I assume that initially only one technology is available, θ^a. At some future date there is an exogenous shock where a new superior technology, incompatible with the old, becomes available, θ^b. In stage 2, downstream firms choose whether to enter and in which region. To enter each downstream firm must pay a fixed cost, f, and choose its technology, θ^k. In stage 3 upstream firms choose quantities, competing a la Cornet. In the final stage downstream firms are assumed to be price takers.

Since establishing up a firm takes more time than altering quantities, I suppose that firms decide on entry before deciding on quantities. Fixed costs bind businesses to a specific technology. Backward induction is used to solve the game, resulting in an equilibrium that is subgame perfect.

Assumption 2: Demand for final products only comes from consumers in the rest of the world :

Where Y^d is the demand for final products, p is the price of final products and η is the elasticity of demand. This functional form is chosen for simplicy

Assumption 3: The cost function for each downstream firm in region i is

Where Wi is the wage in region i, qi is the price of upstream components in region i, p is the share of costs of components in the total cost of production, and y-t is output per downstream firm in region i.

A Cobb-Douglas technology is chosen for simplicity. The cost function gives U shaped average cost curves and upward sloping marginal cost curves ensuring that there is a unique level of equilibrium output for each firm.

Assumption 4: The cost function for each upstream firm in region i is:

Where Xi is the output per upstream firm in region i and /βθwi is marginal cost.

Assumption 5: Trade costs on components produced by upstream firms are so high that no trade in components takes place between the two regions.

Assumption 6: Labour is immobile between the two regions and each region has a perfectly competitive labour market with the labour supply function, Ljs, defined by:

If Wi is greater than or equal to the reservation wage, wo, the elasticity of labour supply is λ. At a wage below wo, no labour is supplied to these industries - it is all employed in some other industry which is not explicitly modelled here.Again, this functional form is chosen for simplicity.

Assumption 7: The new technology is incompatible with the old technology and augments labor, which impacts the cost functions of enterprises downstream and upstream. The results are unaffected by how technology is included into the model. For example, the new technology may be modeled as a decrease in the marginal cost of upstream enterprises, with identical outcomes. Nonetheless, the outcomes are significantly impacted by the incompatibility of the two technologies.

Solving the model Stages 3 and 4

In each area i, I solve in three phases for prices and quantities for a given number of upstream companies, q, and a given number of downstream firms, mi. I start by doing a pricing and quantity calculation for the downstream market. I then solve for volumes and pricing in the upstream market. Ultimately, I ascertain the market clearing condition component.

First, consider the behaviour of downstream firms. Each firm chooses how much to produce by taking the final price of goods as given. Setting price equal to marginal cost, the inverse supply function for each firm is:

Demand for inputs is derived using Shephard’s lemma, where demand for components, X ^d, in region i is:

and demand for labour by downstream firms, L_i^d, in region i is:

The equilibrium price of final goods is determined by aggregating equation (5) across all firms in both regions and equating this aggregate supply function to the demand function given by equation (1). The equilibrium output for each firm is then determined by substituting the equilibrium price into equation (5). Second, consider the behaviour of upstream firms. Each firm chooses quantity by setting marginal revenue equal to marginal cost, taking as given the quantity of all other upstream firms, the number of upstream firms and the number of downstream firms. The first order condition for each upstream firm in region iis:

Where €i is the absolute value of the elasticity of derived demand for components. It is calculated by differentiating equations (1), (5)and (6 ), with respect to yi, p,qi and X ^d. The derivations are in Appendix 1.

The elasticity of derived demand can be decomposed into two effects: a substitution effect and an output effect. An increase in the price of components relative to the price of labour will lead firms to substitute labour for components. This effect is captured by the first term in equation (9), which is one minus the share of components in total costs, denoted by Ꙡ, multiplied by the elasticity of substitution which is equal to one for a Cobb-Douglas technology. The substitution effect is larger the smaller is the share of components in total costs; and the larger the elasticity of substitution between factors. A change in the price of factors will also lead to an output effect. An increase in the price of components increases the cost of production and hence reduces the amount of output firms are willing to supply, which affects the price and demand for final products. The output effect is larger the larger is the share of components in total costs; and the larger is the elasticity of demand for final products,η. The output effect is smaller in this model than in the ’usual’ case because the entry decisions of downstream firms have already taken place, the number of downstream firms is determined in stage 2 of the game. Equilibrium in the upstream industry is given by equating demand for components (equation (6 )) to the supply of components:

Demand for labour by upstream firms, L_i^u, is derived by Shepard’s lemma:

Finally, labour market equilibrium is determined by equating the labour supply in each region to the sum of labour demand from upstream and downstream firms in each region:

Downstream firms decide whether to enter, and if so in which region and with which technology. There is free entry and exit into the industry so profits are driven to zero. Since each firm is so small relative to  the whole industry we can ignore the integer problem.

New Technology

Assume that regional specialization is an equilibrium with parameter values such that history determines the equilibrium configuration (A,0).

Then there is a technological breakthrough where a new technology becomes available, θ^b<θ^a=1, which is superior to and incompatible with the old technology. Will the new technology be adopted? If so, in which region? What are the equilibrium configurations? For the new technology to be adopted, an existing upstream firm from region 1 must be able to make higher profits by entering either region 1 or region 2 with the new technology, given n1*- l upstream firms in region 1, or a new upstream entrant must be able to make non-negative profits by entering either region with the new technology, given n1* upstream firms in region 1. When calculating the profits of the ’deviating upstream firms, the number of other upstream firms is taken as given, as this is determined in stage 1 of the game, but the number of downstream firms, quantities and prices are re-calculated as these are determined in the subsequent stages of the game. I assume that the fixed cost is paid every period so that even if a firm continues to operate with the old technology it must pay the fixed cost again. The new technology is labour augmenting. If an upstream firm were to enter region 1 with the new technology, it does not derive any of the agglomeration benefits enjoyed by the firms operating with the old technology since the two technologies are assumed to be incompatible. The pecuniary externalities are the same in either region but the wage in region 2 is lower than in region 1. If an upstream firm were to enter region 2 with the new technology, it has the benefit of the new technology as well as the advantage of a lower wage in that region. So a profitable opportunity to enter region 2 with the new technology will arise before that of entering region 1 with the new technology. The lower is θ^b relative to θ^a, the more likely that there will be a profitable opportunity for a single upstream firm to enter region 2.Figure 4 is a plot of the maximum wage a single upstream firm can afford to pay in region 2 and the labour market clearing wage in region 2 for different values of θ^b, given there are n1* old technology firms operating in region

1. The number of upstream firms in region 1, n1* was determined by the zero profit condition in equation and illustrated in Figure 1.

Configuration (A,B) is an equilibrium if the following conditions are satisfied first, the wages in region 1 and region 2 are above the reservation wage; second no existing upstream firm from region 1 or from region 2 can make higher profits by changing its behaviour. No upstream firm will want to enter region 2 with the old technology since it does not derive any benefits from the agglomeration of new technology firms and it would have to pay a higher wage in that region. We need to check that a single existing upstream firm located in region 1 or in region 2 cannot enter region 1 with the new technology and earn higher profits.

Further, a potential entrant cannot enter region 1 with the new technology and earn positive profits given the number of upstream firms in region 1 operating with the old technology and the number of upstream firms in region 2 operating with the new technology. We also need to check that a positive number of old technology upstream firms in region 1 and a positive number of new technology upstream firms in region 2 are earning non-negative profits.

The configuration (A,B) will be an equilibrium for certain parameter values. If θ^b is very low, the price of final goods will fall so low due to the increasing number of new technology firms operating in region 2 that firms in region 1 will not be able to continue to make non-negative profits and will exit.After the introduction of the new technology, the new equilibrium configuration may be (A,B) or (B,A) where the two technologies co-exist. For very low values of θ^b the equilibrium configuration may be (0,B) where the industry in region 1 is completely wiped out and there is an agglomeration of new technology firms operating in region 2 or (B,0) with all the new technology firms agglomerated in region 1. Alternatively, the equilibrium configuration may be (B,B) where there is an equal number of firms in both regions operating with the new technology. If the fixed cost for upstream and downstream firms is paid every period, we cannot say which equilibrium will be the equilibrium. All we can say is that these equilibria exist. However, if the fixed cost is an entry cost which is only paid once then we could say which the equilibrium is. Suppose that (A,0) is given to us by history so that there is only one technology available and all the firms are operating in region 1. Then a new technology becomes available which makes entry in region 2 profitable. A firm in region 1 would only exit if it could not cover its average variable cost. Consequently, the equilibrium configuration would be (A,B) and not (B,A) when θ^B= θ^B*. As the new technology improves, technology A will be abandoned and the industry in region 1 will either disappear or adopt the new technology

Figures 1, 2, 3 and 4.

Ꙡ=.6, a = b = f= .0 5, F = .5; β= 1; η=5; λ= 5 ; θ^A= 1

Figure 2

A shift from η=5to η^*=6.

Figure 3

A shift from λ= 5 to λ^’=6.

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