Role of equations and inequalities in helping a business maximize profit or minimize costs

Equations and inequalities are used in optimization problems in business. If quantities like profit relating to a business is subject to certain constraints and if the constraint conditions and the quantities like profit are linear, linear programming can be used to solve the problems. Companies as well as industries can use this method of solving business situations for finding optimal solutions for the problems of business. This is predominantly used in operations research to provide the best solutions taking into consideration all the constraints of the business. Constraints is another name given to limitations on the quantity of production and the time related to producing the item.

So first equations and inequalities are framed and graphed. Then they are solved by linear programming methods. Prediction of economic growth, solutions for strategic games, factory manufacturing, resources conservation, diets’ designing, and systems of transportation are some of the few industries which employ these. This method can be used by even farmers to improve their produce. Overall designing of equations and inequalities makes the world more efficient economically.

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Comparison of Factors of production between China and Japan

China and Japan have two factors of production, land and labor. Both countries produce two goods, corn, which requires more land, and computers, which requires more labor. Given that China is abundant in land and Japan is abundant in labor, what will be the effect on the terms of trade an increase in Japan's labor supply? What will be the welfare effect of a decrease in land used for corn in China?

Among the two factors of production, land and labour, China has abundance of land, but is short of skilled labour needed for computer manufacture. Japan on the other hand has abundance of skilled labour but is short of land needed for corn production. This is classic case of Ricardian theory.

It is given that both countries produce corn as well as computers. But production of corn in Japan must be costlier in Japan than in China and so also the production of computers in China. When labour force increases in Japan, the cost of production of computers comes down further. If free trade being allowed between China and Japan, people in China will opt for purchase of computers from Japan and the Japanese try to buy corn from China as a result of which gradually Japan will be shifting to specializing in production of computers and China to production of more corn. Japan will have comparative advantage in production in computers and China in production of corn. They can trade with exchanging both corn and computers which works towards gain for both countries. Since both countries geographically are also close by, the transportation costs are negligible thereby increasing the price competitiveness of the goods. The decrease in land used for corn in China will have adverse impact on the cost of corn production which can increase the price of corn.

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Three myths regarding comparative advantage

 The three myths of this comparative advantage are

Myth1

A High wage country cannot afford free Trade with a low wage country. The high wage country will be undersold in everything. This myth is not true because labour is only one of the factors of production and constitutes input cost factor. The high wage country may have abundance of other inputs which are cheaper as a result of which the overall cost of the product may be low and price can be fixed at a competitive level.

Myth2                               

A low productivity country cannot afford free trade with a high productivity country. The former will be upstaged and decimated in industrial sector by the latter.

Again this myth cannot be totally true. In a way it says that a country, which has low productivity should close its borders to outside goods and produce everything by themselves, which is incorrect. Again high productivity is picturised as ‘absolute advantage’. Inspite of a country having a low productivity, it will have comparative advantage in some aspects and they can take advantage of the same.

Myth3

International trade decreases the total number of jobs in a country.

It is true that in some sectors there may be drop in employment on opening up the economy.  But there will be creation of employment in some sectors. As the international trade grows there will be a steady growth in employment. Moreover nowadays, even international organisations opt for employment of local labour for saving costs.

Thus all the three myths arising out of comparative advantage are incorrect.

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Standard Trade Model and variation of the model from Ricardian model and Heckscher-Ohlin theory

The Standard Trade Model combines the ideas of Ricardian model and Heckscher-Ohlin

Model and is based on four key relationships.

1.)    The relationship between PPF and relative supply curve.

2.)    The relation between relative demand and relative prices.

3.)    The relation between World equilibrium, World relative supply and World relative demand.

4.)    The way a nation’s welfare is influenced by the terms of trade.

The principal features of the Standard Trade Theory are

1.)    The Production Possibility curve represents the Productive potential of an economy.

2.)    Factor and goods exist in competitive markets. So all economic agents like suppliers, factor services, households and firms compete in the markets in which they operate.

3.)    A country’s relative supply curve is determined by movement along production possibility frontier at different relative prices of goods.

4.)    Relative demand (RD) and Relative Supply (RS) curves can be used to describe Autarky and World Equilibrium.

Difference between Standard Trade Theory and Other Theories

Ricardian and Heckscher-Ohlin models emphasise on identifying the underlying reasons for comparative advantage. While productivity differences decide the comparative advantage under Ricardian model, factor endowments decide the same in HO model. Standard Trade model adopts common features of various models and develops a set of techniques and tools which can be used for analysis of different trade and trade policy problems,

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Change of Relative prices for goods in the Ricardian model when trade occurs

The movement of relative prices under Ricardian model can be explained by taking two countries, say H and F initially. There are two goods say wine and cheese which are produced in sufficient quantities in both the countries. The quantities produced in both the countries are consumed in the countries themselves. So there is no trade between the countries initially. This situation is called Autarky under which each country is regarded as a closed economy and the situation is a closed economy equilibrium.

Let it be assumed that country H has a higher opportunity cost for cheese in terms of wine relative to country ‘F’. This means that country ‘H’ has to sacrifice more wine to produce one more unit of cheese than in country ‘F’.

Now let us presume that trade between ‘H’ and ‘F’ becomes possible because of certain development which reduce transportation costs. Businessmen notice that cheese is relatively cheap in ‘F’ and wine in ’H’. So buyers in ‘H’ opt for cheese in ‘F’ while buyers of wine in ‘F’ opt for purchase of wine from ‘H’. The situation leads to two developments.

1.)    The demand switch will lower the relative price of Cheese in ‘H’ and relative price wine ’F’. The relative prices in the two countries will then converge and are provided with free trade and negligible transport costs. There will be just one common international price.

2.)    The above price developments will cause manufacturers in ‘H’ to concentrate on wine production and manufacturers in ‘F’ to concentrate on cheese. They then trade with the two commodities to have a mix of the two. Thus Ricardian model separates production and consumption of commodities through relative price mechanism.

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