Country A Has 1500 Units Of Labor And Can Produce Two Goods

Country A Has 1500 Units Of Labor And Can Produce Two Goods Mufact

Country A has 1500 units of labor and can produce two goods: manufactures and food. A’s producers take 5 units of labor to produce one unit of manufactures and 6 units to produce one unit of food. Country B has 1800 units of labor and takes 3 units of labor to produce one unit of manufactures and 9 units to produce one unit of food. Draw the production possibility frontiers for the two countries.

Draw the world relative supply curve for manufactures. Would trade take place in between A and B in Adam Smith’s world? What good would A export? Each acre of land and food is produced using only fifteen hours of labor. If the economy’s total resources are 1800 hours of labor and 180 acres of land, how much labor and land are allocated to manufacture and food production respectively? If the labor supply grows by 5046, what happens to the allocation?

Paper For Above instruction

The given problem involves analyzing the production possibilities, trade dynamics, resource allocation, and productivity changes between two countries, Country A and Country B. This analysis employs concepts from international trade theory, resource allocation, and economic growth, illustrating the fundamental principles that underpin comparative advantage and specialization.

Production Possibility Frontiers for Countries A and B

The production possibility frontier (PPF) for each country illustrates the maximum output of two goods—manufactures and food—given their resource constraints and the productivity (labor requirements). For Country A, with 1500 units of labor, the maximum outputs are calculated by dividing the total labor by the labor per unit for each good:

  • Manufactures: 1500 / 5 = 300 units
  • Food: 1500 / 6 = 250 units

Thus, Country A’s PPF is a line connecting the points (300, 0) for manufactures and (0, 250) for food. Similarly, for Country B with 1800 units of labor:

  • Manufactures: 1800 / 3 = 600 units
  • Food: 1800 / 9 = 200 units

Country B’s PPF connects (600, 0) and (0, 200). These PPFs are straight lines because of constant labor productivity, indicating constant opportunity costs.

World Relative Supply Curve for Manufactures

The relative supply curve details the quantity of manufactures supplied relative to food at different price ratios. In a Ricardian model, countries specialize based on comparative advantage—Country A has a comparative advantage in manufactures (lower labor cost), whereas Country B has a comparative advantage in food (despite higher labor units per food unit, their absolute costs are still relevant). When both countries trade, the world relative supply curve is determined by their individual supply curves, which intersect at the points of specialization. As the relative price of manufactures increases, more supplies from the country with comparative advantage (A) increase, shifting the world supply curve rightward.

In Adam Smith’s world, where freely moving factors of production and no barriers exist, trade would be inevitable. Countries would export the good in which they have a comparative advantage. Therefore, Country A would export manufactures, and Country B would export food, provided markets are open and factor mobility is unrestricted.

Resource Allocation under Fixed Land and Labor

The problem states that each acre of land and food production employs 15 hours of labor, with total resources of 1800 hours of labor and 180 acres of land. The total labor can be allocated between manufacturing and food production. If x is the hours allocated to manufacturing, y to food, then:

  • x + y = 1800

Assuming land is equally allocated, and labor per acre is fixed, the individual allocations depend on the productivity and demand, but if resource allocations are proportional, then:

  • Labor for manufacturing: (Labor allocated to manufacturing)
  • Labor for food: (Labor allocated to food)

As the total labor grows by 5046 hours, the resource pool increases, enabling both sectors to expand production, assuming constant productivity. The increased resources would allow greater specialization and increased total outputs, potentially shifting the consumption possibilities frontier outward. The exact reallocation depends on relative prices and preferences, but generally, more resources translate to higher output in both sectors.

Analysis of Trade and Production Dynamics with Cost and Productivity Changes

In a scenario where Canada is a high-priced producer of manufactured goods relative to the US, the supply and demand curves for both countries can be modeled to understand trade patterns. Canada's higher prices lead to a lower willingness to import, reflected by a downward-sloping import demand curve, and an upward-sloping domestic supply curve. The intersection determines the equilibrium quantity traded, with imports representing the difference between domestic demand and supply at the world price.

Furthermore, the case of Luxembourg importing a good at a world price of $10, with domestic supply S = 50 + P and demand D = P, illustrates how market equilibrium involves setting supply equal to demand:

S = D → 50 + P = P → P = $10,

where the imported quantity is the excess demand at this price, calculated as D - S at P = 10.

Japanese Automobile Industry Productivity and Cost Comparison

The Japanese automobile industry's growth from 1955 involves examining production increases, cost reductions, and cumulative experience. Starting with 100,000 cars annually at $2,000 each, growth rates of 50% for five years and 25% for subsequent years lead to significant expansion. The cost reduction model posits a 20% decrease per doubling of experience, which reduces the relative costs compared to the US, assuming US costs remain constant at $1W in 1955.

Calculating the year when Japanese costs equal US costs involves exponential growth and cost reduction formulas, considering cumulative production as experience. With compound growth and cost reduction, Japanese costs would equal US costs approximately in a specific year, which can be estimated through iterative calculations or exponential equations.

Considering a discount rate of 6%, the net present value of cost savings can be evaluated to determine if industry protection was economically justified by 1970. The long-term productivity gains and reduced costs demonstrate the benefits of technological learning and scale economies, indicating that even with initial investments, Japan recovered its industry costs over time, leading to competitive parity with US automakers.

Factor Usage and Production Efficiency

The last part of the problem references the use of 60 hours of labor for 5 units of something—probably a typo or incomplete, but if it implies that the average labor per unit is 12 hours, then optimizing factor use involves assessing productivity advancements such as the Toyota Production System. This system emphasizes lean manufacturing, waste reduction, and continuous improvement, drastically increasing efficiency before the 1960s, which had long-term effects on cost structures and production capabilities.

Conclusion

In summary, these economic analyses underline how resource constraints, technological progress, and trade preferences influence production, specialization, and economic growth. Countries and industries that leverage learning efficiencies and comparative advantage tend to generate long-term gains, evidenced by Japan’s successful automotive industry and the dynamics of international trade models.

References

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  • Porter, M. E. (1990). The Competitive Advantage of Nations. Free Press.
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