Economy A Producing Two Goods X And Y Using Both Capital

economy A Is Producing Two Goods X And Y Using Both Capital And L

Economy A produces two goods, X and Y, utilizing both capital and labor in their production processes. The labor force can produce either 300 units of Y or 100 units of X, or any linear combination of these two outputs. The stock of capital can produce either 200 units of Y or 400 units of X, or any linear combination thereof. Currently, the economy produces and consumes 50 units of X. An increase of 10% in the capital stock occurs without affecting the productivity of either capital or labor. The question is whether this increase leads to a fall in the competitive price of X from 4 Y per X to ½ Y per X, and to explain why.

Paper For Above instruction

The given scenario involves analyzing the impact of an increase in capital stock on the relative prices of goods X and Y in a two-good, two-factor economy—capital and labor. To determine whether the statement that the price of X falls from 4 Y to ½ Y is true, it is essential to understand the underlying principles of production possibility frontiers (PPFs), factor prices, and competitive markets.

The initial data suggest that the economy's production possibilities are constrained by its inputs. The marginal productivity of each factor determines the relative prices of the goods, as per the theory of competitive equilibrium. According to the information, the labor force can produce either 300 units of Y or 100 units of X, implying a marginal rate of transformation (MRT) between these goods. Specifically, the MRT, which is the rate at which X can be transformed into Y in production, initially is 300 Y for 100 X, or 3 Y per 1 X. Conversely, capital can produce 200 Y or 400 X, suggesting an MRT of 200/400 = 0.5 Y per X. These ratios indicate how efficiently each good can be produced using the factors and exhibit the opportunity costs involved.

Before the increase in capital stock, the initial prices of the goods are aligned with their marginal rates of transformation and their factor costs, adjusted in the market by supply and demand. The question states that initially, the price of X is 4 Y per X, which exceeds the MRT implied by the initial production constraints. This suggests a market distortion or other factors influencing prices, but for simplicity, we focus on the theoretical implication of an increase in capital stock.

The increase of 10% in capital stock enhances the economy’s ability to produce both X and Y without affecting productivity—meaning the productivity per unit of capital remains the same. Since capital is now more abundant, the economy can produce more of both goods, especially those goods that are capital-intensive, which in this case appears to be X given the initial ratios.

In the context of competitive markets, an increase in capital supply, with constant productivity, generally leads to a decrease in the relative price of the good that can be more intensively produced with additional capital—here, X. This is because the increased capital stock shifts the production possibility frontier outward, allowing for greater output of X at a lower opportunity cost, effectively reducing the price of X relative to Y. As the market adjusts, the equilibrium price of X would decrease relative to Y, reflecting the increased supply and lowered marginal cost of producing X.

Given the information, the initial price of 4 Y per X is high compared to the MRT of 0.5 Y per X produced via capital, indicating a market where the price may be above the marginal cost of production for X. With more capital available, the marginal cost of producing X declines, and competitive pricing would drive the price downward toward the new equilibrium, which tends toward the marginal rate of transformation, i.e., approximately 0.5 Y per X.

Therefore, the assertion that the price of X falls from 4 Y per X to ½ Y per X following a 10% increase in capital stock is consistent with economic theory on supply shifts and cost reductions associated with increased capital. The equilibrium price tends to align with the marginal rate of transformation in perfectly competitive markets, especially when productivity remains unaffected, and additional capital can be employed efficiently in production.

In conclusion, the statement is true because, with increased capital stock, the relative cost of producing good X decreases, leading to a corresponding reduction in its price from 4 Y to approximately ½ Y. This outcome aligns with the fundamental economic principles of supply, marginal productivity, and competitive equilibrium.

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