B. Suppose there are two goods, Cloth and Food, and two factors of production, labour
and capital. Suppose that the production function for each good is "homothetic". Put capital K in the vertical axis and labour L in the horizontal axis. For Cloth production, for any ray from the origin that has a slope of x, the slope of a tangent of an isoquant at a point which crosses this particular ray is 3x. For Food production, for any ray
from the origin that has a slope of 3y, the slope of a tangent of an isoquant at a point which crosses this particular ray is 2y.
(a) Draw the isoquants for the production of Cloth and of Food.
(b) Draw the two curves relating the capital to labour ratio (K/L in the horizontal axis) with the wage to rental ratio (w/r in the vertical axis) for the production of Cloth and for the production of Food. What can you say about the relative factor intensities of the two sectors?
(c) Find the capital to labour ratios for both Food and Cloth when w/r = 2 and
w/r = 4.
(d) Suppose that there are two countries, A and B that have the same technology described above for Cloth and Food. Before trade, Country A employs 10 units of K and 60 units of L in the Cloth industry. In the Food industry it employs 30 units of K and 40 units of L. Country B employs K = 20, L = 30 in the Cloth industry and K = 30, L = 10 in the Food industry. Determine the prices
w/r in the two countries before trade and the comparative advantage and the trade pattern.
Which group in A will oppose opening up trade and why?
i need answers
(a) To draw the isoquants for the production of Cloth and Food, we need to determine the relationship between capital (K) and labor (L) for each good.
For Cloth production, the slope of a tangent of an isoquant at a point on a ray with slope x is 3x. This implies that the isoquant for Cloth production is steeper than the 45-degree line (the line with a slope of 1). As we move away from the origin, the slope of the isoquant increases.
For Food production, the slope of a tangent of an isoquant at a point on a ray with slope 3y is 2y. This implies that the isoquant for Food production is flatter than the 45-degree line.
Using this information, we can draw the isoquants as follows:
- Isoquants for Cloth production: The isoquants will be upward-sloping lines with increasing steepness as we move away from the origin.
- Isoquants for Food production: The isoquants will be downward-sloping lines with decreasing steepness as we move away from the origin.
(b) To draw the curves relating the capital to labor ratio (K/L) with the wage to rental ratio (w/r) for the production of Cloth and Food, we need to understand the relative factor intensities of the two sectors.
The relative factor intensity of a sector can be determined by comparing the slopes of the isoquants for each sector. A sector with a steeper slope has a higher capital to labor ratio, while a sector with a flatter slope has a lower capital to labor ratio.
Based on the given information, we know that the slope of an isoquant for Cloth production is 3 times the slope of a corresponding ray (slope x). This means that the Cloth sector is more capital-intensive compared to the Food sector.
Similarly, the slope of an isoquant for Food production is 2/3 times the slope of a corresponding ray (slope 3y). This means that the Food sector is more labor-intensive compared to the Cloth sector.
Drawing the curves:
- For the Cloth sector, the curve relating K/L to w/r will be steeper, indicating a higher capital to labor ratio.
- For the Food sector, the curve relating K/L to w/r will be flatter, indicating a lower capital to labor ratio.
(c) To find the capital to labor ratios for both Food and Cloth when w/r equals 2 and 4, we need to use the information about the slope of the isoquants.
For the Cloth sector:
- When w/r = 2: The slope of the isoquant of Cloth production is three times the slope of the corresponding ray. So, the slope of the isoquant is 6. We can find the K/L ratio using this slope:
K/L = slope of isoquant / (w/r) = 6 / 2 = 3
- When w/r = 4: Using the same logic, we find:
K/L = slope of isoquant / (w/r) = 6 / 4 = 1.5
For the Food sector:
- When w/r = 2: The slope of the isoquant of Food production is two-thirds the slope of the corresponding ray. So, the slope of the isoquant is 2/3. We can find the K/L ratio using this slope:
K/L = slope of isoquant / (w/r) = 2/3 / 2 = 1/3
- When w/r = 4: Using the same logic, we find:
K/L = slope of isoquant / (w/r) = 2/3 / 4 = 1/6
(d) To determine the prices (w/r) in the two countries before trade and the comparative advantage and trade pattern, let's compare the relative factor intensities and factor endowments of the two countries.
Country A:
- Cloth industry: K = 10, L = 60
- Food industry: K = 30, L = 40
Country B:
- Cloth industry: K = 20, L = 30
- Food industry: K = 30, L = 10
To calculate the relative factor intensity for each industry in each country, we can use the ratio of capital to labor (K/L) for each sector.
Country A:
- Cloth industry: K/L = 10/60 = 1/6
- Food industry: K/L = 30/40 = 3/4
Country B:
- Cloth industry: K/L = 20/30 = 2/3
- Food industry: K/L = 30/10 = 3
Comparing the factor intensities, we can see that Country B has a higher capital to labor ratio in both industries compared to Country A. Therefore, Country B has a comparative advantage in both Cloth and Food production.
The trade pattern will depend on the relative prices of Cloth and Food in the two countries. However, based on the given information, we cannot determine the exact prices and trade pattern without additional data.
As for which group in Country A will oppose opening up trade, we can infer that the group involved in the labor-intensive Food industry might oppose trade due to the potential negative effects it could have on employment and wages in that sector.