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?