3. This question is a computational question on the Specific Factors model. There is a small country who may or may not be trading with the rest of the world. There are two final goods, microchips (M) and apples (A). There are three types of labour used in production, general labour which is used in both industries, high-skilled labour which is used only in production of microchips, and low-skilled labour which is used only in production of apples. The technologies for producing the goods in the small country are given by: QM = (GM)(5):7 QA = (GA):3 (L)?, where GM and G A are input of general labour into microchips and apples respectively; and S and L are the supplies of high-skilled labour and low-skilled labour respectively. There are four types of households in the small country and each household has one unit of labour but the type of labour they have may vary. Households are described in the following table. Table 1: Households Household Type Number of Households Type of Labour Utility Function 1 400 High-Skilled (dm). (da)? 2 500 Low-Skilled (dm) 5 (da).5 3 600 General Purpose (dm) (da) 1 4 300 General Purpose (dm) (da). Recall that if the utility function takes the Cobb-Douglas form of U(dm,dA) = (dm)(da)1-8, then the Marshallian demands take the following form: dm = 8 da = (1-8) B) (%) where I is household income. Let the wage of high-skilled workers be denoted ws, the wage of low-skilled workers as WL, and the wage of general-purpose workers as wg. If the small country trades with the rest of the world, it does so at price ratio CEP: = 2.00. 2 (3.A.) (30 points) By calculating equilibrium variables in autarky and in trade for the small country, complete Table 2. Table 2: Equilibrium Variables Variable Autarky Trade 2.00 G GA (ws/WL) Utility of a Type 1 Household Utility of a Type 2 Household Utility of a Type 3 Household Utility of a Type 4 Household 0.70 0.21 0.17 0.30 3. This question is a computational question on the Specific Factors model. There is a small country who may or may not be trading with the rest of the world. There are two final goods, microchips (M) and apples (A). There are three types of labour used in production, general labour which is used in both industries, high-skilled labour which is used only in production of microchips, and low-skilled labour which is used only in production of apples. The technologies for producing the goods in the small country are given by: QM = (GM)(5):7 QA = (GA):3 (L)?, where GM and G A are input of general labour into microchips and apples respectively; and S and L are the supplies of high-skilled labour and low-skilled labour respectively. There are four types of households in the small country and each household has one unit of labour but the type of labour they have may vary. Households are described in the following table. Table 1: Households Household Type Number of Households Type of Labour Utility Function 1 400 High-Skilled (dm). (da)? 2 500 Low-Skilled (dm) 5 (da).5 3 600 General Purpose (dm) (da) 1 4 300 General Purpose (dm) (da). Recall that if the utility function takes the Cobb-Douglas form of U(dm,dA) = (dm)(da)1-8, then the Marshallian demands take the following form: dm = 8 da = (1-8) B) (%) where I is household income. Let the wage of high-skilled workers be denoted ws, the wage of low-skilled workers as WL, and the wage of general-purpose workers as wg. If the small country trades with the rest of the world, it does so at price ratio CEP: = 2.00. 2 (3.A.) (30 points) By calculating equilibrium variables in autarky and in trade for the small country, complete Table 2. Table 2: Equilibrium Variables Variable Autarky Trade 2.00 G GA (ws/WL) Utility of a Type 1 Household Utility of a Type 2 Household Utility of a Type 3 Household Utility of a Type 4 Household 0.70 0.21 0.17 0.30
