The exponents on the utility function are both supposed to be 1/2, not 1/2 and 2/2

Problem Set 3 1 Specic Factor Model [60 points] Two countries, Home and Foreign, produce two goods, Cotton and Desks, using three factors of produc- tion, Land (T), Machines (M) and Labor (L). Land owners are self-employed. They hire labor at unitary wage to from workers, and produce Cotton according to the production function: 1 ] QC = TZLE, where LC denotes units of labor hired to produce Cotton. The income of Land owners is given by the prots 1}: = chc ch. Machine owners are also self-employed. They hire labor at unitary wage mg and produce Desks according to the production function: % Lo new QD=M their income is given by the profits I D = PDQ D wLD. The Home country is endowed with the following factor amounts: T=1,M=9,L=16 The Foreign country is endowed with the following factors: T\" = LM\" = 4,L = 64 Preferences are identical in the two countries and are described by the following utility function: 1 2 U(DC,DD) = BEBE, AsSume for now that the two countries are in autarky. Throughout, you should use Desk as the numeraire good by setting its price to one pg = Pb = 1. 1. What are the specific factors in this problem? Using the information on the endowments of the specific factors, rewrite the production functions in the two countries as a function of the mobile factor only. [3 pt] 0 The specific factors in this problem are and 0 Using the information on the endowments of the specicctors, the production functions can be written as: 2. Consider the Home count_r}f. Plot the production possibility frontier, labeling axes and intercepts, and the slope. What is the value of the vertical intercept of the PPF, i.e, the point (0, Q0)? What is the value of the horizontal intercept? [9 pt] Vertical intercept of the PPF is found as the units produced of good D when which means: (0! QB); where QD = Horizontal intercept of the PPF is found as which means: The slope at point (QC, QD) is equal to: 3. Find the marginal product of labor in the two sectors [5 pt] We find: MPLC = MPLD = 4. Given prices of Computers and Desks, pc and pp, using the equilibrium condition in the labor market, nd the allocation of Labor to the production of the two goods as a function of the relative price P = id rn- [5pts] The equilibrium condition in the labor market says that which means: 5. Consider an increase in the relative price pc. What is the effect of this price change on the income of the land-owners (Ic) and capital owners (I D)? Explain briey [5 points] 6. Consider the Foreign country: Given prices p2 and p}, and relative price p* = p'C/ pf), what is the allocation of Labor to the production of the two goods as a function of the relative price p*? [Hint: same as question 4., but for Foreign] [5 pts] The equilibrium condition in the labor market says that which means: 7. From parts 4 and 6, derive the relative supply of the two goods in both countries, i.e. RS( p) and RS*(p)? [5 points] [Hint: The relative supply function expresses the relative equilibrium production of C as a function of the relative price p. From the production functions, we can express the relative equilibrium production of C as ..] The relative supply expresses the relative production of C as a function of the relative price. From the produc- tion functions, we can write: so that: 8. Using the information on preferences, derive the relative demand for each country. [3 pts] 9. (i) Using relative demand and relative supply find for each country the equilibrium autarky relative A Aer price: 6%) and (4%) . (ii) Which country has a comparative advantage in Cotton? (iii) Can you guess the source of comparative advantage in this problem? [10 points] (a) Setting relative demand equal to relative supply at Home and at Foreign, we nd: i. For Home ii. For Foreign (b) Therefore, given , it follows that has a comparative advantage in Cotton. (c) The pattern of trade and comparative advantage in the specic factor model is determined by