1. (Specific Factors Model: Autarky Economy) In this economy two countries, Home and Foreign. produce two...

  

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1. (Specific Factors Model: Autarky Economy) In this economy two countries, Home and Foreign. produce two goods, Computers and Desks, using three factors of production, skilled labor (H), unskilled labor (L) and capital (K). Technology. Technology is the same in both the Home and Foreign countries. In both countries, skilled workers are self-employed. They rent capital at the rental rate r and produce computers according to the production function: Qc = H¹/2K/2 (1) Their income is given by Rc = PcQc-rKc, where Kc is the capital employed to produce computers. Unskilled workers are also self-employed. They rent capital and use it to produce desks according to the production function: QD=L²/3K/3 Their income is given by RD = PpQD-rKp, where Kc is the capital employed to produce computers. Endowments. Home country is endowed with the following factor amounts: H = 9, K =20, L = 4. The Foreign country is endowed with the following factors: H* = 1, K* = 20, L* = 4. Preference. Preferences are identical in the two countries and are described by the following utility function: -1/3-2/3 U(XC, XD)= X³x2/3 (3) In the economy all the factors are always fully employed. Assume for now that the two countries are in autarky. (a) In this model, what are the specific factors to produce each product? (b) Given the production functions, write down the PPF for the Home country using the idea that capital is employed in both sectors. Plot it on a graph with QD as the horizontal axis and Qc as the vertical axis. (c) Suppose prices of Computers and Desks, Pc and Pp. Consider the Home country and find the autarky equilibrium return to capital r using the graph showing the Value of Marginal Product of Capital P MPK for both goods, following the steps: i. Draw the capital demand for these two industries in one graph. (Hint: capital demand in each industry is determined by P* MPK = r.) ii. What is equilibrium capital rental rate r and the allocation of Capital to the production of the two goods (as a function of Pc and Pp)? iii. What are the corresponding outputs of each product (as a function of Pc and Pp)? In particular, what is the relative supply function Qc/QD as a function of Pc/PD? (d) Suppose the output prices are Pc and PD, and given that the capital rental rate r is a function of Pc and Pp, solve for the demand for computers and desks by solving the consumer utility maximization problem for skilled workers and unskilled workers at Home country. In particular, what is the relative demand function Xc/Xp as a function of Pc/PD? (e) Using relative demand and relative supply, find the equilibrium autarky relative price for the Home country. Draw the relative supply and relative demand function for Home in one figure and mark the equilibrium point as A. [NOTE: because you can only find the relative price Pc/Pp, you could use Desk as the numeraire good by setting its price Pp to one.] (f) What is the effect of this price change on the income of the skilled (RS) and unskilled workers (RU). 1. (Specific Factors Model: Autarky Economy) In this economy two countries, Home and Foreign. produce two goods, Computers and Desks, using three factors of production, skilled labor (H), unskilled labor (L) and capital (K). Technology. Technology is the same in both the Home and Foreign countries. In both countries, skilled workers are self-employed. They rent capital at the rental rate r and produce computers according to the production function: Qc = H¹/2K/2 (1) Their income is given by Rc = PcQc-rKc, where Kc is the capital employed to produce computers. Unskilled workers are also self-employed. They rent capital and use it to produce desks according to the production function: QD=L²/3K/3 Their income is given by RD = PpQD-rKp, where Kc is the capital employed to produce computers. Endowments. Home country is endowed with the following factor amounts: H = 9, K =20, L = 4. The Foreign country is endowed with the following factors: H* = 1, K* = 20, L* = 4. Preference. Preferences are identical in the two countries and are described by the following utility function: -1/3-2/3 U(XC, XD)= X³x2/3 (3) In the economy all the factors are always fully employed. Assume for now that the two countries are in autarky. (a) In this model, what are the specific factors to produce each product? (b) Given the production functions, write down the PPF for the Home country using the idea that capital is employed in both sectors. Plot it on a graph with QD as the horizontal axis and Qc as the vertical axis. (c) Suppose prices of Computers and Desks, Pc and Pp. Consider the Home country and find the autarky equilibrium return to capital r using the graph showing the Value of Marginal Product of Capital P MPK for both goods, following the steps: i. Draw the capital demand for these two industries in one graph. (Hint: capital demand in each industry is determined by P* MPK = r.) ii. What is equilibrium capital rental rate r and the allocation of Capital to the production of the two goods (as a function of Pc and Pp)? iii. What are the corresponding outputs of each product (as a function of Pc and Pp)? In particular, what is the relative supply function Qc/QD as a function of Pc/PD? (d) Suppose the output prices are Pc and PD, and given that the capital rental rate r is a function of Pc and Pp, solve for the demand for computers and desks by solving the consumer utility maximization problem for skilled workers and unskilled workers at Home country. In particular, what is the relative demand function Xc/Xp as a function of Pc/PD? (e) Using relative demand and relative supply, find the equilibrium autarky relative price for the Home country. Draw the relative supply and relative demand function for Home in one figure and mark the equilibrium point as A. [NOTE: because you can only find the relative price Pc/Pp, you could use Desk as the numeraire good by setting its price Pp to one.] (f) What is the effect of this price change on the income of the skilled (RS) and unskilled workers (RU).

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In this model what are the specific factors to produce each product The specific factors to produce computers are skilled labor and capital The specific factors to produce desks are unskilled labor an... View the full answer