autarky relative price pc bepfin terms B u s i n e s s F i n a n c e

2. Consider the specific-factors model (2 goods, 3 factors, where labor is the flexible factor) for a given country with the following Cobb-Douglas production technologies:

QC = K1/2L1/2 (clothing) C

QF =T1/2L1/2 (food) F

where L = LC + LF is the aggregate endowment of labor in each sector and K (capital) and T (land) are the specific factors in each sector.

(a) Assume that all consumers in the country have Leontief preferences—one unit of food must always be combined with exactly one unit of clothing.

i. What do indifference curves look like for these consumers? (2 points)

ii. What does the relative demand curve look like? What QC/QF will consumers choose given

any pc/pf ? (3 points)

(b) What is the Marginal Rate of Transformation (MRT) between clothing and food in in this sector? (That is, how many more units of food can be made in this economy if one less unit of clothing is made). Answer the following parts:

i. What is the MRT in terms of the marginal product of labor in the food sector and the marginal product of labor in the clothing sector? (3 points)

ii. SolveforthemarginalproductoflaborineachsectortowritetheMRTintermsofK,T,LC,LF. What do you get? (4 points)

(c) At the output bundle of QC and QF that maximizes national revenues, what relationship between pC /pF and the MRT must hold? Given what the MRT is in part (b)(ii), what does this relationship mean LC/LF has to be given K,T,pC,pF? (3 points)

(d) The production function QC = K1/2L1/2 means that that given the national endowment of K, to C

make QC units of clothing it takes LC = Q2C /K units of labor. Similarly, the production function QF = T1/2L1/2 means that with a national endowment of T, to make QF units of food it takes

F

LF = Q2F /T units of labor. Plug these expressions in for LC and LF in your answer to (c)—then

re-arrange to show what the relative supply level QC will be in terms of K and pC when the QF TpF

producer maximization condition holds. (4 points)

(e) Using your relative supply and relate demand curves, what will the autarky relative price pC be

pF

in terms of the relative endowment of the two factors K/T ? Plot the relative demand and relative

supply curve for this economy. (5 points)

(f) Suppose that Home is endowed with 200 units of K and 100 units of T. Foreign is endowed with 300 units of K and 3000 units of T. Which good does Home have comparative advantage in? If the two countries open to trade, which good will Home export, and which good will Home import? (8 points)

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