Problem Set 4 - Solutions. Suppose when Russia opens to trade, it imports automobiles, a capital-intensive good.

Transcription

1 roblem Set 4 - Solutions uestion Suppose when ussi opens to trde, it imports utomobiles, cpitl-intensive good. ) According to the Heckscher-Ohlin theorem, is ussi cpitl bundnt or lbor bundnt? Briefly explin. According to the HO theorem country exports the good tht uses it bundnt fctor intensively Therefore ussi is lbor bundnt becuse it imports the cpitl-intensive good. b) Wht is the impct of opening trde on the rel wge in ussi? According to the Stopler-Smuelson theorem, the bundnt fctor gins from trde. The opening to trde rises the price of the lbor-intensive good, which leds to n increse the reltive demnd for lbor nd increse the reltive wge (W/ goes up). The increse in reltive wges reduces the lbor/cpitl rtio in both industries, which leds to rise in the mrginl product of lbor nd the rel wge (becuse W/ = ML). c) Wht is the impct of opening trde on the rel rentl on cpitl? The rel rentl goes down. d) Which group (cpitl owner or lbor) would support policies to limit free trde? Briefly explin. The cpitl owners suffer loss due to the decrese in the reltive price of utomobiles. They will support policies to limit free trde uestion onsider country, cll it Home, tht produces computers () nd food () using cpitl (K) nd lbor (L). The techniques of production in ech industry re Leontief, nd hence unit fctor requirements re fixed nd given by: K = 3; K = ; L = nd L = 4. Note: ij is the number of units of fctor i required to produce unit of good j. ) Which industry is cpitl intensive? How does the cpitl-lbor rtio in ech industry depend on the reltive wge /K? The computer industry is cpitl intensive: K L Becuse we hve Leontief production function the rtio is independent 3 K K 4

2 b) Suppose tht the world price of computers is $6 nd the world price of food is $. Assume tht the Home country produces both goods. Wht re the free trde fctor price levels W nd? Under perfect competition, the mrginl revenue (price) of ech product hs to be set equl to the its mrginl cost: W W We cn solve liner equtions in unknowns: K K L L 6 3 W 4W W, nd 4 c) Wht is the shre of revenue going to lbor in ech industry? Under perfect competition: There is no profit, so revenue = fctor income Shre of revenue = shre of production costs K s shre of revenue (lbor receives the rest): omputers: ood: K K +W L = 4(3) 4(3)+ () = 3 4 K 4() = K +W L 4()+ (4) = 3 d) Similr to (b) nd find W = nd = 8 e) Similr to (c) nd find /3 for omputers nd /3 for ood, f) Suppose tht it hs n ggregte endowment of 00 units of cpitl nd 50 workers. How mny computers nd units of food will the economy produce? Here, we use the mrket clering conditions Lbor : L pitl : K L K The solution to this system of equtions is L K g) Similr to (f) nd find = 40 nd = 0 uestion 3 5, nd 5

3 ) As we sw in problem set, the reltive demnd for the obb-dougls utility is b) We hve shown in question tht when the endowments of cpitl nd lbor re 00 nd 50, the outputs of ech industry re the sme = = 5. It follows tht in utrky, reltive supply is: S D c) In equilibrium, becuse of perfect competition, the price of ech good equls its mrginl cost. It follows tht: 3 W, nd 4W Tking the rtio of both eqution, using the fct tht the reltive price is, we obtin: 3 W 4W 3 W 4W W d) If in the oreign country preferences re the sme s in the Home country, reltive demnd will not chnge. The supply cn be obtin by solving the following system of equtions: 3 00, nd 4 00 We find tht: 0 nd 40 Therefore the reltive supply is:

4 nd Using the sme rgument s for Home: uestion 4 ) The closed economy equilibrium in oreign equilibrium is represented by points lbeled A nd the ssocite curves. D S * * 6 W 8W W 3 4W W 3

5 b) or oreign we hve n increse in the reltive price of shoes. So, move from A to B. Higher reltive wges nd cpitl/lbor rtio. c) el wges re equl to mrginl products of lbor in ech sector (i.e., W/c = c MLc / c = MLc nd W/s = s MLs / s = MLs). Similrly, rel rentls re equl to mrginl product of cpitl (/c = MKc nd /s = MKs) rom prt (b) bove, chnges in fctor intensities reflect n incresed intensity in the bundnt fctor which implies n increse in the mrginl product of the bundnt fctor (lbor) nd decrese in the mrginl product of the scrce fctor (cpitl). d) or Home, the reltive price of crs increses nd, s result, the cr isovlue curve shifts down. The new reltive wge (W/) nd cpitl/lbor rtio re now lower. As result, pitl is better off nd lbor is worst off.