Homework #7: Answers. Commodity a kj a Lj Price $16 $14 $10 $14 $16

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1 Text questions, Chpte 8, poblems 1-3. Homeok #7: Anses 1. Assume tht input-output coefficients e fixed. The tble shos cpitl equiements pe unit output ( kj ) nd lbo equiements pe unit output ( j ) to poduce one unit ech of commodities 1-5. Also shon e peviling pices fo ech commodity. Commodity kj j Pice $16 $14 $10 $14 $16. If the economy hs lbo/cpitl endoment tio of 3:1, ht does it poduce? Wht e the ge te nd ents on cpitl? Constuct the unit vlue isoqunts fo ech of these sectos nd plot the endoment tio (denoted k in the digm). Fom the pictue, it is esy to see tht the economy ill poduce goods 4 nd 5. To find the ge nd entls consistent ith these, use the zeo pofit conditions. In mtix fom, these e:

2 P P P P The deteminnt of the mtix A [ ij ], *A* -2, *A * -2, *A * -24. Thus: *A * / *A* 2/2 1; *A * / *A* 24/2 12. b. If the old pice of commodity 1 should tiple, ould thee be ny chnge in this county s poduction ptten? Fcto Pices? Rel income? If the old pice of commodity 1 tiples, fom $16 to $48, the unit vlue isoqunt fo commodity 1 ould shift tod the oigin sufficiently f tht only goods 1 nd 5 e no poducible. We cn solve fo the ne fcto pices s bove: The deteminnt of the mtix A [ ij ], *A* -15, *A * -16, *A * Thus: *A * / *A* 16/15; *A * / *A* 176/15. c. At the initil pices shon in the tble, ho ould fcto pices diffe in n economy ith the sme technology but cpitl/lbo tio of 3:1? This endoment tio is shon by the line kn in the digm. Unde initil pices, ith endoment tio kn, the economy ould poduce goods 1 nd 2. Using the method fom the pevious to pts (i.e. Cme s ule) e cn solve fo 12 nd 1. d. Fo the economy ith the oiginl lbo/cpitl tio of 3:1, ho ould poduction pttens nd fcto pices chnge if commodity 3 s pice on old mkets should ise by 40 pecent? A 40 pecent incese in the pice of good 3, ith endoment tio k, ill esult in goods 3 nd 5 being poduced. Using the zeo pofit conditions, e cn find 2/3 nd 13 1/3.

3 e. Descibe the ptten of tde fo n economy ith cpitl/lbo endoment tio of 1:1. Fo n economy ith / tio of 1:1, the economy ill specilize in the poduction of commodity Using Figues 8.4 nd 8.5, sho ho n incese in the old pice of commodity 2 ould ffect el ges in to counties shing the sme technology, both of them poducing commodity 2, but ith the home county hving n endoment tio of 0I (Figue 8.5) nd the foeign county ith endoment tio 0M. The essentil fct fom figue 8.5 is tht the Home county hs n endoment tio tht pemits poduction of goods 1 nd 2, hile the foeign county hs n endoment tio tht pemits poduction of goods 2 nd 3. Tht is, these endoments lie in diffeent cones of divesifiction. The elevnt pt of figue 8.4 is epoduced belo. An incese in P 2 ill shift the unit vlue isoqunt fo good 2 tod the oigin. et T : / nd T* */*, nd denote vlues folloing the pice chnge ith N. If the pice chnge is sufficiently smll tht both counties continue to poduce the sme goods s befoe the pice chnge, it must be the cse tht T > TN nd T* < T*N. Note tht this could hve been pedicted fom the Stolpe-Smuelson theoem nd the fct tht good 2 is -intensive fo the Home county, but -intensive fo the Foeign county. If the pice chnge is sufficiently lge tht both counties become specilized to poduction of good 2, the sme eltionships ill hold (i.e. T > TN nd T* < T*N), but no this ill follo fom the eltionship beteen the initil tngencies beteen unit isocost nd unit vlue isoqunt nd the slope of the unit vlue isoqunt t the intesection ith the endoment ys.

4 3. In figue 8.2 points HN nd FN sho ech county devoting the sme esouces to the diffeentited clothing secto s it did in utky. Suppose tht the Home county is eltively lbo-bundnt nd clothing is lbo-intensive eltive to food.. Ho ould this lte the numbe of fims devoted to clothing in ech county? The fct tht the Home county is -bundnt nd clothing poduction -intensive mens tht, ith identicl homothetic pefeences, poduction costs in utky ill be loe in the Home county. Thus, thee ill be moe fims opeting in the Home county, ceteis pibus, unde this ssumption thn unde the ssumption identicl endoments. b. Could the Home county poduce ide viety of clothing ith tde thn the (lge) Foeign county? This could esult in thee being moe clothing poduces in the Home county thn bod. Whethe o not this ctully hppens ould depend on the y tht size nd eltive cost intect. Thus, fo sufficiently lge diffeence in size nd sufficiently simil endoment, the lge (Foeign) county ill continue to poduce moe vieties. On the othe hnd, fo sufficiently simil size nd sufficiently lge diffeence in endoments, the Home county could poduce moe vieties.

5 Wokbook poblems, 1, 2, nd 6 1. Unit-vlue Isoqunts, Poduction Ptten, nd Fcto Pices: The isoqunts dn belo sho the mounts of cpitl nd lbo equied to poduc $1 oth of ech of the goods.. Suppose the endoment of this economy is shon by the k / y. Wht good(s) ill be poduced? Recll tht these e unit vlue isoqunts, defined eltive to equilibium commodity, nd thus fcto, pices. Since k lies in the cone detemined by tngency beteen isocost A nd isoqunts 3 nd 2, those goods ill be poduced. b. Suppose tht thee is n influs of okes nd the cpitl/lbo tio flls to kn /N. No ht ill be poduced? Becuse kn flls in the cone detemined by the tngency beteen isocost B nd the 2 nd 1 isoqunts, those 2 goods ill no be poduced. c. Wht hppened to the ge/entl tio s the k tio fell? As k moved ithin it s oiginl cone, thee s no chnge in the / tio. Once it pssed outside the cone, the / tio flls smoothly long the 2 isoqunt (s the / tio is being detemined by MRTS in 2 poduction). Finlly, once it psses into the second cone, the / tio is fixed by the slope of the common tngent i.e. the slope of isocost 2. d. Wht hppens to the ge/entl tio s comped to (c) if the pice of good 1 doubles?

6 The doubling of the pice of good 1 ill cuse the unit vlue isoqunt to shift hlfy to the oigin. This ill cuse the equilibium / tio to ise. Note, this chnge my cuse good 2 to go out of poduction, fist being eplced by good 3, nd, if the shift is popotionlly lge enough, to speciliztion in good The Fcto-Pice Equliztion Theoem Once Agin: Conside to-county old, hee both counties hve the sme technology fo poducing clothing nd food s illustted by the folloing unit-vlue isoqunts:. Wht is the nge of fcto endoment tios tht ill yield fcto pice equliztion? Indicte this nge in the digm. Any endoment in the cone of divesifiction is consistent ith fcto-pice equliztion. b. Does this nge depend upon commodity pices? Yes. Recll tht these e unit vlue isoqunts. Thus, thei loction, nd the loction of the tngencies tht define k F nd k C e detemined by commodity pices. Thus, diffeent commodity pices ould poduce diffeent cone.

7 6. ove of Viety vesus Indiffeence to Viety: The Home nd Foeign counties ech possess the sme technology fo poducing blue nd ed schmoos. Poduction of single schmoo (blue o ed) equies 30 units of cpitl nd 30 units of lbo, hile the second schmoo equies only n dditionl 10 units of cpitl nd 10 units of lbo. The thid schmoo equies 5 units of cpitl nd 5 units of lbo ext. Ech dditionl schmoo equies only one ext unit of cpitl nd one ext unit of lbo to be poduced. If the fist schmoo is ed the othe schmoos poduced must be ed to cptue the incesing etuns to scle.. Ech county is endoed ith 60 units of cpitl nd 60 units of lbo. Suppose consumes in ech county demnd blue nd ed schmoos in equl popotions. Wht ill ech county poduce in utky? Becuse people pefe to consume ed nd blue schmoos in equl popotions, ech county ill poduce both vieties in utky. With identicl technologies, this ill involve the lloction of 30 nd 30 to ech viety. This pemits poduction of 1 ed nd 1 blue schmoo in ech county. b. If consumes e indiffeent bout the colo of schmoos, ht does ech county poduce in utky? In this cse ech county ill llocte ll fctos to the poduction of only one viety. In this cse, totl of 18 units cn be poduced (i.e give the fist thee units, this leves 15 dditionl units of nd fo totl of ). c. No suppose tht the to counties begin to tde nd tht consumes ce bout the colo of the schmoo. Wht ill ech county poduce in tde equilibium? Wht hppens to the numbe of schmoos poduced in ech county eltive to you nse to pt (b)? Wht is the numbe of fims in ech county? In this cse ech county ill specilize in diffeent viety of schmoo, poducing 18 units, nd tde. In this cse, ech county ill consume 9 ed nd 9 blue schmoos. The totl numbe poduced in ech county is the sme s in pt (b), the diffeence is tht ech county must poduce diffeent viety. Thee e gins both fom incesed efficiency (eltive to pt ) nd incesed viety in consumption (eltive to pt b). Note tht, becuse these e intenl economies of scle, thee must be 1 fim in ech county.

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