7/25/2019 15. General Equilibrium With Production II

1/5

General Equilibrium, Production IITwo inputs, two goods, two consumers

Assumptions1) isoquants convex/smooth2) inputs essential to production of goods3) production function returns to scales4) production has no externalities

*eciency in consumption !" identical for all individuals

Production Possibilities

!esource/technical limitations restrict #hat economy canproduce

"et of feasi$le output $undle % production possibility set

o All com$os of goods that can $e produced

Production possibility frontier% set&s outer $oundary

Production possibility function (ppf):marginal rate of

product transformation'identical)

'1) texttreatment % $/c ecient production requires exploitationof comparative advantage

Comparatie !dantage

(#o agents "Cand an riday

'#$)o "C can produce at most

%& coconut

or, '& s

o #$ can produce at most

*& coconuts

or, %* s

more producers #ith di+ opp, -ost %. smooth out ppf

'2) di+erent inputs are more productive in production of di+erent goods0variation on comparative adv some inputs $etter suited to production of certain goods that othe

inputs

Production E+ciency wit omogenous $actors, -i.erent Production Tecnologies economy producing food and manufactures $oth use land '() and la$our ')

o $oth inputs omogenous every hectare of land is the same all #or5ers clones of each

othero 6xed amount of land availa$le 6xed amount of la$our $oth are supplied perfectly

inelastic

assume $oth goods are produced using -o$$78ouglas -onstant !eturns to "cale

techo use of each input A9:; is characteri

7/25/2019 15. General Equilibrium With Production II

2/5

assume food % land7intensive 'high land/la$our ratio in production) manufacture % la$our

intensive 'lo# ratio)o production functions

!llocation of Inputs

A-(9!" are allocated $et#een industries

o Any land not used in food #ill $e used in

manufactureso Any la$our not used in food productionused in manufactures

o $oth inputs fully employed $ut it matters ho# its allocated amongt#o industries

Edgewort /owley /o0

variation hori

7/25/2019 15. General Equilibrium With Production II

3/5

#"PT

!eallocate some la$our

o -hange in la$our used in food 7d

o -hange in food d % 7d*=')

o -hange in la$our used in man, Kd

o -hange in man d % d*=')

!eallocate some land

o -hange in land used in food 7d(

o -hange in food d % 7d(*=(')

o -hange in land used in man Kd(o -hange in man d % d(*=(')

!ight one@

Gf production eciency attained 'moving $et#een 1 output com$o on the == to another on the

==)o (he t#o ratios '=&s and =(&s) must $e the 4!#E

o 8oesn&t matter #hich one #e use

rom Hox

o At any factor allocation on eciency locus slope of isoquant for 1 output % slope of

another Hoth isoquants B$ac57to7$ac5C

Isoquant 4lope

-hange amount land used $y man $y d( change amount la$our used $y d change in manufactur

output

Along isoquant change n output % E

At ecient factor allocations

o "lopes of 2 isoquants are the same

o rearrange

o ratio of marginal products of land % = of la$our

o $oth equal !( of food into manufactures

Coordination Production and Consumption

#hich are =areto ecient for consumers@

!" doesn&t % !=(

7/25/2019 15. General Equilibrium With Production II

4/5

o Gnecient coordination of production and consumption

!" % !=( necessary for =areto optimal economic state

Lhen exchange ecient !"!-% !"

o Hoth % ratio of prices in exchange 'consumption)

o !"-ommon'-) % =/=- consumers

Gf producers sell at competitive M slope of == '!=() % ratio of prices

changed $y sellers

!=('-) % =/=- producers!" % !=( -onsumer =rice !atio % =roducer =rice !atio

!llocatie E+ciency (Product5#i0 E+ciency) Condition

9utput at #hich sum of consumers surplus K producers surplus is maximi

7/25/2019 15. General Equilibrium With Production II

5/5

7 !=( deduced from ratios of = of 2 inputs

Relative Price of X for consumers:7 -ompetitive exchange !;A(GO; price 'ratio of consumer prices)o 1stdetermine incomes of 2 consumers

'rent*capital supplied) K '#age*la$our supplied)

o su$stitute total income for each into expression for -o$$78ouglas demands

set quantities demande for P % to quantitiey availa$le 'produced) and solve for =x

o then do the same for good Q solve for =y

o form ratio =x/=y % relative price of P

7 factor prices r# and amoutns of factores supplied are RaR$a$7 demands for P

7 then can 6nd price of P that clears mar5et for P $y setting sum of quantities demand % to amountavaila$le

7 solve relative consumer price of P as =x/=y7 this is #hat #e compare to !=( 'relative price of P '=x/=y) for producers)

*if producer prices % - 'rent of =5 or #age over =l) total revenue is less than the amount of factorpayments

$/c prices of capital and la$out #ere BfudgedC to yield num$ers #ith only 1 deciman