7/25/2019 9. Trading From Endowment

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Trading from EndowmentBuying & Selling, Labour Supply

Buying and Selling

Trade involves exchange when something is bought something else must be sold

o What will be bought/sold? Who will be a buyer/seller?

o How are incomes generated?

o How does value of income depend on commodity prices?

o Hoe can we put all this together to explain better how price changes aect demands?

Endowment Endowment ():list of resource units with which a consumer starts (goods consumer has before

he enters maret!Ex. (!, ") " (#$%&! customer endowed with (#$ units good #% & units good &!

'ndowments value?

Which consumption bundles may it be exchanged?

o )# " &% p& " * (!, ")" (#$%&! p!! # p"" " &+#$ , *+& " &-

o .or any bundle costing no more than endowments value

Budget $on%traint% e'i%ited

iven p# 0 p& budget constraint for consumer with endowment !, "is

1m2

3udget set4 %

p#x# , p&x& "

p##

, p&& p#(x# #!

, p&(x&5&! " $ sum of thevalues of a consumers net demand%" $

et emand% (di between what consumer ends up with (6! and initial endowment!% the amount that is

bought/sold suppose (!, ")" (#$%&! 0 p#" &% p&" *

o constraint4 p#x# , p&x& p#!, p&"" &-

if consumer demands (x#+%x&+! " (7%8! * good # units exchange for & good & units

o net demands: x#+ 5 !" 75#$ " 5* 0 x&+5"" 85# " ,&

o p#"&% p&"* p#(x#5#! , p&(x&5&! " & x (5*!,*x& " $

purchase of & extra good & units at 9* each is funded by giving up * good # units at 9& each

*ri+eo-er +ur'e:utility maximi:ing gross demands for which endowment can be exchanged

ro%% demand%: amount of the good that the consumer actually ends up consuming (x#%x&!

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Labour Supply

Worer endowed with /m" nonlabour in+ome 0r% of time w0i+0 +an be u%ed forlabour1lei%ure

(,m)

;onsumption price " p+ w" wage rate

Worers budget constraint< ;%= " gross demands for the consumption good for

leisure

Labour Supply $ur'e t0at

Slope% 2pward and t0enBend% Ba+3ward

Labour Supply re%pon%e%, o'ertime, wage in+rea%e

Buying, Selling 4ppli+ation%

Sub%titution E-e+tominate% 5n+omeE-e+t (LabourSupplied 5n+rea%e%)

5n+ome &Sub%titutionE-e+t%, 6age

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30> is analogous to borrowing and lending in a model of utility maximi:ation overtime

(intertemporally!

3asis of trade/exchange

Supply of onLabour 5nput%

.irm " supplier in intermediate input maret/ individuals suppliers in primary

ndividual selling renewable re%our+e4 (land!can use over and over again< supply in perfectly

inelastic with respect to input price onrenewable re%our+e(oil!4 once used gone< supply is perfectly inelastic% analy:ing e@uilibrium

within a single period

Supply of Labour

Wor (time that generate income! leisure (all other use of time!

)references can be reduced to preferences over consumption bundles composed of & goods

(leisure/income!

& constraints4

o time +on%traint:total time to wor/leisure " total time available

T total time, h 0our% of wor3,x10our% %pent at lei%ure h + x1

= To 5n+ome +on%traint:individuals income is sum of income earned from wor and non5wor

income

W indi'id wage rate,A nonwor3 in+ome income (x")" incom

from wor (w0) # 4

Lei%urein+ome budget +on%traint:

o wx1 + x2 = A + wT

o w pri+e of lei%ure

o A + wT = full income

ndividual choosing bundle to maximi:e utility subAect to constraint that value of

leisure (wx#! , income (x&! " to full incomeo >olution4

Baximi:ing bundle x#+%x&+% supplies h+ hours of labour< at that total

income " C , wT (non/wage income!

3udget constraint slope " 55wndierence curve tangent to leisure5income budget constraint

e%pon%e% to $0ange% in on6or3 5n+ome

Deisure " normal goodif response to in+rea%ein non5wor income C is an

in+rea%ein hours of leisure and de+rea%ein hours of woro Eon5wor income initially 9F$$ per wee

o nitial e@uilibrium " #&$ of the #-G to leisure% 8G to wor

o ncreases from F$$ G$$ demand for leisure increases to #*G% *$ to

wor

Deisure " inferior goodis response to in+rea%ein non5wor income C is a

de+rea%ein hours of leisure% in+rea%ein wor

e%pon%e% to $0ange in 6age ate ncrease in wage rate initially 9#$ to 9&$< demand for leisure increases by #8

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o ;hange of leisure broen into positive income of (#8$5##*! &7 hours 0

negative substitution eect of (##* #&-! 5#* hourso =esponse income 0 substitution eect4

3 reducing income Aust enough to attain lower indierence curve

" budget line< would choose ; ncreases hours of leisure by &7

>ubstitution eect reduce hours of leisure% increase

wor by #* hours ncome substitution net eect " increase in leisure by

#8 and decrease in wor

Deisure " normal good

income eect of wage increase leads to increasein hrs leisure and decrease in woro Sub%titution e-e+t4 wage increase decrease in hrs of leisure and increase in

woro ncome and sub are cross purposes< results ambiguous

Deisure " inferior good income and sub eects are complementary< result

unambiguous

Labour Supply $ur'e%

6ierent wage rates% each point " bundle of leisure/income used to get labour supply curve