presentation7 labor leisure continued - drexel universityjpd48/presentation7_labor_leisure... ·...
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Macroeconomics+Labor+–+Leisure+Model+Con3nued+
ECON+321+
Extra+Credit+Quiz+4+1.+What+concept+is+observed+in+this+graph?+
Extra+Credit+Quiz+4+
2.+Given:+U(c,h)+=+ch+– subject+to+the+budget+constraints.+
1. c+=+y+=+Al+2. h+l+=+H;+ ++
+where+H+is+the+3me+endowment,+h+is+leisure+and+l+is+labor+supplied.+
+(a)+Set+up+the+maximiza3on+problem.++(b)+Find+the+op3mal+levels+of+c,+l,+and+h.++(c) +Show+me+a+graph+with+c+on+the+y"axis'and+h+on+the+x"axis'including+a+convex+u3lity+func3on+a+budget+constraint,+c*,+h*,+l*,+and+H.++(d) +Find+the+marginal+rate+of+subs3tu3on.+
Consump3on+and+Labor+:+Mirror+Image+
c+
l+
c*+
l+=+H+Y+h+c=+A+(H+–+h)+=+Al'
l=labor'h=leisure'
U3lity+is+increasing+this+way+
Wealth+(Income+effect)+
c+
l++++++++++l1+
c1+
+ +Income Effect: Income ++ +c+#; h #; l +
+++++++l2+
c2+
c+=+wl+x2++
c+=+wl+x1++
x1+
x2+parallel+shi[+
Wages:+Income+and+Subs3tu3on+Effects++
c+
l++++++++++l*+
c*+
Income Effect: # # Wage +++c+#; h #; l %Substitution Effect: # Wage +++c+#; h #; l +Overall+Effect: + + + Wage +++c+#; h ?#; l ? ++
c+=+w2l+x++
c+=+w1l+x++
Wages:+Income+and+Subs3tu3on+Effects++
c+
l+++l1++
c2+
Star3ng+at+Point+“A”+there+is+an+increase+in+the+wage+with+(w2>w1).++The+line+rotates+up+and+we+will+be+at+point+“C”.++We+can+isolate+the+subs3tu3on+effect+with+a+parallel+shi[+to+point+“B”.++The+subs3tu3on+effect+is+seen+from+“A”+to+“B”+++We+Isolate+the+Income+effect+looking+from+“B”+to+“C”. ++
c+=+w2l+x++
c+=+w1l+x++
+++++++++l2++
c1+
C+
A+
B+
Wages:+Income+and+Subs3tu3on+Effects++
• In+the+long+run,+the+Income+Effect+dominates,+however,+over+the+business+cycle,+the+Subs3tu3on+effect+dominates.+
• Let’s+look+at+the+empirics.+
Labor+Supply+and+Demand+
wR+
L+
LD+
LS+Look+at+LS+and+we+see+the+subs3tu3on+effect+domina3ng+at+the+Macro+level.+
wR++=++Real+Wage+
wR+++=++w/(Price+level)+
Labor+Demand+
• Y+=+AKαL1Yα+
• π+=+PyAKαL1Yα+–+wL+–+rK+– where+Py+is+the+price+of+the+output+good.+– r+is+the+rental+rate+of+capital.+
• MaxL+π+=+PyAKαL1Yα+–+wL+–+rK+– Suppose+K+is+fixed+in+the+short+run.+
• dπ/dL+=+(1Yα)PyAKαLYα+–+w+=+0+marginal+revenue+ marginal+cost+
Labor+Demand+
marg+rev,+marg+cost+
L+
w
L*+
marg+revenue+
marg+cost+
€
dπdL
= (1−α)PyAKαL−α − w = 0
LD* = K (1−α)PyAw
%
& ' (
) *
1α
Marginal Revenue = (1−α)PyAKα
Lα
Labor+Supply+:+Subs3tu3on+Effect+
wR+
L+
LD+
LS+
Should+actually+look+like+this.+
Income+Effect+Dominates+
Subs3tu3on+Effect+Dominates+
Exam+Review+
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