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+