Consumption-leisure model - Lecture 10

Question 1

how do we set up the consumption-leisure model

Answer 1

Y axis- income per given time (year, week)

X axis- hours of leisure per given time (year, week)

T is all the time you have in the given time frame
T is the X intercept

from the origin to point L is the amount of leisure

T-L is the amount of work

w- wage rate
wT- is wage rate and all the time you have
wT the Y intercept

connect point wT and T and then we can find how much leisure a person gets for a given income- this is the budget constraint

income=Y=w(T-L)

Question 2

how would you explain indifference curves on the consumption-income model

Answer 2

draw the consumption-income model and the budget constraint.
plot a point on the budget constraint
at that point put the indifference curve

if there is another indifference curve past the original budget constraint it wouldn’t be possible as you cannot get more time

if there is an indifference curve shifted inwards it would show less utility and that the time allocation was wrong

Question 3

increase in wage rate consumption-leisure model how to draw and explanation

Answer 3

we would increase wT which would make the the budget constraint more steep

there would be a new indifference curve which would cross the new budget constraint
as there is more utility to operate at that point

1) there would be less leisure and more hours worked as the person can gain a higher income if the new point is to the left of the original point

2) there would be more leisure and less hours worked as the person has a high enough income to satisfy them so they need to work less hours
this point would be to the right of the original point

Question 4

income and subsitution effects for backwards bending labour supply wage increase

Answer 4

original budget constraint
increase in wages
budget constraint more steep
new indifference curve which is further than the original indifference curve
draw a tool parallel to the new budget constraint
make it a tangent to the original indifference curve

the difference between the original point where the indifference curve and the budget constraint cross and the point where the tool is a tangent to the indifference curve is the substitution effect

the difference between the tool tangent and the new budget constraint + indifference curve is the income effect