Question

Question 1
(show your solutions)

A. John earned $30 per hour (after taxation) in their job. Assume that John has no other sources of income or savings. Write down the equation of John’s consumption budget constraint (for a single working day). Using a model with consumption on the vertical axis and hours of free time on the horizontal axis, plot John’s budget constraint. Label all relevant elements of this diagram and state the value of the horizontal and vertical intercepts.

B. Now, add an indifference curve to the model you developed (A.) and label it IC1. This indifference curve should be at a utility maximising point and show John’s corresponding choice of consumption and hours of free time. As you have not been given any information regarding John’s preferences, state one assumption that you have made about John’s utility maximising choice and one assumption that you have made about the slope of John’s indifference curve.

Answer 1

(Question 1)

(A) John earned $30 per hour (after taxation) in their job. Hence, let us denote his wage as

w=$30

It is assumed that john has no other source of income or savings.

Now, let us denote John's hours of work or 'Labor' is denoted by 'L'. Also, his hours of free time or 'Leisure' is denoted by 'l'.

A single day gives 24 hours of time endowment to John.

Hence, L+l=24........(1)

Also, let John's Consumption is denoted by C and price of the Consumption good is P=1(say)

• Now, we will write down John's budget line below.

John's total expenditure on consumption goods is P.C and his total Labor income is w.L. As there is no other source of income and savings, hence

P.C=w.L

or, C=30×L {as P=1 and w=$30}

or, C=30.(24-l) {from (1)}

or, C+30.l = 720.........BL

Hence, John's budget constraint for a single working day is: C+30.l = 720.

• Now a model with consumption on the vertical axis and hours of free time or Lisure on the horizontal axis is plotted below.

The line cuts the horizontal axis at B and the vertical axis at A.

The value of the horizontal intercept(A): 24

The value of the vertical intercept(B): 720

Slope of the budget line is: -30

(B) Now, we added an indifference curve IC1 on John's budget line in the previous diagram above. John maximizes his utility at that point where the IC1 is tangent to his budget constraint.

Hence, in the diagram we can see John is maximizing utility at point E and the corresponding Consumption and Leisure is shows as C* and l* respectively.

• As we are not given any information about John's preferences, hence

✓ We assumed that, John is rationally choosing between Consumption and Leisure. John Chooses the optimal bundle where the Slope of IC1 equals the Slope of the budget line i.e.-30.

That's what we assumed for John's utility maximising choice.

✓ Also, we assumed that, John has convex indifference curves. Hence, to Consume one more unit, John needs to sacrifice a certain amount of Leisure as his labor income is constant. And more choice of Consumption and Leisure is better for John.

That's what we assumed for the slope of John's indifference curve.

Hope the solution is clear to you my friend.