Question

QUESTION 1:

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.

QUESTION 2:

A. The arrival of COVID-19 brought financial hardship for John’s employer. As a result, John has had their hourly wage cut by 20%. Write down a new equation for John’s consumption budget constraint (for a single working day). Using the same model developed in Question 1, plot John’s new budget constraint. Clearly state the value of the horizontal and vertical intercepts.

B. Now, add a second indifference curve to the model you developed in Q1 and Q2.A and label it IC2. This indifference curve should be at a new utility maximising point and show John’s corresponding choice of consumption and hours of free time. State what has happened to John’s choice of consumption and free time. What can be said about John’s overall level of utility after the onset of COVID-19?

Answer 1

Q1.A) In a day there are 24 hours which John can allocate between working and enjoying free time.

While he works, John earns $30 per hour. So, given that John has no other sources of income or savings, the maximum income that he can have in a day is when he works continuously for 24 hours. In that case, John's income = 24*$30 = $720.

If he decides to enjoy entire day, then he would get 24 hours of leisure and $0 consumption. Hence, the x-intercept is 24 hours.

Price of leisure can be measured by taking into consideration the opportunity cost of leisure. When John indulges in 1 hour of leisure, he foregoes $30 (which he would have earned by working the same hour). Hence, opportunity cost of leisure = $30. So, price of leisure = opportunity cost = $30.

Let price of consumption be p2. If he spends 24 hours working, then he can get $720/p2 units of consumption. Hence, y-intercept = $720/p2.

John’s consumption budget constraint (for a single working day)

price of consumption * units of consumption + price of leisure * units of leisure = income

p2C + w r = 720

p2 * C + 30 * r = 720

Where p2 = price of consumption

C = consumption

w = price of leisure = $30

r = units of leisure

Plot consumption on y-axis and hours of free time on x-axis. John's budget constraint has been plotted in figure 1.

figure 1

Q1.B) Let the indifference curve be IC1 (see figure 2)

figure 2

one assumption that about John’s utility maximizing choice: The optimal combination of leisure and consumption puts John on the highest level of utility that he can attain, given his income.

one assumption that you have made about the slope of John’s indifference curve: averages are preferred over extremes: if John is consuming more, then he is willing to substitute more of consumption so as to gain an additional unit of free time. Similarly, if John is having more leisure time, then he is willing to substitute more of leisure so as to gain an additional unit of consumption.

John’s corresponding choice of consumption on utility maximizing point is C1 and hours of free time is L1.

Q2.A). John has had their hourly wage cut by 20% due to COVID-19. John's new wage = $30- 20% of $30 = $24

While he works, John earns $24 per hour. So, given that John has no other sources of income or savings, the maximum income that he can have in a day is when he works continuously for 24 hours. In that case, John's income = 24*$24 = $576.

If he decides to enjoy entire day, then he would get 24 hours of leisure and $0 consumption. Hence, the x-intercept is 24 hours. X-intercept remains the same because the number of hours in a day has not changed.

Price of leisure can be measured by taking into consideration the opportunity cost of leisure. When John indulges in 1 hour of leisure, he foregoes $24 (which he would have earned by working the same hour). Hence, opportunity cost of leisure = $24. So, price of leisure = Opportunity cost = $24.

Let price of consumption be p2. If he spends 24 hours working, then he can get $576/p2 units of consumption. Hence, y-intercept = $576/p2.

John’s consumption budget constraint (for a single working day).

price of consumption * units of consumption + price of leisure * units of leisure = income

p2C + w r = 576

p2 * C + 24 * r = 576

Where p2 = price of consumption

C = consumption

w = price of leisure = $24

r = units of leisure

Plot consumption on y-axis and hours of free time on x-axis. John's new budget constraint has been plotted in red color in figure 3.

figure 3

Q2.B) the changes after drawing IC2 are shown in figure 4

John’s corresponding choice of consumption at new utility maximizing point is C2 and hours of free time is L2. John decided to consume less and enjoy more.

John’s overall level of utility after the onset of COVID-19 has appeared to fall because he is now consuming at a lower level of utility (IC2) as compared to before.