Question

 

Q1 Take a typical worker, Jordan. Before the onset of COVID-19, Jordon earned $30 per hour (after taxation) in their job. Assume that Jordan has no other sources of income or savings. Write down the equation of Jordan’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 Jordan’s budget constraint. Label all relevant elements of this diagram and state the value of the horizontal and vertical intercepts.

Q2 Now, add an indifference curve to the model you developed in Q1 and label it IC1. This indifference curve should be at a utility maximising point and show Jordan’s corresponding choice of consumption and hours of free time. As you have not been given any information regarding Jordan’s preferences, state one assumption that you have made about Jordan’s utility maximising choice and one assumption that you have made about the slope of Jordan’s indifference curve.

Q3 The arrival of COVID-19 brought financial hardship for Jordan’s employer. As a result, Jordan has had their hourly wage cut by 20% (a common occurrence around the world at the moment). Write down a new equation for Jordan’s consumption budget constraint (for a single working day). Using the same model developed in Q1-Q2, plot Jordan’s new budget constraint. Clearly state the value of the horizontal and vertical intercepts. MACQUARIE BUSINESS SCHOOL Department of Economics

Q4 Now, add a second indifference curve to the model you developed in Q1-Q3 and label it IC2. This indifference curve should be at a new utility maximising point and show Jordan’s corresponding choice of consumption and hours of free time. State what has happened to Jordan’s choice of consumption and free time. What can be said about Jordan’s overall level of utility after the onset of COVID-19?

Q5 Using the model created in Q1-Q4, show the income effect, substitution effect and overall effect of Jordan’s wage decrease. Compare the relative size of the income and substitution effects shown on your model. What can be inferred about Jordan’s preferences for free time and consumption from this comparison?

Answer 1

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

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

If he decides to enojoy 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 Jordan 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 = opportuinty 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.

Jordan’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. Jordan's budget constraint has been plotted in figure 1.

Figure 1

Q2. Let the indifference curve be IC1 (see figure 2)

figure 2

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

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

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

Q3. Jordan has had their hourly wage cut by 20% due to COVID-19. Jordan's new wage = $30- 20% of $30 = $24

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

If he decides to enojoy 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 Jordan 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 = opportuinty 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.

Jordan’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. Jordan's new budget constraint has been plotted in red color in figure 3.

figure 3

Q4. the changes after drawing IC2 are shown in figure 4

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

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

E. Wage is the opportunity cost of leisure. As wage rate falls, it means the Opportunity cost of leisure has decreased. In a sense it means that leisure has become cheaper now. So substitution effect says that Jordan should increase the amount of leisure and he should decrease the amount of consumption.

On the other hand income effect induces Jordan to work more at a lower wage rate and consume less. This is because at a lower wage, income of person reduces and with decrease in income, demand for all normal goods falls. Since leisure can be assumed to be a normal good, with the decrease in wage rates, leisure should fall and work should increase.

In order to find substitution effect, use Hicksian approach. Use figure 5 as a reference. Give Jordan an amount of income such that he is able to just afford the level of utility (IC1) which he was getting at a when wage rate was high. Budget constraint is shown in light blue color in figure 5. Jordan now consumes at point e3 in the diagram where L3 is corresponding leisure hours. Since, the increase is leisure is just due to change in wage rate, shift from L1 to L3 is substitution effect.

Now, take the income back from him (so that budget constraint is now red line), he reaches L2. Since this change is entirely due to change in income, we say that it is income effect. Therefore, shift from L3 to L2 is income effect.

The total effect is substitution effect plus income effect. Total effect is change from L1 to L2.

Substitution effect induces Jordan to increase leisure and income effect compels him to reduce it. But the net effect is increase in leisure so it can be argued that substitution effect is powerful than income effect.

Since on decreasing wage rate (income), the consumption falls so it can be said to be a normal good. Similarly, on decreasing wage rate, number of hours worked falls, but lesiure increases, it can also be said to be a normal good.

Figure 5