Intermediate Macroeconomics Questions, due on April 29, 3:00pm (UTC+8)

The time trend is sloping upwards since the Gini coefficient has increased from 0.08 to 0.14. This means that the policies of the government are contributing to a larger reduction in inequality relative to the absence of government intervention.

c) Briefly describe and interpret the type(s) of variability in the time trend.

There two types of variability exhibited by the time trend: a structural break in the early 1990s and cyclical variability associated with recessions.

There is a structural break in the early 1990s since the slope of the time trend abruptly changes. The structural break in the early 1990s suggest that the role of government in reducing income inequality increased since the early 1990s and then declined afterwards.

There is a larger reduction in the Gini coefficient during recessions, which suggests that the government plays a more interventionist role in redistributing when the population is facing hardships (e.g., loss of employment).

d) Briefly explain whether Table 1 on p. 82 and Figure 2 on p. 111 respectively of the textbook provide conflicting evidence about changes in income inequality since the early 1980s.

Source: IRPP (2016)

Source: IRPP (2016)

Table 1 provides mixed evidence about changes in after-tax income inequality, which has been decreasing during the period 2000 – 2011 but not during the other subperiods. A decrease in after-tax income inequality occurs if the income of the lower quantiles rises faster than the income of upper quantiles.

In contrast, market income inequality has increased as only those in the highest income brackets (top decile) have been benefiting from economic growth.

e) Briefly explain how your findings from parts a) – c) help reconcile any discrepancies in part d).

The findings are consistent with one another as they examine two different types of income inequality (with or without the role of government). In addition, we must account for the increased role of government in redistributing income during the examined period.

Note: Table 1 on p. 82 and Figure 7 on p. 88 are found in "Trends in Income Inequality in Canada and Elsewhere" by Andrew Heisz. Figure 2 on p. 111 is found in "Who Are Canada’s Top 1 Percent?" by Thomas Lemieux and W. Craig Riddell.

Question 3

According to Statistics Canada (2019), the relative GDP per capita of Quebec is in 1950 and that of Ontario in the same year is, where the benchmark group is Canada. In addition, the average growth rate of Quebec is 2.1 % and that of Ontario is 1.9 %.

a) Briefly explain why the regional inequality between Ontario and Quebec will disappear at some point in the future under the assumption that the average growth rates remain unchanged.

Ontario has a higher initial income per capita than Quebec but is growing at a lower rate than Quebec. This implies that Quebec’s and Ontario’s income per capita will be equalized at some point in time.

b) Calculate how long it will take for the regional income inequality between Ontario and Quebec to be eliminated.

The equations governing income over time for Ontario and Quebec are given by:

What we know is that at some point in the future .

This implies that:

Now we have a single equation with one unknown .

Note: The answer is subject to rounding error in the magnitude of several years.

c) In 2010, Quebec’s relative GDP per capita has decreased to 85.6. Briefly explain whether such fact is compatible with Quebec’s positive average growth rate of 2.1 %.

The relative GDP per capita is measured relative to Canada’s GDP per capita, which assumes a value of 100 in every year.

If the (positive) growth rate of Quebec is lower relative to Canada’s, the relative GDP per capita of Quebec decreases in relation to Canada but it increases in absolute terms.

Question 4

Consider a closed economy, in which the production function is . Total national investment, is therefore determined by, . In addition, suppose that and . Suppose that two provinces – British Columbia (BC) and Manitoba (MB) – share all of the above characteristics but their differ with respect to their productivity: the productivity in BC is and that in MB, . In addition, suppose that and .

a) Convert the aggregate production function into the per worker production function. Do NOT skip steps.

Divide both sides of by : .

Collect exponents on the right-hand side: . This expression is also equal to .

Then use the relationship and to find .

BC:

Substitute the parameter values and the production function into the equation.

There are two steady states: and : and

MB:

Substitute the parameter values and the production function into the equation.

There are two steady states: and : .

c) Solve for the steady state output per worker and consumption for each of the two equilibria in each province.

British Columbia:

The production function implies that:

The consumption quantities are:

Manitoba:

The production function implies that:

The consumption quantities are:

d) In a single graph, illustrate the steady-state equilibria found in parts b) and c). Draw all relevant curves and carefully label your graph.

The construction of the graph is demonstrated in three layers.

First, determining the state through the savings and capital requirement functions for each province. Then, constructing the productions for each province. Third, inserting the initial conditions into the graphs and describing the pattern of regional inequality in the short-run and the long-run.

e) Briefly describe the changes to regional income inequality in the short-run (transitional dynamics to a steady state) and in the long-run (differences between steady states).

The regional income inequality first decreases and during some point in the transition to each province’s own steady state becomes completely eliminated. Then, regional income inequality increases during the transition to each province’s steady state. This is because the output (income) per worker of British Columbia declines and that of Manitoba increases.

Once each province reaches its steady state, the regional income inequality, persists.

f) Briefly explain whether the facts provided in this question conform with the empirical evidence provided in the lecture notes for the two provinces with respect to the initial conditions and the regional inequality in the short-run and in the long-run.

The initial conditions are incorrect. The graph by Olfert (2016) indicates that BC’s income per capita exceeds MB’s, while in the question this information is being reversed. See Figure 1 in the lecture notes on the Measurement of Economic Inequality.

Source: Olfert (2016)

Barring the initial conditions in 1980, the pattern of regional inequality between the two provinces is correct with respect to the fact that regional inequality first decreased and then it increased.

The growing gap between the two provinces is consistent with the argument of convergence to different steady states.

The sigma convergence analysis also supports the argument that the two provinces are in a transition to a steady state as opposed to in a steady state.

g) Briefly explain how the model in this question should be modified to conform with the empirical evidence provided in the lecture notes.

The following information in the question must be modified:

The initial conditions must be reversed, i.e., the output per worker in BC exceeds that in Manitoba in 1980.

Then, the model will be able to fully explain the pattern of regional income inequality between the two provinces since 1980.

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