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

In a closed economy, the output produced in an economy equals income. Each FNR is assumed to have an economy operating in isolation from the rest of the world under the closed economy assumption.

b) Solve for the steady state capital per worker for each of the two equilibria.

Substitute the production function into the equilibrium condition and then the parameter values . You may find the roots in the following manner: . By multiplying by 10 both sides and collecting terms, we determine that . This yields the values of the two steady states: and .

c) Solve for the steady state output per worker for each of the two equilibria.

d) Suppose that the federal government makes it a criminal offense for FNRs to hire lawyers to pursue land claims (based on actual legislation introduced in 1927). As a result, the transaction costs increase to

i. Briefly describe the transitional dynamics for each of the two FNRs.

The investment curve shifts down, which means that:

· at now . Consequently, capital per worker for the FNR with is decreasing until it converges to the new .

· at now . Consequently, capital per worker for the FNR with is perpetually declining.

ii. Briefly describe the impact on income per capita in the short-run and in the long-run for each of the two FNRs.

Due to the positive relationship between capital per worker and output per worker, the answers from the previous part imply that:

· at now . Consequently, income per worker for the FNR with is decreasing until it converges to the new .

· at now . Consequently, capital per worker for the FNR with is perpetually declining.

iii. Briefly describe the impact on the short-run and the long-run income disparities across the two FNRs.

The impact on income inequality in the short-run is ambiguous as income per capita for both FNRs is declining.

Income inequality in the long-run is increasing since the income per capita for the relatively more prosperous FNR stabilizes at the steady state , while the income per capita for the relatively less prosperous FNR keeps on declining.

Question 2

Consider a closed economy where the production function is given by for each of the following two cities, Toronto (T) and Oshawa (O), which differ with respect to their productivity: and . Both cities share the following parameters and . Suppose that is the size of the population/workforce and also that . In addition, you have access to the following actual data reported in Table 1.

Table 1

Source: Statistics Canada (2014)

a) Transform the production function into per worker terms to .

Divide both sides of by : and simplify to and further to and finally convert into per capita: .

Substitute into to obtain: .

b) Derive and then solve for the predicted long-run growth rate of capital per worker and of output per worker.

The long-term growth rate of capital is solved for in a similar manner:

Toronto:

Oshawa:

c) In a single graph in space, illustrate the predicted long-run growth performance of the Toronto and Oshawa.

d) Briefly describe the transitional dynamics and their impact on the short-run and the long-run income inequality between Toronto and Oshawa.

Toronto’s capital per worker is perpetually increasing, while Oshawa’s capital per worker is decreasing towards the steady state at .

As a result, both the short-run and the long-run the income inequality is increasing. However, once Oshawa converges to the steady state, the income inequality between Toronto and Oshawa will be decreasing at a slower rate as Oshawa’s income per capita is no longer declining.

e) Briefly explain whether the actual growth performance of Toronto and Oshawa from 2001 – 2009 is qualitatively consistent with the predictions of the model.

The predictions of the model are qualitatively consistent with the actual data as Toronto has a sustained positive growth rate, while Oshawa has a sustained negative one.

The increasing income inequality between the two cities is consistent with the concept of divergence in the Solow model with a linear production function.

Question 3

For Figure 3 below, answer the following questions.

a) Briefly describe and interpret the initial condition for the group of occupational task requirements (manual vs. non-manual).

The initial conditions indicates the composition of skill type of the 1970 -1974 immigration cohorts.

The general trend is:

· downward for non-routine cognitive and analytical skills,

· upward for manual routine and non-routine skills.

This implies that for people with the same educational attainment, e.g., competition of university, a smaller share of university graduates worked jobs that required non-routine cognitive and analytical skills and a larger share worked jobs that required manual routine and non-routine skills.

c) Briefly describe and interpret the type(s) of variability in the time trends for each of the two groups of occupational task requirements.

There is a structural break in the 1990s that increased the share of university graduates working non-routine cognitive, analytical and interactive skills at the expense of the manual routine and non-routine skills.

d) Briefly explain why Figure 3 conveys a different picture than the corresponding figure about the occupational task requirements provided in the lecture notes.

Both Figure 2 and 3 investigate the type of jobs that immigrants over time. Figure 2 explores this relationship by abstracting away from the completed schooling of the immigrants, Figure 3 takes this information into account.

e) Briefly explain what Figure 3 implies about:

i. the nature of the type of occupations immigrants take on in the context of increased skilled immigration,

Figure 3 indicates that for immigrants for the same level of education, a smaller share of the more recent cohorts of immigrants were working jobs with analytical and cognitive skills.

In contrast, Figure 2 indicates that a larger share of the more recent cohorts of immigrants were working jobs with analytical and cognitive skills.

ii. the consequences of the changing occupational distribution over time on raising the standard of living.

Figure 3 suggests that the additional training of immigrants after the reform is only partially utilized as a smaller share of the immigrants with completed higher education work jobs with analytical and cognitive tasks. This suggests that the human capital stock is not being fully utilized with an adverse impact on output and, in turn, income per capita.

Source: IRPP (2016)

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