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

Substitute the production function into the equilibrium condition and then insert the parameter values to obtain:

Use the substitution and multiplying both sides by 10 gives:

The roots of the quadratic equation are determined from the formula:

Which are and .

This implies that 11.67 and

c) (2 pts.) Solve for the steady state output per worker, , for each of the two equilibria corresponding to .

d) (8 pts.) Briefly describe the transitional dynamics in response to the reduction in the transaction costs from to

Word limit for the entire part d): 100 words. The word limit does not apply to mathematical symbols or expressions. Penalties for non-compliance will be imposed.

i. (2 pts.) Briefly describe the transitional dynamics for each of the two FNRs.

The investment curve shifts up, which means that:

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

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

ii. (2 pts.) Briefly describe the impact on human capital per worker in the short-run and in the long-run for each of the two FNRs.

Human capital per worker in both FNRs is increasing in the short-run until they converge to the steady state .

Human capital per worker in both FNRs is increasing in the long-run remains unchanged at .

Human capital per worker in both FNRs is increasing in the short-run until they converge to the steady state .

Human capital per worker in both FNRs is increasing in the long-run remains unchanged at .

iv. (2 pts.) Briefly describe the impact on the short-run and the long-run income disparities across the two FNRs.

The income disparities across the two jurisdictions are decreasing in the short-run and are completely eliminated in the long-run once the two FNRs are at .

e) (8 pts.) In a single properly labeled graph in () space, illustrate the steady-state equilibria corresponding to and as well as transitional dynamics of the two FNRs.

f) (4 pts.) In a single graph, construct the Lorenz curves for the income inequality corresponding to and to in an imaginary jurisdiction consisting of only the two FNRs.

Note:

g) (4 pts.) Calculate the Gini coefficient for the income inequality corresponding to and for that corresponding to in an imaginary jurisdiction consisting only the two FNRs.

For ,

.

The Gini coefficient.

For , there is perfect income inequality. The Gini coefficient.

h) (4 pts.) The federal government is interested in evaluating the impact of signing treaties with FNRs. Calculate the range of values of , for which big push educational policies pursued by the federal government are no longer necessary for FNRs to escape the poverty trap.

This is the horizontal distance between whose numerical values are .

Question 2 (26 pts.)

Answer the following set of questions about Figure 1 in the Appendix found on p. 4 of the exam.

Word limit for the entire question: 400 words. Penalties for non-compliance will be imposed.

a) (8 pts.) Briefly describe and interpret the actual performance of Alberta with respect to:

i. (2 pts.) the initial condition.

Alberta’s GDP per capita was approx. 16 % higher than Canada’s in 1950. (Numbers between 15 and 20 % are accepted as correct.)

Alberta’s income per capita increased relative to Canada over the period 1950 – 2005.

iii. (4 pts.) the type(s) of variability observed in the time trend.

There was a structural break in 1972 when the trend of Alberta’s income per capita was closing in to Canada’s was reversed.

Alberta experienced cyclical fluctuations during the period that bounced around the trend prior to the structural break and around the new trend after the structural break.

b) (2 pts.) Briefly explain from the perspective of the Solow growth model why the shape of the steady state line is a straight horizontal line prior to 1972.

The horizontal steady state line indicates than Alberta’s steady state was unchanged between 1950 to 1972.

c) (2 pts.) Briefly interpret the numerical value of the initial condition of the steady state line.

The Alberta’s steady state income per capita was approximately 10 % higher than Canada’s in 1950.

d) (2 pts.) Briefly describe the phenomenon from the perspective of the Solow growth model that impacted the steady state line in 1972/73.

Alberta experienced a change in one or more of the parameters of the Solow model that resulted in Alberta converging to a new steady state value.

e) (2 pts.) Briefly explain whether the 1972/73 phenomenon is also captured by the analysis of sigma-convergence for the Canadian provinces.

Alberta (and other oil producing provinces) experienced an abrupt change relative to the non-oil-producing provinces with respect to their convergence behaviour in 1972/73. This abrupt change here is reflected in an upward shift of the steady state line.

f) (4 pts.) Briefly describe and interpret the predicted line from the perspective of the Solow growth model.

The predicted line indicates that until 1972 Alberta was converging to the steady state value of approx. 1.10 and afterwards it was converging to the steady state value of approx. 1.28.

g) (4 pts.) Briefly explain whether:

i. (2 pts.) in the short-run, Alberta’s income per capita is diverging from that of Canada.

No, Alberta is converging to its own steady state. That is, the relevant concept is conditional convergence, not divergence.

ii. (2 pts.) in the long-run, Alberta’s income per capita is diverging from that of Canada.

No, in the long run the approx. 28 % gap in the living standard between Alberta and Canada is sustained.

h) (2 pts.) Based on the information provided in Figure 1, briefly explain whether your analysis from parts a) – g) challenges the view that regional inequality in Canada has decreased over time.

The analysis challenges the view that regional inequality has decreased since Alberta has been following the reverse of what we observe for regional inequality in Canada as a whole.

APPENDIX

Figure 1: Alberta’s relative economic performance

Legend: The horizontal axis measures Year (e.g., 50 represents the year 1950). The vertical axis measures relative GDP per capita where Canada serves as the benchmark jurisdiction. Each of the three curves represent Alberta’s actual, predicted and steady state performance respectively.

Source: Coulombe (2000)

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