Department of Economics, Faculty of Economic and Management Sciences, University of Pretoria EKN 325 - Introductory Growth and Development Economics, 2019 Memorandum Answer all four questions below 1a) Making use of the basic Solow model model and capital accumulation equation kΛ = sy − (n + δ)k, compute the steady state output per worker, y ∗ , and explain why the Chinese government may have implemented the one-child policy in the late 1970s. [15 marks] I expect the student to compute the steady state, interpret the steady state and link to the one-child policy in China. π = π²πΆ π³π−πΆ (÷ π³) π = ππΆ [2 marks] In steady sate: πΜ = 0: 0 = π π¦ − (π + πΏ)π 0 = π π πΌ − (π + πΏ)π (π + πΏ)π = π π πΌ π π 1−πΌ = (π + πΏ) π π π∗ = ( )π−πΆ π+πΉ [5 marks] In steady state: π¦ = ππΌ πΆ π π∗ = ( )π−πΆ π+πΉ [3 marks] According to the Solow steady state, countries with higher levels of investment, low population growth rates and low rates of capital depreciation have higher incomes per worker. As such, increasing population growth reduces the capital per worker accumulation. [2 marks] The high population growth rate in China during the late 1970s may have contributed to the lower incomes per worker. The government was struggling to sustain the population levels. Therefore, the one-child policy was implemented for the purpose of reducing the rapid population growth rate so that the capital accumulation can increase and the population levels will become sustainable in the future. [3 marks] b) Nearly three decades later, China’s one-child policy was relaxed. Reconcile this decision with the economic implication1of the steady state output per worker in Romer’s endogenous growth model. [10 marks] I expect the students to show and explain the steady state in Romer’s model with production function stated, and link to relaxation of one-child policy. In Romer’s model, the production function is given as: which describes how capital stock (K) and labour (L) combine to produce output (Y) using the stock of ideas (A). [1 marks] In the steady state, output per worker is given as: [2 marks] According to Romer, economies that have higher rates of capital accumulation, higher levels of technology and low capital depreciation rates will be richer. However, Solow’s negative population growth effect on output per worker is countered in Romer’s model with the notion that technology is captured in ideas embedded in people. More populous economies have greater potential innovators with ideas. Therefore the more researchers, the more ideas, which increases the productivity of the economy. [2 marks] The one-child policy in China may have resulted in a slowdown of the productivity due to a shrinking labour force and lack of innovation (new ideas to increase technology and productivity) as there were fewer children being born. Spillover consequences included a growing proportion of elderly people that needed support from a depleted younger generation, putting strain on economy’s resources. (students can discuss other consequences, but need to link to them to less potential for ideas in economy and low productivity) [5 marks] 2a) Making use of the quantity-quality framework and diagram/s (provide necessary equations), illustrate and explain why population growth rises with income when income is low and falls at higher income levels. [15 marks] I expect students to explain the quantity-quality framework using necessary equations, as well as provide one or both of the diagrams below to answer the question. The quantity-quality framework theory is an economic description of family decisions regarding the number of children to have and the education they receive. The budget constraint is as follows: where the budget (y) depends on subsistence consumption (c), resources spent on 2 spent on educating children (E). children such as food and clothing (M) and amount The utility of the family is given as: π where utility (V) depends on number of kids (π = π π¦ ) in relation to resources available, and amount of education that each child has ( π’ = πΈ + Μ Μ Μ π’) in relation to resources and initial education that child may acquire outside of formal schooling (i.e. basic skills). Rewrite utility function as: Substitute the M with budget constraint: Solve utility function w.r.t education (E): [8 marks] Families will increase spending on education as incomes increase. This quantity-quality framework may explain the population transition dynamics observed in countries that are moving out of the Malthusian stagnation into sustained growth era. In the Malthusian period, there is an income effect. Population growth rises with income per capita. However with increasing technology (g), the incentive for education has risen such that families’ fertility decisions have shifted from quantity to quality of children (i.e. substitution effect between number of children and educating them). As such, population growth declines with rising income per capita. This dynamic is explained in the following diagram/s. [5 marks] [2 marks for any or both diagrams] 3 in terms of population growth and b) In your opinion, where is South Africa income transition dynamics? [10 marks] I expect students to know basic statistics about South Africa. It was discussed in class. South Africa exhibits a negative correlation between income per capita and population growth implying that the economy is transitioning from Malthusian stagnation into a sustained growth era. Population growth is decreasing as income per capita rises suggesting that a substitution effect is taking place as families trade number of children in favour of educating them. South Africa is currently among the countries with low fertility rates at 2-3 children. [10 marks] (students may also use a graph to illustrate correlation) 3) In the model of globalisation and trade, the output per worker along the balanced growth path is given by : a) Explain the steady state output in detail. [15 marks] I expect the students to explain each component in detail given the production function. The production function is given as: [2 marks] Where output is produced using capital stock(K), skilled labour (hL), as well as imported intermediate goods. [1 mark] According to the steady state: 4 Component 1 – Solow’s model (countries with higher levels of investment, technology and lower population growth and lower rates of capital depreciation will be richer). Component 2 – countries with skilled labour (human capital accumulation) to use the technology in the economies will be richer. Countries that also spend more time acquiring skills are better equipped to use the technology in the economy. Component 3 – countries that are open are able to import technologies to improve their productivity. However, it is a combination of having available technologies (domestic or imported) and the skills to use the technologies that will contribute to productivity. Component 4 – world technological frontier capturing technological change over time. As long as technology keeps progressing, growth in output per worker continues to rise. [3 marks each component] b) Reconcile the results with the Financial Times’ article on the current problem facing Germany’s small and medium sized manufacturing companies. [10 marks] I expect the students to link the benefits of having a skilled labour and open country to the problem facing Germany’s manufacturing sector as per the article. The article states that Germany’s small and medium-sized manufacturing companies are facing loss in production capacity due to skills shortages in the country. As a result of the country’s low population growth rates, they have been unable to fill the job vacancies available in the sector. This has resulted in a shrinking labour force and slowdown in economic performance. One of the government’s solution to deal with the skills shortage was to take advantage of the influx of refugees (e.g. Syrian refugees due to crisis) and absorb the skilled ones into the manufacturing sector. And even if the migrants were unskilled, Germany countered this by offering apprenticeship training. This solution is possible because Germany is an open country. If it had been a closed country, they would be struggling to address their skills shortage causing further delay in productivity to the manufacturing sector. Another solution was to increase the retirement age so that the manufacturing sector can retain the skilled workers to transfer knowledge to the young apprentices being hired. This relates to the technology diffusion highlighted in the model. [10 marks] 4a) Using the Solow model augmented with nonrenewable resources, compute the growth rate of output per worker along the balanced growth path and interpret the result. [15 marks] I expect the students to compute the steady state and explain result. The production function is given as: Where output is produced using capital stock (K), labour (L), technology (B) and energy input from nonrenewable resources. The total stock of energy remaining in the economy 5 depletes over time at the rate at which the nonrenewable resource is being used: Therefore the amount of energy used in production each period is: Dividing the production function by (π πΌ ) and substituting the energy (E): Taking the logs and derivatives of production function: where π = ππ΅ /(1 − πΌ) πππ πΎΜ = πΎ/(1 − πΌ). Along the balanced growth path, the growth rate of output per worker is: [10 marks] Faster population growth leads to increased pressure on finite resource stock, reducing per capita growth. An increase in the depletion rate (π πΈ ) reduces the long-run growth rate of the economy. Resources are used up more quickly, leaving a smaller resource stock and therefore lower output each period. [5 marks] b) Based on the results obtained above in (4a), reconcile with the empirical evidence on prices of finite resources, per capita energy use and air pollutants in the U.S. [10 marks] I expect students to explain that empirical evidence on prices of finite resources and air pollutants in US is contrary to what the model states. According to Solow’s model with nonrenewable resources, there is a delay in the growth of output due to the drag by population growth putting strain on land and finite resources such as coal and oil. The model therefore implies that we should observe an increase in the energy use of these finite resources and an increase in their prices (demand is higher than supply of finite resources). In addition, we should also observe increase in air pollution due to increased usage of these resources. However, the empirical evidence shows that while per capita energy use has increased over time, the prices of the nonrenewable resources are declining, as well as the air pollutants. One of the reasons to explain this contradictory evidence is the increase in technology which has assisted in producing cleaner and more efficient ways of using nonrenewable resources, as well as substituting nonrenewable resources for 6 energy. In addition, as incomes per renewable ones such as solar, wind and water capita continue to rise, pollution begins to fall as the economies find advanced ways to use resources. The Constant Elasticity of Substitution production function also explains the contradictory evidence, highlighting the possibility of substituting nonrenewable resources for renewable ones. [10 marks] 7