SOLOW’S MODEL Consider following information from China and New Zealand in table: China New Zealand Real per capita GDP growth, 2012-2019 (average %) 6.5% 1.6% Real GDP per capita, 2012 (in constant 2017 USD) 11,169 32,989 Real GDP per capita, 2019 (in constant 2017 USD) 16,655 45,555 Average savings rate, 2012-2019 (% of real GDP) 43.7% 21.4% Capital stock, 2019 (in millions of constant 2017 USD) 14,283,969 409,160 Population (in millions) 1,434 4.8 Population growth (in %) 0.5% 1% Capital depreciation rate (in %) 3% 3% Production function in both economies has following functional form: Yt = A* K1/3 * L2/3 Where Yt denotes aggregate GDP in period t, Kt is aggregate capital stock, Lt is employment (assumed equal for whole population) and A is total factor productivity. Using information provided in table, explain from SOLOW MODEL perspective what factors could explain differences in average GDP per capita growth between China and New Zealand between 2012 and 2019. Assume in this case that both countries have SAME RATE of TECHNOLOGICAL PROGRESS. Are data consistent with CONVERGENCE HYPOTHESIS for per capita income? Explain Find for each of countries level of capital stock per capita (k) and output (Y) as well as total factor productivity (A) in 2019.

ENGR.ECONOMIC ANALYSIS

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SOLOW’S MODEL

Consider following information from China and New Zealand in table:

	China	New Zealand
Real per capita GDP growth, 2012-2019 (average %)	6.5%	1.6%
Real GDP per capita, 2012 (in constant 2017 USD)	11,169	32,989
Real GDP per capita, 2019 (in constant 2017 USD)	16,655	45,555
Average savings rate, 2012-2019 (% of real GDP)	43.7%	21.4%
Capital stock, 2019 (in millions of constant 2017 USD)	14,283,969	409,160
Population (in millions)	1,434	4.8
Population growth (in %)	0.5%	1%
Capital depreciation rate (in %)	3%	3%

Production function in both economies has following functional form:

Y_t = A* K^1/3* L^2/3

Where Y_t denotes aggregate GDP in period t, K_t is aggregate capital stock, L_t is employment (assumed equal for whole population) and A is total factor productivity.

Using information provided in table, explain from SOLOW MODEL perspective what factors could explain differences in average GDP per capita growth between China and New Zealand between 2012 and 2019. Assume in this case that both countries have SAME RATE of TECHNOLOGICAL PROGRESS.
Are data consistent with CONVERGENCE HYPOTHESIS for per capita income? Explain
Find for each of countries level of capital stock per capita (k) and output (Y) as well as total factor productivity (A) in 2019.
Find capital stock (k), output (y) and consumption (c) per capita in STATIONARY STATE. Assume that total factor productivity (A) remains fixed at its 2019 level for each country.
Find GOLD RULE levels of capital stock (k*), output (y*) and per capita consumption (c*).
Assume now that each country decides to apply GOLD RULE SAVINGS RATE. Will welfare increase or decrease after they switch from savings rate in effect in 2019 to GOLD RULE RATE? Calculate per capita consumption (c) that each economy would have achieved if it had applied GOLD RULE SAVINGS RATE.

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Step 1: Define solow growth model

A solow growth model or exogeneous growth model is an economic model of long run growth. It explains long run growth by capital accumulation measurement , labor and population growth and increase in productivity driven by technological progress

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