Assorted Questions and Solutions on Economic Growth

Problem 61. Which of these statements is true of Thomas Robert Malthus's views on population growth? More than one of these answers may be possible.

(a) Malthus thought that war was a preventative check on population growth.
(b) Malthus thought that we should embrace the positive checks on population growth - such as diseases and famines - instead of attempting to eliminate them.
(c) Malthus fully anticipated modern technological growth and predicted catastrophic population growth despite improvements in technological productivity.
(d) Malthus believed that food production grew arithmetically, while population grew geometrically, in the absence of positive and/or preventative checks on population growth.
(e) Malthus encouraged population growth so that more geniuses might come about and invent life-enhancing technologies.
(f) Malthus thought that the foremost effect of increases in productivity would be that people would have more children.

Solution 61. The correct statements about Malthus's views are as follows:
(d): Malthus believed that food production grew arithmetically, while population grew geometrically, in the absence of positive and/or preventative checks on population growth.

(f): Malthus thought that the foremost effect of increases in productivity would be that people would have more children.

Problem 62. The developing country of Gricbaxlia has a current per capita GDP of $3400. Due to newly instituted free-market reforms, the annual continuously compounded per capita GDP growth rate in Gricbaxlia is expected to be 5% for the foreseeable future. How long will it take before the Gricbaxlian per capital GDP is $78000?

Solution 62. We use the formula Y = Xe^rt, where r is the annual growth rate, X is the initial GDP, Y is the desired level of GDP, and t is the time it takes for GDP to grow from X to Y. Here, t is our unknown, X = 3400, Y = 78000, r = 0.05.

We rearrange the formula Y = Xe^rt thus:

Y/X = e^rt; rt = ln(Y/X); t = ln(Y/X)/r = ln(78000/3400)/0.05 = t = 62.6586679 years

Problem 63. Which of these are ways in which the per capita GDP growth of a country can be permanently increased? More than one answer is possible

(a) Increase in the rate at which government prints money.
(b) Government subsidies to companies deemed to be acting in the "public interest."
(c) Improvements in technology, productivity, and the capital stock.
(d) A stimulus to aggregate demand due to an increase in spending by the government or the private sector.
(e) A decrease in the natural rate of unemployment due to the repeal of employment regulations.
(f) An increase in the labor force participation rate due to the repeal of policies that lead to large numbers of discouraged workers.

Solution 63. The following are ways in which per capita GDP growth can be permanently increased:
(c): Improvements in technology, productivity, and the capital stock.
(e): A decrease in the natural rate of unemployment due to the repeal of employment regulations.
(f): An increase in the labor force participation rate due to the repeal of policies that lead to large numbers of discouraged workers.

Problem 64. Total output in the country of Cobbland can be modeled by the following equation: Y = 750L^0.6K^0.4. At time T = 0, total labor in Cobbland was equal to 15, and total capital was equal to 50. By time T = 1, total labor has increased to 30, and total capital has increased to 60. What was the rate of output growth in Cobbland during that year?

Solution 64. Cobbland's output follows a Cobb-Douglas function, Y = AL^1-αK^α.

We need to find the output at T = 1, divide it by the output at T = 0 and subtract 1 to get the rate of growth.

At T = 0, output was Y = 750L^0.6K^0.4 = 750*15^0.650^0.4 = 18209.75156

At T = 1, output was Y = 750L^0.6K^0.4 = 750*30^0.660^0.4 = 29688.92799

Rate of output growth was 29688.92799/18209.75156 - 1 = 0.6303862189

Problem 65. In a Cobb-Douglas function Y = AL^1-αK^α, what is the name for the term A?

(a) Total product of capital
(b) Marginal product of capital
(c) Marginal product of labor
(d) Total factor productivity
(e) Marginal factor productivity
(f) Total product of labor
(g) Capital stock

Solution 65. A in a Cobb-Douglas function is called (d): Total factor productivity.

See Mr. Stolyarov's complete index of Intermediate Macroeconomics Problems and Solutions here.