Questions for Week 9 Flashcards
(18 cards)
What is a production function, and what does it describe?
A production function shows the relationship between inputs (capital and labour) and output in an economy, describing how changes in inputs affect the level of output.
What does it mean if a production function has constant returns to scale?
Constant returns to scale mean that if all inputs (capital and labour) are doubled, output also doubles.
This property is common in aggregate production functions, such as the Cobb-Douglas.
What is the Cobb-Douglas production function, and how does it demonstrate diminishing returns?
The Cobb-Douglas function is Y=AK^αL^(1−α), where A is total factor productivity (TFP). It shows diminishing returns to capital and labour individually, as increasing one input while holding the other constant yields progressively smaller increases in output.
How do you verify constant returns to scale in the Cobb-Douglas function?
To check, double both K and L in Y=AK^αL^(1−α). Since (2K)^α(2L)^(1−α)=2Y, the function exhibits constant returns to scale.
How is the per capita production function derived from the aggregate production function?
Divide both sides of the production function by L, yielding y=Ak^α, where y=Y/L (output per worker) and k=K/L (capital per worker). This function shows diminishing returns to capital per worker.
What happens to output per worker if the value of A (TFP) doubles?
The per capita production function shifts upward, resulting in higher output per worker for any given level of capital per worker.
What is growth accounting, and what is its purpose?
Growth accounting decomposes output growth into contributions from capital, labour, and TFP. It helps identify whether growth is driven by input accumulation or productivity improvements.
Write the growth accounting equation and explain each component.
The growth accounting equation is: ΔY/Y=ΔA/A+αΔK/K+(1−α)ΔL/L, where:
ΔY/Y = output growth rate,
ΔA/A = TFP growth rate,
α and 1−α = income shares of capital and labour, respectively.
In an economy where output grows at 3.5%, and both capital and labour grow at 2%, with labour’s share of income as 75%, what is the TFP growth rate?
Using growth accounting: ΔA/A=3.5%−[0.25(2%)+0.75(2%)]=1.5%.
What is the contribution of capital and labour to growth in this example?
Capital’s contribution is 0.25×2%=0.5% and labour’s contribution is 0.75×2%=1.5%.
What is the concept of diminishing returns in the context of economic growth?
Diminishing returns imply that as additional units of a single input (e.g., capital) are added, holding other inputs constant, each additional unit produces progressively less additional output.
How does diminishing returns affect long-term growth?
It limits the growth impact of increasing one input alone. Sustained long-term growth generally requires improvements in TFP or balanced increases in multiple inputs.
How does economic growth affect living standards over time?
Economic growth increases GDP per capita, raising average income and improving living standards. Sustained growth is essential for poverty reduction and higher living standards in the long run.
What is the rule of 70, and how is it used?
The rule of 70 estimates the doubling time of an economy’s output at a constant growth rate.
Doubling time = 70 / growth rate.
Richland has a GDP per capita of $10,000 growing at 1% annually, and Poorland has $5,000 growing at 3%. How do their incomes compare after 10 and 20 years?
After 10 years, Richland’s income = 10,000×(1.01)^10=11,046 and Poorland’s income = 5,000×(1.03)^10=6,720. After 20 years, Richland = $12,202, Poorland = $9,031.
How long will it take Poorland to catch up to Richland?
Solving 5,000×(1.03)^t=10,000×(1.01)^t, Poorland catches up in approximately 35-36 years.
Which policy is likely to raise long-term living standards: increasing home buyer assistance, expanding higher education, or boosting money supply?
Expanding higher education raises human capital and TFP, leading to sustained growth. Increasing consumption or money supply affects short-term AD but has limited long-term growth effects.
How does an aging population impact economic growth?
An aging population reduces the labour force share, potentially slowing growth unless offset by productivity gains or increased labour participation among older demographics.
