Problems

How do you calculate national savings, public savings, and private savings in an economy?

National Savings = Private Savings + Public Savings; Private Savings = Y−T−C; Public Savings = T−G.

How much richer will the fast-growing country be after 10, 20, 50, and 100 years at 2% and 3% growth rates?

Use Future Value formula: Future Value=Present Value×(1+growth rate)time for each period.

How do you calculate the average annual growth rate of GDP over 20 years?

Use the formula: Growth Rate=(GDP Today/GDP 20 Years Ago)^(1/20)−1.

How long will it take for GDP to quadruple at a constant growth rate of 5%?

Use the Rule of 70: Time to Quadruple=log⁡(4)/log⁡(1.05).

What was GDP 15 years ago, given current GDP is $3 billion and a 2% growth rate?

Use the formula: GDP in the Past=Current GDP÷(1+growth rate)^time.

How do you decompose the GDP growth rate into contributions of technology, capital, and labor?

Derive using: Technology: dA/A; Capital: 0.3⋅dK/K; Labor: 0.7⋅dL/L.

If GDP grows at 2% per year, capital at 0.5%, and labor at 1%, what are the contributions to GDP growth?

Technology contribution: 2%−(0.5%×0.3)−(1%×0.7); Capital contribution: 0.5%×0.3; Labor contribution: 1%×0.7.

How would you compute the contributions of technology, capital, and labor to GDP growth without knowing α and β?

Estimate α and β using national accounts data for capital and labor shares.

How do you calculate real GDP growth from nominal GDP growth and inflation?

Real GDP growth = Nominal GDP growth - Inflation rate.

What is the formula to calculate returns to scale for a production function Y = AK?

Returns to scale = Sum of exponents in the production function.
Example: For Y = AK, returns to scale = 1, indicating constant returns to scale.

How do you derive the real wage for a representative firm?

Real wage = Marginal Product of Labor (MPL).
Example: For Y = AK^αL^β, MPL = αA(K^αL^(β-1)).