Introductory Macroeconomics, Hilary Term 2024

Problem Set 1

  1. A data question. Find a website with international data on real GDP per person from 1950 to the present, expressed in a common currency. (The World Bank's World Development Indicators are an option. Or the Penn World Table. Or look at the Our World in Data website. Or the OECD database. There are more where these came from.) Pick at least five countries you are interested in, calculate their real GDP per person relative the the United States, and plot the resulting series. Comment on anything interesting you find. Have your countries converged towards the US?

  2. Two countries, Richland and Poorland, are described by the Solow model with exogenous population growth and technical progress. They have the same Cobb-Douglas production function F(K, L) = Kα(AL)1-α but with different quantities of capital and labour. Richland saves 32 per cent of its income, while Poorland saves 10 per cent. Richland has a population growth of 1 per cent per year, while Poorland has population growth of 3 per cent. Both nations experience technical progress at a rate of 2 per cent per year and depreciation at 5 per cent per year.

    1. What is the per effective worker production function f(k̃)?

    2. Solve for the ratio of Richland's steady-state income per worker to Poorland's.

    3. If the Cobb-Douglas parameter α takes the conventional value of about 1/3, how much higher should income per worker be in Richland compared to Poorland?

      4. (a - c are drawn from Mankiw & Taylor.)

    4. What is the ratio of the marginal product of capital in Richland to Poorland? Can this be an equilibrium in a globalised world?

  3. Use diagrams and plots of the paths of key variables over time to analyse what happens in the Solow model (with exogenous population growth and technical progress) in response to:

    1. A permanent increase in the rate of investment.

    2. Destruction of part of a nation's capital stock in a war.

    3. A steady increase in women's labour force participation over twenty years.

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