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Chapter 4: Classic Theories of Economic...
Graphing and Quantitative Exercises

  1. Consider the Harrod-Domar model. Suppose that initially, a developing country's capital-output ratio (k) is 5, and the savings rate (s) is 12%.
    1. What will be the initial GDP growth rate?
    2. Suppose that technological advances cause the capital-output ratio to fall to 4. How will this affect the GDP growth rate?
    3. Starting again from the initial situation, suppose instead that the national savings rate is increased to 15%. How will this affect the GDP growth rate?
    4. What does the Harrod-Domar model tell us about the sources of economic growth?

  2. Consider Figure 4.1 in the Todaro-Smith textbook. Draw a single graph with real wage in the modern sector (MPLM) on the vertical axis, and quantity of modern sector labor (QLM) on the horizontal axis. Draw a labor supply curve that is initially perfectly elastic (i.e., horizontal) but that becomes steeply and positively sloped at a certain point. Draw a single downward-sloping labor demand curve that intersect the perfectly elastic portion of the labor supply curve.
    1. What area represents total modern sector output? What areas represent share of output paid to laborers in the form of wages and the share of output paid to capitalists?
    2. Suppose reinvestment of profits causes an increased demand for labor in the modern sector. Draw a new labor demand curve to the right of the original curve, but still intersecting the perfectly elastic portion of the labor supply curve. What happens to total output and to the returns paid to laborers and capitalists?
    3. Suppose now that further reinvestment of profits causes an increased demand for labor in the modern sector. However, all surplus labor has already migrated to the modern sector, so the new labor demand curve will now intersect the steep portion of the labor supply curve. What happens to total output and to the returns paid to laborers and capitalists?

  3. Consider a Solow growth model with the following production function:

    Y = K0.5(AL)0.5

    where Y is output, K is the capital stock, L is labor, and A is a measure of labor productivity. If A = 2, L = 20,000, and K = 400, what is output?

  4. Consider again the Solow growth model and the following production function:

    Y = K0.3(AL)0.7

    1. If A = 2, L = 20,000, and K = 400, what is output?
    2. Suppose the labor force grows by 5% so that it is now 21,000. By how much does output increase?
    3. Starting again with the conditions in part a, what is capital increases by 5%, so that it is now 420. By how much does output increase?

  5. Draw a graph similar to Figure A4.1 in the textbook. Specifically, graph output per worker, y, on the vertical axis, and capital stock per worker, k, on the horizontal. Draw in the production function y = f(k), the investment function s·f(k), and the straight line that has slope equal to (n + )·k.
    1. What is a steady-state equilibrium? Mark the steady-state equilibrium on your graph as k1*.
    2. Suppose many years of hard work in population policy is finally paying off such that the population growth rate falls to n2. Mark the new steady-state equilibrium on your graph as k2*. Explain in words what has happened to this economy.

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