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ECON60411

Macroeconomics

Test 1

You have 30 minutes to complete this test.

The Solow growth model takes the saving rate, s, the population growth rate, n, the rate of technological progress, g, and the depreciation rate of capital, δ, as exogenous. There are two inputs in the model: capital, K, and effective labor, AL. Assume a Cobb-Douglas production function, so that total production is given by

Define k as the capital per effective worker, k ≡ K AL, and y as the output per effective worker, y ≡ Y AL.

1. Use the production function given above and derive explicitly the evolutionary equation for k. (You are asked to derive the equation. You will not get any credit by simply writing down the equation.)

(10 points)

2. Solve explicitly for the steady-state value of k, k*.

(10 points)

3. The elasticity of output per unit of effective labor on the balanced growth path, y*, with respect to the saving rate, s, is

while the elasticity of output per unit of effective labor on the balanced growth path, y*, with respect to the rate of population growth, n, is

Use the above two expressions to show whether it is differences in savings rates or differences in population growth rates across countries that have a quantitatively greater impact on differences in y*.

(10 points)