solow model

(See attached file for full problem description with equations)

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The Classical Model

1. Consider an economy with the following production function:
,
where the subscript refers to values in year t. Assume that (i) in year t=0, government expenditure is G0=100; (ii) the labor supply curve is vertical, and N is fixed always at 1000; (iii) consumption satisfies the equation Ct=0.8Yt (note that consumption is assumed not to depend on the interest rate).

In class, we have always assumed that the capital stock is fixed. However, we have also seen that increased government expenditure crowds out investment and this may have adverse consequences for the future. This question asks you to explore these consequences.

Capital evolves over time according to the following equation:

,

where =0.1 is the capital depreciation rate. This equation says that the capital stock is increased over the previous period's stock by the amount of investment, but declines each year as a result of the 10% depreciation rate.

Assume that at time t=0, the capital stock is given by K0=1000 (that is, one can imagine that the values given above have been constant for some time). In year t=1 the government raises its expenditure in real terms from 100 to 102, and keeps it there for ten years. Then, in year t=11, the government drops its expenditure back down to 100. Use a spread sheet to plot the time paths of consumption, output, and investment for each year from t=0 to 50. What do you conclude about the persistence of the effects of changes in fiscal policy?

2. Consider a production function of the form:
.
If both capital and labor are paid their marginal product, what fraction of real national income is paid as wages to labor, and what fraction is paid to the owners of capital. How much profit is made by the representative firm? Using data about the shares of capital and labor that you can find in the lecture notes, what do you conclude is a reasonable value of  for the United States?