Suppose that we have a standard real intertemporal model with investment. The country experiences a natural disaster and the current capital stock K is greatly reduced. In other words, suppose that the representative firm begins the current period with a lower capital stock K. It is still the case that the economy will last for only two periods. Assume that the marginal product of labor MPN is increasing in K as in Lecture Note 4.
1) Graphically show the impact of the natural disaster on the representative firm’s current demand for labor.
2) Graphically show how the changes to labor demand curve from Part (1) affects the output supply curve. Show how the current output Y and the real interest rate r is impacted due to this shift of the output supply curve.
3) The decrease in K increases investment by the firm, because the future marginal product of capital will be higher. Graphically show how this impacts the output demand curve.
4) Combining the movements of output supply curve from Part (2) and the output demand curve from Part (3), show what happens to r and Y by comparing before and after the natural disaster. [Hint: The direction of the change of r should be very clear, while how Y changes will be ambiguous.]
5) Based on what you know how r changes from Part (4), graphically show how the labor supply curve changes. Combining this with the labor demand curve shift from Part (1), how does the w and N change as the result of this natural disaster?