Economics 102

Spring 2003

Quiz 4  (25 points)

L. Stone

 

1.  Using the Solow model, CAREFULLY and fully explain (a) how growth through capital deepening occurs, and (b) why it must eventually stop. You must use a graph to explain this, and you must label everything on your graph appropriately. (15 points)

 

 

 

Your graph must include the production function, savings function, and depreciation function. The vertical axis should be labeled Y, and the horizontal axis should be labeled K. At minimum, you must show, given some level of capital stock, the quantity of output, savings, and depreciation. See Appendix to Chapter 8.

Explanation: Growth through capital deepening occurs as long as savings exceeds depreciation. The difference between savings and depreciation is net investment, the addition to the capital stock in the next period. As long as net investment is positive, the capital stock will grow in the next period, and thus output will be higher.

However, savings grows at a decreasing rate (due to diminishing returns to capital) while depreciation grows at a (constant) linear rate. Thus, eventually, savings will just be sufficient to cover the depreciation of the existing capital stock, net investment will be zero, and growth through capital deepening will stop.

 

 

2.  Carefully explain the effect of an increase in the rate of depreciation on steady state capital stock and output.  Your answer should give some idea of how this would take place, and you may wish to draw a graph to support your answer.  (10 points)

 

If the economy is already at the steady state, when the rate of depreciation increases, S<D, and I <0.  Thus the capital stock must shrink, because there is not enough savings to cover depreciation, and as the capital stock shrinks, output falls, until we reach a lower steady state output.