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.