第8章-修改后.ppt

The equation that appears above the graph is the equation of motion modified to allow for technological progress. There are minor differences between this and the Solow model graph from Chapter 7: Here, k and y are in “per effective worker” units rather than “per worker” units. The break-even investment line is a little bit steeper: at any given value of k, more investment is needed to keep k from falling - in particular, gk is needed. Otherwise, technological progress will cause k = K/LE to fall at rate g (because E in the denominator is growing at rate g). With this graph, we can do the same policy experiments as in Chapter 7. We can examine the effects of a change in the savings or population growth rates, and the analysis would be much the same. The main difference is that in the steady state, income per worker/capita is growing at rate g instead of being constant. Explanations: k is constant (has zero growth rate) by definition of the steady state y is constant because y = f(k) and k is constant To see why Y/L grows at rate g, note that the definition of y implies (Y/L) = yE. The growth rate of (Y/L) equals the growth rate of y plus that of E. In the steady state, y is constant while E grows at rate g. Y grows at rate g + n. To see this, note that Y = yEL = (yE)?L. The growth rate of Y equals the growth rate of (yE) plus that of L. We just saw that, in the steady state, the growth rate of (yE) equals g. And we assume that L grows at rate n. Remember: investment in the steady state, i*, equals break-even investment. If your students are comfortable with basic calculus, have them derive the condition that must be satisfied to be in the Golden Rule steady state. This section (this and the next couple of slides) presents a very clever and fairly simple analysis of the U.S. economy. When asked, students often have reasonable ideas of how to estimate MPK (look at stock market returns), n and g, but very few offer suggestions on how to