Econ 701/ Manopimoke Spring 2015 Homework 6 Econ 701 1

Econ 701/ Manopimoke Spring 2015 Homework 6 Econ 701 1. Suppose the US Congress enacts legislation that discourages saving and investment, such as the elimination of the investment tax credit that occurred in 1990. As a result, suppose the investment rate falls permanently from s’ to s’’. Examine this change in the Solow model with technological progress, assuming that the economy begins in steady state. Sketch a graph of how (the natural log) of output per worker evolves over time with and without the policy change. Make a similar graph for the growth rate of output per worker. Does the policy change permanently reduce the level or the growth rate of output per worker? 2. Consumption is equal to output minus investment. c=(1-­‐s)y. I n the context of the Solow model with no technological progress, what is the savings rate that maximizes steady-­‐state consumption per worker? What is the marginal product of capital in this steady state? Show this point in a Solow diagram. Be sure to draw the production function on the diagram, and show consumption and saving and a line indicating the marginal product of capital. Can we save too much? 3. The basic idea of solving dynamic models that contain a differential equation is to first write the model so that along a balanced growth path, some state variable is constant. In the model with technological progress, we used y/A and k/A as state variables. In the model with human capital, we used y/Ah and k/Ah. Recall, however, that h is a constant. This reasoning suggests that one should be able to solve the growth model to get the solution for y/Ah, k/Ah and y(t) in steady state using y/A and k/A as state variables. Show how to do this. 4. The Mankiw, Romer and Weil model that incorporates human capital differs slightly from the version of the extended Solow model that we have considered in class. The key difference is the treatment of human capital. More specifically, in the Mankiw, Romer and Weil model, human capital is accumulated just like physical capital, so that it is measured in units of output instead of years of time. Assume production is given by 𝑌 = 𝐾 ! 𝐻! (𝐴𝐿)!!!!! where α and β are constants between zero and one and whose sum is also between zero and one. Human capital is accumulated just like physical capital: 𝐻 = 𝑠! 𝑌 − 𝛿𝐻 Econ 701/ Manopimoke Spring 2015 where 𝑠! is the constant share of output invested in human capital. Assume that physical capital is accumulated as in: 𝐾 = 𝑠! 𝑌 − 𝛿𝐾 Also, the labor force grows at rate n and technological progress occurs at the rate g. Solve the model for the path of output per worker y = Y/L along the balanced growth path as a function of 𝑠! , 𝑠! , n, g, α and β. Discuss how the solution differs from: !
𝑠
!!!
!
𝑦!∗ =
ℎ𝐴 𝑡 . 𝑛+𝑔+𝛿
(Hint: Define state variables such as y/A, h/A, and k/A). 5. Suppose there is a one-­‐time increase in the productivity of research. What happens to the growth rate and the level of technology over time? Illustrate your answer using relevant graph(s) and explain your reasoning.