Now set the rate of depreciation of human capital and the savings rate for human capital to the same values as those for physical capital. Does this change the rate of growth in equilibrium? Discuss what this changes about the predictions of the model and what it doesn’t change.

Problem set

2. Growth theory

a. Go to canvas and retrieve the file “Growth theory work sheet.xlsx”, and make a copy of it (so you can go back to the original version if something gets messed up).

b. Open the work sheet and find the column that contains the production function. Ignoring, for the moment the values of the parameters, whose version of the Solow model is this (assuming that 0<f+b<1 and both f and b are positive)? Is the production function increasing in each of its inputs? Does it display decreasing returns to each input? Does it display constant returns to scale?

c. Now look at the parameters of the model. What input has no effect on output? So, taking into account the values of the parameters, what version of the Solow model is this?

d. In the spread sheet graph IQTL as a function of time. What does the graph show?

e. With the parameters as they are, Is the initial value of IQTL greater than the equilibrium value or less than the equilibrium value? How can you tell? What is the equilibrium value? What is the rate of growth of output? What is the rate of growth of output per worker? How does this fit with what we learned in class about this model.

f. Given your estimate of the equilibrium value of IC/TL change the starting value of K so that IC/TL is greater than the equilibrium value. How does this change your graph from d?

g. Now double the savings rate for investment in physical capital. How does this change your results. (After you answer this question set it back to .1)

h. Now set the rate of depreciation of human capital and the savings rate for human capital to the same values as those for physical capital. Does this change the rate of growth in equilibrium? Discuss what this changes about the predictions of the model and what it doesn’t change.

i. Now try the following. Set the exponent on H to .7 so that 1-b-f = 0. What does this mean for the contribution of labor growth to output growth? Note the values of the rate of growth of Y and Y/L. Now double the savings rate on physical capital. What happens to the growth rate? Why is this different from the result in g?