Exercise 2. Government in the Solow model with human capital When we were setting up the basic Solow model in Chapter 3 we were careful to explain that the savings rate, s, in S, = sY, could be interpreted as s = (1- cP){1 - c9), where we now assume if= 0, and constant values for the private propensity to consume out of disposable income, cP, and for the spending share, c9, of government that balanced its budget each period. The model could thus be interpreted to include a government and obviously a government could be interpreted into the general Solow model considered in Chapter 5 in exactly the same way. This exercise asks you to show how government can be included in the model of this chapter.

Assume that the government always taxes all income by the constant rater, and in each period spends !he constant fraction sf, of the tax revenue on education and the remaining tax revenue on government consumption (thus balancing its budget each period and not investing in physical capital). What the government spends on education accumulates as human capital with the households.

Assume that out of their disposable incomes households invest the fractions~ in physical capital and the fraction sf.J in human capital. In all remaining respects the model is as in this chapter. Show that the model presented in this chapter can be interpreted to cover the case with a government if the parameters of the chapter are: sK = (1 - r) s~ and sH = s~ + (1 - r)sf.J.