Consider the simple static macroeconomic competitive equilibrium model introduced in the lecture, in which a representative consumer decides on consumption and leisure, and thus labor supply, a representative rm decides on labor demand and production, and the government has to respect a budget constraint. Suppose that government spending makes private rms more productive; for example, govern- ment spending on roads and bridges lowers the cost of transportation. This means that there are now two effects of government spending, the first being the effects discussed in lecture of increase in G and the second similar to the effects of an increase in nation's capital stock K. (a) Show that the equilibrium effects on consumption, hours worked, and output for an increase in government spending of this type. (Hint: consider income and substitution effects.)