Suppose that government spending makes private firms more productive; for example, government 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 of an increase in G and the second being similar to the effects of an increase in the nation's capital stock K.

(a) Show that an increase in government spending that is productive in this fashion could increase welfare for the representative consumer.

(b) Show that the equilibrium effects on consumption and hours worked of an increase in government spending of this type are ambiguous but that output increases. You must consider income and substitution effects to show this.