Consider an economy that consists of consumers, firms, and a government.

The representative consumer has preferences over bundles of consumption goods c, and

leisure `, satisfying the standard properties: more is preferred to less; preference for

diversity; normality. The consumer is endowed with total hours h. The representative

firm faces a constant returns to scale production function Y = zF(q(G) K, Nd

), where

Y is output of consumption goods, z is TFP, K is physical capital, and Nd

is labour

input, and q(G) is the productivity of capital that is a function of exogenous government

expenditures G. The amount of capital K is fixed. The firm is owned by the consumer,

and as a result any real firm profits will be distributed to the consumer in the form of

dividends, denoted . The government purchases a quantity G of consumption goods,

and finances them by taxing the representative consumer lump-sum. However, government expenditures G also affect positively the productivity of firms, i.e., q

0

(G) > 0. Let

T denote real taxes, and assume that the government balances its budget. Let the real

wage per hour worked in terms of the consumption good be w.

(a) Assuming that the economy is initially in equilibrium, suppose that there

is a negative shock that reduces the economy's productivity z. What will be the

effects of the decrease in z on aggregate output, consumption, employment, welfare,

and the real wage? Explain your results carefully. Are the effects on consumption,

employment, and real wages consistent with fluctuations in productivity being a

source of business cycles?

(b) Suppose now that in response to the negative productivity shock the

government raises expenditures G to boost the economy. Note, that in this economy

the increase in G will also affect the productivity of capital. What will be the effects

of the increase in G on aggregate output, consumption, employment, welfare, and

the real wage? Will the government policy response be effective in boosting the

economy? (Note: here you have to examine the effects of the increase in G in

combination with the decrease in z from part (a)).