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(K, N^d), where Y is output of consumption goods, z is TFP, K is physical capital, and N^d is labour input.

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. 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. 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)).