SUS OF ers, us, and a resentative consumer has preferences over bundles of consumption goods c, and leisure l, satisfying the standard properties: more is preferred to less; preference for diversity; normality. The consumer is endowed with an endowment of total hours h. The represen- tative firm faces a constant returns to scale production function Y = zF(K, Nd), where Y is output of consumption goods, z is TFP, K is physical capital, and Nd is labour 1 input. The amount of capital is assumed to be given and fixed. The firm is owned by the household, and as a result any real firm profits will be distributed to the consumer in the form of dividends, denoted II. 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) Define a competitive equilibrium for this economy. (b) Derive the production possibilities frontier and explain what its slope captures. (c) Show the competitive equilibrium on a carefully labeled graph, and explain what condition holds at that equilibrium. (d) Assuming that the economy is initially in equilibrium, suppose that there is a natural disaster that destroys half of the economy's capital stock. What will be the effects of this disaster on aggregate output, consumption, employment, and the real wage? Explain your results.
SUS OF ers, us, and a resentative consumer has preferences over bundles of consumption goods c, and leisure l, satisfying the standard properties: more is preferred to less; preference for diversity; normality. The consumer is endowed with an endowment of total hours h. The represen- tative firm faces a constant returns to scale production function Y = zF(K, Nd), where Y is output of consumption goods, z is TFP, K is physical capital, and Nd is labour 1 input. The amount of capital is assumed to be given and fixed. The firm is owned by the household, and as a result any real firm profits will be distributed to the consumer in the form of dividends, denoted II. 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) Define a competitive equilibrium for this economy. (b) Derive the production possibilities frontier and explain what its slope captures. (c) Show the competitive equilibrium on a carefully labeled graph, and explain what condition holds at that equilibrium. (d) Assuming that the economy is initially in equilibrium, suppose that there is a natural disaster that destroys half of the economy's capital stock. What will be the effects of this disaster on aggregate output, consumption, employment, and the real wage? Explain your results.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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can you please solve part c and d of this practice problem
Transcribed Image Text:6. Consider an economy that consists of consumers, firms, and a government. The rep-
resentative consumer has preferences over bundles of consumption goods c, and leisure
l, satisfying the standard properties: more is preferred to less; preference for diversity;
normality. The consumer is endowed with an endowment of total hours h. The represen-
tative firm faces a constant returns to scale production function Y = zF(K, Nd), where
Y is output of consumption goods, z is TFP, K is physical capital, and Nª is labour
1
input. The amount of capital is assumed to be given and fixed. The firm is owned by the
household, and as a result any real firm profits will be distributed to the consumer in the
form of dividends, denoted II. 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) Define a competitive equilibrium for this economy.
(b) Derive the production possibilities frontier and explain what its slope captures.
(c) Show the competitive equilibrium on a carefully labeled graph, and explain what
condition holds at that equilibrium.
(d) Assuming that the economy is initially in equilibrium, suppose that there is a natural
disaster that destroys half of the economy's capital stock. What will be the effects
of this disaster on aggregate output, consumption, employment, and the real wage?
Explain your results.
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