Consider an economy of population size P and with GDP 6. Suppose in a given time...

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Consider an economy of population size P and with GDP 6. Suppose in a given time period each household in this economy chooses to have = l()' children (assume a, and are strictly positive), and the population evolves according to PnP, where P' denotes tomorrows population size. (a) What is the economy's steady state population size, P**? (b) Consider the described economy in steady state. Now suppose a catastrophic event dimin- ishes the population by half. Compute the values that P and n* take in the short run and in the long run. Explain the short run and the long run evolution of P and n* intuitively. (c) Consider the described economy in steady state. Now suppose the economy's technology improves such that GDP doubles from to 20. Compute the values that P and n* take in the short run and in the long run. Explain the short run and the long run evolution of P and n* intuitively. Does the technology improvement lead to a long run increase in GDP? Does it lead to a long run increase in GDP per capita? Consider an economy of population size P and with GDP 6. Suppose in a given time period each household in this economy chooses to have = l()' children (assume a, and are strictly positive), and the population evolves according to PnP, where P' denotes tomorrows population size. (a) What is the economy's steady state population size, P**? (b) Consider the described economy in steady state. Now suppose a catastrophic event dimin- ishes the population by half. Compute the values that P and n* take in the short run and in the long run. Explain the short run and the long run evolution of P and n* intuitively. (c) Consider the described economy in steady state. Now suppose the economy's technology improves such that GDP doubles from to 20. Compute the values that P and n* take in the short run and in the long run. Explain the short run and the long run evolution of P and n* intuitively. Does the technology improvement lead to a long run increase in GDP? Does it lead to a long run increase in GDP per capita?