Economics

1: Discuss whether the following statements are true or false. (a) The Harrod-Domar model states that a country's per capita growth rate depends on its rate of savings, whereas the Solow model states that it does not. (b) According to the Harrod-Domar model, if the capital-output ratio in a country is high, that country will grow faster. (c) To understand if there is convergence in the world economy, we must study countries that are currently rich. (d) Middle-income countries are more likely to change their relative position in world rankings of GNP than poor or rich countries. (e) In the Solow model, a change in the population growth rate has no effect on the long-run rate of per capita growth. (f) In the Solow model, output per head goes down as capital per head increases, because of diminishing returns. 2: Consider the Solow model with a production function , where is a fixed technological parameter. Explicitly solve for the value of the per capita capital stock and per capital income. How do these values change in response to a rise in (a) the technological parameter , (b) the rate of saving , (c) , (d) , the depreciation rate, and (e) the population growth rate ? 3: Complementarities arise in all sorts of situations. Here is a tax evasion problem. Suppose that each of citizens in a country needs to pay a tax of every year to the government. Each citizen may decide to pay or to evade the tax. If an evader is nabbed, the law of the country stipulates payment of a fine of mount , where. However, the government's vigilance is not perfect, because it has limited resources to detect evaders. Assume that out of all the people who evade taxes, the government has the capacity to catch only one, and this person is chosen randomly. Thus, if people have decided to evade taxes, each has probability of being caught. In what follows, we assume that people simply calculate the expected losses from each strategy and choose the strategy with the lower expected loss. (a) If the number of evaders is , show that the average (expected) loss to an evader is. This is to be compared with the sure loss faced by someone who complies, which is. (b) Why is this situation like a coordination game? Describe the complementarity created by one citizen's actions. (c) Show that it is always an equilibrium for nobody in society to evade taxes. Is there another equilibrium as well? Find it and describe when it will exist. 4: Draw Lorenz curves and calculate the Gini coefficient and the coefficient of variation for the income distribution: (100, 200, 300, 400); (50, 25, 75, 25). The first set of numbers represents the various incomes, whereas the second set of numbers represents the number of people earning each of these incomes.