Chapter 19, Problem 6TY

1. In this question, assume all dollar units are real dollars in billions. For example, $100 means $100 billion. Argentina thinks it can find $105 of domestic investment projects with a marginal product of capital (MPK) equal to 10% (each $1 invested in year 0 pays off $0.10 in every later year). Assume a world real interest rate r*is 5%, and initial external wealth W (W in year -1) is 0. a. You find that the formula on the lecture slide: > r*, which means that a country will ΔΟ AK take on investment projects as long as the marginal product of capital (MPK) is at least as high as the real interest rate. Using this formula, answer if Argentina should conduct the project. b. If the projects are not done, GDP = Q = C = $200 in all years. Compute the present value of Q and C. c. If Argentina conducts the projects (investing $105), what is the present value of Q and C? d. If Argentina conducts the projects, what is the present value of C? Is Argentina better off with the investment?

2. Consider a world of two countries: Highland (H) and Lowland (L). Each country has an average output of 9 and desires to smooth consumption. All income takes the form of capital income and is fully consumed each period. Initially, there are two states of the world: Pandemic (P) and Flood (F) each occurring with 50% probability. Pandemic affects Highland and lowers the output there to 8, leaving Lowland unaffected with an output of 10. Flood affects Lowland and lowers the output there to 8, leaving Highland unaffected with an output of 10. a. Assume that households in each country own the entire capital stock of their own land. Fill in the numbers on the following table. Pandemic Highland's income Lowland's income Flood Variation about the mean b. Assume that each country owns 50% of the other country's capital. Fill in the numbers on the following table. Pandemic Flood Variation about the mean Highland's income Lowland's income c. Compare your answer to (a) and (b). Does…

3. This question explores IS and FX equilibria in a numerical example. a. The consumption function is C = 1.5 + 0.8(Y - T). What is the marginal propensity to consume (MPC)? What is the marginal propensity to save (MPS)? b. The trade balance is TB = 5 [1-()] - (0.2(Y-8). What is the marginal propensity to consume foreign goods (MPCF)? What is the marginal propensity to consume home goods(MPCH)? c. The investment function is I = 3 - 10i. What is investment when the interest rate is equal to 0.10=10%. d. Assume government spending is G. Add up the four components of demand and write down the expression for D. Make sure that you simplify the equation. e. Derive the equation for the good market equilibrium using Y = D.