please only help with g h i. Thanks
pts) The purpose of this problem is to improve your intuition for the market-clearing portion of a competitive equilibrium. You should have plenty of experience working with constrained optimization problems (parts a-c). Parts d-f have you connect these two constrained-optimization problems together, using a market-clearing condition. Finally, parts g-i are meant to get you thinking about what it means to borrow and save, by modifying the assumptions of the model Suppose we have an economy with two types of households: Minnesotans (M) and Wisconsinites (W). Both types live for two periods and have the same utility function and discount rates B E (0, 1), but may differ in their endowments and consumption allocation. There is an equal population of each type. The market clearing condition for the first period is cyr + ew = ya + yw, and likewise similar for the second period. There are no firms or government. The utility maximization problem for a household of type i e {M, W} is: max{log a + Blog c,} subject to at=+ Problems: (a) Define the competitive equilibrium in this economy. Make sure to specify all the relevant problems and conditions. For households, you may write out each type's problem seperately or write a single maximization problem indexed by i. (b) Solve for the intertemporal Euler equation for a household of type i. Set up the Lagrangian for a household, find the FOCs, and then combine them to get an expression about the Marginal Rate of Substitution between goods today and goods tomorrow.) (c) Solve for consumption allocations in period 1 and 2 for household of type i as functions of their income (y, y') and prices (r). (One way to do this is by combining a household's Euler Equation with their budget constraint.) (d) Suppose that the endowments are given by: (UM, VM) = (2, 1) and (yw, yw ) = (1, 2), and that S = 0.8 Use the households' Euler conditions and market clearing conditions to solve for the market-clearing interest rate in this economy. Each possible value for r will result in the two households making different consumption decisions. Almost every potential interest rate will have the households making decisions which are individually affordable, but societally impossible. Your job is to find the interest rate such that the individual decisions allow the market to clear. That is, what interest rate makes the aggregate consumption equal to aggregate income in each period?) (e) Substitute the market clearing interest rate back into your consumption functions from part (c) and solve for the equilibrium allocations. Which household is borrowing in the first period and which household is saving? What is the economic intuition for this? (f) Why does household M have higher consumption in each period? Explain. (g) Now suppose the Midwest opens up to trade with the rest of the world, and acts as a small open economy. The Midwest can now borrow and lend at the world interest rate rw = 0.5. How does the definition of competitive equilibrium change? "Two changes: The interest rate becomes erogenous. What other equation changes?) (h) Calculate the consumption allocations for consumers of each type in the small open economy. (i) What are the Net Exports for the Midwest in each period? (Hint: Y=C+1+G+NX, and there is no investment or government in this model, so Y = C + NX )
