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 ,3 E {0,1}, but may diiTer in their endowments and consumption allocation. There is an equal population of each type. The market clearing condition for the rst period is end + cw 2 3m + yw, and likewise similar for the second period. There are no rms or government. The utility maximization problem for a household of type 1' E {1141: Hf} is: Hmeesaa-hed} -.'.'.' IE1 subject to _ a __ e '*+1+-r_i'"'+1+l~ 'roblems: {a} Dene 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 t. {b} Solve for the intertemporal Euler equation for a household of type 1i. {Set up the Lagrangian for a household, nd the F003, and then comb-inc them to get an eapreeeton about the Marginal Rate of Suhst-itution between. goods today and goods tolrnonr-a-nruyI [c] Solve for consumption allocations in period 1 and 2 for household of type t as [mictions of their income [gt-,yg} and prices {r} {d} Suppose that the endowments are given by: (gm. Flu} = {2:1} and (my, yin; = {1: 2}: and that 33 = 113 Use the households' Euler conditions and market clearing conditions to solve for the marketclearing interest rate in this economy. (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 rst 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