2. Another issue facing millennials is the growing income and wealth inequality. We will use our model to understand the implications of this issue. A. Begin from the baseline preferences and endowments. Assume Xavier is wealthier than Yuri. Xavier has an endowment of 1100 pounds for each period (E1=E2=1100). Yuri has an endowment of only 900 pounds in each period (E1=E2=900). Note that each period's market supply is unchanged (1100 + 900 = 1000 + 1000 = = 2000). Determine the equilibrium interest rate. r = % B. Begin from the baseline preferences and endowments. Assume Yuri is wealthier than Xavier. Xavier has an endowment of only 900 pounds in each period (E1=E2=900). Yuri has an endowment of 1100 pounds for each period (E1=E2=1100). Note that each period's market supply is unchanged (1100 + 900 = 1000 + 1000 = 2000). Determine the equilibrium interest rate. r = % C. Begin from the baseline preferences and endowments. A third person named Zena joins our economy. Zena is very impatient with utility function 0.80 In(C1)+0.20 In(C2). However, Zena has no endowment and hence no wealth. Incorporate Zena into the market clearing equation and determine the equilibrium interest rate. r = % D. Explain how the wealth distribution and the real rate are connected. Write at least five sentences. We begin with an endowment economy like that discussed in the video. • Xavier's utility function is 0.51 In(C₁) + 0.49 In(C₂). He begins with an endowment of 1000 pounds for consumption today and 1000 pounds for tomorrow (E1-E2=1000). People consume three to five pounds of food daily, so 1,000 per year is reasonable. Well, at least it is a nice round number. • 0.51*(1000*P₁+1000*P₂) Xavier's demand: C₁ = C2 = P1 0.49* (1000*P₁+1000*P₂) P2 Yuri's utility function is 0.52 In(C₁) + 0.48 In (C₂). He starts with the identical endowment of 1000 pounds for consumption today and 1000 pounds for tomorrow (E1=E2=1000). Yuri's demand: C₁: 0.52*(1000 P1+1000*P₂) = P1 0.48*(1000*P₁+1000*P₂) C2 P2 • The first period market clearing equation is as follows. (0.51* (1000 P₁+1000*P2)) P1 + (0.52 * (1000 * P1+1000*P₂)) P1 = 1,000+ 1,000 = 2,000 Setting P₁=$1 then the market clearing condition becomes (0.51 * (1000+ 1000*P2)) + (0.52 * (1000 + 1000*P2)) = 2000 510+510*P2 + 520 + 520*P2 = 2000 10301030 P2 = 2000 1030 P2 2000-1030-970 P2 = 970 ≈ $0.9417 1030 • The real interest rate answers, "By how many percent more is a unit of food valued today than tomorrow?" r = real interest rate = (P1 - P2) P2 P1 = P2 - 10.06186 or 6.19%