2. Suppose that the quantity theory of money holds. So, the equation of exchange holds for this economy and money demand (MD) is proportional to nominal income Further, assume that we are in a classical economy in which real output (Y) is fixed by supply- side factors at 10,000 units and the money supply (M,) is fixed at 8000 units. a) Suppose that individuals initially wish to hold a quantity of money balances equal to one-fifth of their nominal income i.e., k = 1/5. Use the money market equilibrium condition to determine the initial equilibrium price level for this economy. b) Now suppose that individuals in this economy increase their money demand and wish to hold money balances equal to one-fourth of their nominal income, i.e., k is now 1/4. With output fixed by supply-side factors at 10,000 units and money supply unchanged at 8000 units how does this increase in money demand affect the equilibrium price level? How would you explain this change in the equilibrium price level? c) Graphically illustrate your answers to parts (a) and (b) in an aggregate demand-aggregate supply graph. For the aggregate demand curve(s), explicitly indicate some of the (P,Y) combinations used to graph the curve(s) on your graph. Also indicate the initial and new equilibria.1. [42 points] Suppose that you have an iid random sample {Xi, Y} of three data points (X1, Yl) = (0, 0) ; (X2, Y2) = (2,3); (X3, Y3) = (4,3). (a) (2 point) Calculate the sample mean of X; and Yi. (b) (6 points) You run a simple linear regression of Y, on Xi. Calculate the OLS estimates of the slope and intercept. (c) (3 points) Calculate the predicted value and residuals for each of three data points. (d) (6 points) Calculate the TSS, ESS and SSR. (e) (4 points) Check whether TSS=ESS+SSR and interpret the equation. (f) (3 points) Calculate the R for the regression. (g) (3 points) Interpret R2 in words. (h) (4 points) Calculate the sample covariance between the residuals and Xi, which is defined in general as 1 Et-, (Xi - X)(ui - u), where n is the sample size and u; is the residual. (i) (4 points) Calculate the sample covariance between the residuals and predicted value, which is defined in general as I EL, (Yi - Y)(ui - u), where n is the sample size and Y; is the predicted value. (j) (4 points) Draw a graph to show (1) the three data points (2) the estimated regression line and (3) their residuals. (k) (3 points) Draw the point (X, Y) in the graph above and explain why the point (X, Y) is always on the regression line.1. Consider a competitive exchange economy with two consumers and two goods. Suppose that consumer i has initial endowments wi = (wj, w2), where w; > 0, i = 1, 2 and j = 1, 2. His preferences are given by the following utility function: U' = aln(x;) + (1 -a) In(x2), where 0