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3 (15 marks) Desired consumption and investment are C# = 3600 -2000r +0.1: 14 = 1200-4000r. As usual, Y is output and r is the real interest rate. Government purchases G are 1200. a) Find an equation relating desired national saving S\" to r and Y. b) What value of the real interest rate clears the good market when Y = 6000? Use both forms of the goods market equilibrium condition. What value of the real interest rate clears the goods market when Y = 6400? Graph the IS curve. c) Government purchases rise to 1320. How does this increase change the equation for national saving in part (a)? What value of the real interest rate clears the goods market when Y= 6000? Use both forms of the goods market equilibrium condition. How is the JS curve affected by the increase in G? Answer: a S?=Y- c?-G=Y (3600 2000r + 0.1 ) 1200 =4800 + 2000r + 0.9Y. b. (1) Using the equation that goods supplied equals goods demanded gives Y = Ci+P+G = (3600 2000r + 0.1Y) + (1200 4000r) + 1200 = 6000 6000r + 0.1Y. So 0.9Y = 6000 6000r. At full employment, Y = 6000. Solving 0.9 x 6000 = 6000 6000r, we getr=0.10. (2) Using the equivalent equation that desired saving equals desired investment gives st 4800 + 20007 + 0.9Y = 1200 4000r 0.9Y = 6000 6000r When Y= 6000, r = 0.10. So we can use either equation to get the same result. When Y= 6400, we get r = .04. c. When G = 1320, desired saving becomes S# = 4920 + 2000r + 0.9Y. S# is now 120 less for any given r and Y; this shows up as a shift in the S\" line from S' to S' in Fig. 9.15. Setting =I" we get 4920 + 2000r + 0.9= 1200 4000r 6000r + 0.9= 6120. At Y= 6000, this is 6000r = 6120 (0.9 x 6000) = 720, so r = 0.12. The market- clearing real interest rate increases from 0.10 to 0.12