(A) Given: C = 100 + 0.75Yd (where Yd = Y-T) I = 120-600i G = 200 T = 20 + 0.2Y Ms/P = 300 Md/P = 50+0.5Y-600i Where: C = Consumption Y = Income I = Investment G = Government spending T = Taxes i = interest rate Ms/P = RealMoney Supply Md/P = Real Demand for Money (a) Derive the IS and LM curves (10 Marks) (b) Obtain the equilibrium: i. Interest rate (5 Marks) ii. Income (3 marks) iii. and consumption (2 marks)
(a)
"Y = C+I+G"
"Y = 100 + 0.75(Y-20-0.2Y) + 120-600i + 200"
"Y = 420+0.6Y-15-600i"
"0.4Y = 405-600i"
"IS\\space curve : Y = 1012.5 - 1500i"
Money Demand = Money Supply,
"50+0.5Y-600i = 300"
"LM\\space curve : i =\\frac{(0.5Y-250)}{600}"
(b)
(i)
"i =\\frac{ (0.5Y-250)}{600}"
"i = 0.189"
Equilibrium interest rate : "i = 18.9\\%"
(ii)
Substituting value of i in IS curve equation, we get,
Substituting value of i in IS curve equation, we get,
"Y = 1012.5 - 1500 \\times \\frac{ (0.5Y-250)}{600}"
"Y = 1012.5 - 1.25Y + 625"
"2.25Y = 1637.5"
Equilibrium Income : "Y = 727.7"
"C = 100+0.75(Y-20-0.2Y)"
"C = 100+0.6Y-15"
Equilibrium Consumption : "C = 521.6"
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