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(Solved): 4) Consider the following closed economy with a money supply targeting central bank: YCI(PM)d ...
4) Consider the following closed economy with a money supply targeting central bank: with and . (a) Solve the IS relation for , plot it in -space and explain the economic meaning of the IS relation. Solve the LM relation for , add it to the graph and explain the economic meaning of the LM relation. (b) For the given economy, calculate the equilibrium values of income , the nominal interest rate , investment , and the budget balance . (c) Calculate the equilibrium values of , and when the central bank increases the money supply to . Augment the graph from (6.4) (a) by adding the effects of this increase in money supply. (d) Assume now again that and that the government increases government spending by just before the next general election. Calculate the equilibrium values of and . Augment the graph from (6.4) (c) by adding the impact of this fiscal policy action.
e) The central bank fears that the measure in (d) could lead to "overheating" of the economy. The central bank therefore wants to consider policy measures to bring back equilibrium output from the value in (d) to the value from (b). Describe the corresponding policy action of the central bank and calculate the equilibrium values of and . Augment the graph from (6.4) (d) by adding the impact of this monetary policy action.
Expert Answer
(A) The IS relation is derived by equating aggregate demand to aggregate output in the goods market. In this economy, it can be expressed as: Y=C(Y ? T) + I(Y, i) +? where C(Y-T) is consumption, I(Y,i) is investment, and ? is government spending. By substituting the consumption and investment functions into the IS equation and solving for i, we get: Y= 2,000 - 2,000i This equation shows the negative relationship between income and the interest rate in the goods market, indicating that as income increases, the interest rate decreases, and vice versa. The IS curve can be plotted on a (Y,i) space as a downward sloping line.The LM relation, on the other hand, is derived from the money market equilibrium condition, where the demand for real money balances equals the supply of real money balances. It can be expressed as: (M/P)^d=2Y - 8,000i where (M/P)^d is the demand for real money balances, M is the nominal money supply, P is the price level, Y is income, and i is the nominal interest rate. Solving for i, we get: i=0.25Y - 0.00125(M/P)^d This equation shows the positive relationship between income and the interest rate in the money market, indicating that as income increases, the interest rate increases, and vice versa. The LM curve can also be plotted on a (Y,i) space as an upward sloping line.Final Answer:The LM curve can also be plotted on a (Y,i) space as an upward sloping line.