Problem Set #3 ECN 101 SSI Modjtahedi Due: Thursday July 23, 2015 Question 1: Consider the following model a version of which you saw in Proem Set 2. An economy is described by the following model:

Page 1 of 3 Problem Set #3 ECN 101 SSI Modjtahedi Due: Thursday July 23, 2015 Question 1: Consider the following model a version of which you saw in Proem Set 2. An economy is described by the following model: 𝑌 = 𝐴𝐷 Goods market equilibrium 𝐴𝐷 = 𝐶 + 𝐼 + 𝐺̅ Aggregate demand 𝐶 = 𝐶̅+ 𝑐𝑌𝑑 Consumption function 𝑌𝑑 = 𝑌 − 𝑇𝐴 + 𝑇𝑅̅̅̅̅ Disposable income 𝑇𝐴 = 𝑡𝑌 Tax function 𝐼 = 𝐼 ̅− 100𝑖 Investment function 𝑀̅ 𝑃̅ = 2000 Supply of real balances 𝐿 = 0.20𝑌 − 60𝑖 Demand for real balances It is known that: 𝐼 ̅= 1700 𝐺̅= 2,500 𝑇𝑅̅̅̅̅ = 1,000 𝐶̅= 1,000 𝑐 = 0.80 𝑡 = 0.375 a) Find the equilibrium values of the real GDP and the interest rate. Show these in an IS-LM diagram fully labeled. b) Suppose that the Fed reduces the money supply and as a result the supply of real balances goes down to 1700 units. Find the immediate (overshooting) and ultimate equilibrium values of the interest rate. Show both the comparative static and transitional dynamic results in an IS-LM diagram. Provide an economic interpretation of the results. c) Suppose that the government reduces the tax rate to t = 0.25 in order to stimulate the economy. Find the new equilibrium values of the interest rate and real GDP (the answers may not be pretty, so use two decimal places). Show the results in an IS-LM diagram. Provide an economic interpretation of the results. Page 2 of 3 Question 2: Now assume that the price level is endogenous and that the money market can be characterized as follows: 𝑀̅ 𝑃 = 200,000 𝑃 𝐿 = 0.20𝑌 − 60𝑖 Assume that wages and prices are fully flexible (the classical case). a) Find the equation of the aggregate demand function. Give me a detailed economic interpretation of why it is downward sloping (the kind we discussed in the class). b) Assume that the potential level of GDP equals Y* = 11,200. Find the equilibrium values of P and i. c) Suppose that money supply increases by 10%. Find the new equilibrium values of P and i. d) Suppose the government increases its purchases by 250 units. Find the new equilibrium values of P and i. What will happen to I? Page 3 of 3 Question 3: The economy of a country is characterized by the following two functions: (𝑃 − 𝑃 𝑒 ) = 𝛾(𝑌 − 𝑌 ∗ ) 𝑆𝑅𝐴𝑆 𝑃 = 𝐴 − 𝐵 × 𝑌 𝐴𝐷 Note that the AD function is not quite realistic because it is linear. But a non-linear function such as the one in question 2 would significantly complicate the calculations. So let’s stick with this simple function. Assume the following: 𝑃 𝑒 = 100 𝑌 ∗ = 11,200 𝛾 = 0.10 𝐴 = 1220 𝐵 = 0.10 a) Is the economy currently in a state of long-run (classical) equilibrium? b) Assume that due to a reduction in consumer confidence aggregate demand is unexpectedly reduced so that we now have A = 1,185. Find the short-run and long-run P and Y. Show parts a and b in the same graph. c) In part b calculate the cyclical rate of unemployment when A = 1,185, assuming that Okun’s a = 0.50.

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