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**Unformatted text preview: **Page 1 of 8 THE UNIVERSITY OF TORONTO AT SCARBOROUGH Division of Management ECM B06S – Macroeconomic Theory and Policy: A Mathematical Approach TUTORIAL #1 - SOLUTIONS Q1. Exhibit: Quantity Consumed and Price of Good Base Year Later Year Price of Good A 100 200 Quantity of Good A 100 200 Price of Good B 100 100 Quantity of Good B 100 100 In the exhibit, the citizens of country XYZ come to desire more of good A. As a result the quantity and price of the good both rise. a) Compute nominal GDP in the base year and the later year. (Nominal GDP t ) = G P it C Q it where i = A or B and t = Base (t=0) or Later year t = Base Year (t=0), (Nominal GDP BASE YEAR ) = 100(100) + 100(100) = 20,000 t = Later Year, (Nominal GDP LATER YEAR ) = 200(200) + 100(100) = 50,000 b) Compute real GDP in the base and later years (in base-year prices). (Real GDP t ) = G P i0 C Q it where i = A or B and t = Base(t=0) or Later year t = Base Year (t=0), (Real GDP BASE YEAR ) = 100(100) + 100(100) = 20,000 t = Later Year, (Real GDP LATER YEAR ) = 100(200) + 100(100) = 30,000 Page 2 of 8 c) Compute the GDP deflator in the later year, using your answers to parts a and b. PGDP t = (Nominal GDP t )/(Real GDP t ) PGDP LATER YEAR = 50,000/30,000 = 5/3 = 1.67 d) Compute the Consumer Price Index (CPI) the fixed-weight price index for the later year, using the base-year quantities as weights. CPI t = ( G P it C Q i0 )/( G P i0 C Q i0 ) = (Nominal cost of basket)/(Real cost of basket) CPI LATER YEAR = [200(100) + 100(100) ]/{ 100(100) + 100(100) } = 30,000/20,000 = 3/2 = 1.50 ASIDE: By construction (1) CPI BASE YEAR = PGDP BASE YEAR = 1.00; and (2) Real GDP BASE YEAR = Nominal GDP BASE YEAR Q2. Suppose that a closed economy is described by the following set of equations (Note: Subscripts that read “BAR” refer to fixed values of variables): Y = Y BAR = F(K BAR ,L BAR ) = 2,400 , C = 250 + 0.75(Y - T) , I = I(r) = 400 - 10r , G = G BAR = 300 , and T = T BAR = 200 . a) Find the levels of saving, investment, income and the real interest rate consistent with equilibrium....

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