Import Multiplier Calcuation

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The Multiplier with imports We assume that countries are spending fixed % of their GDP on buying goods in other countries, e.g. on imports. Example. Suppose C = 200 + 0.5DI T = 100 Tr = 0 G = 100 I = 200 IM = 0.2Y X =300 Here IM = 0.2Y, which implies that 20% of GDP are spent on imports. Remember that DI = Y – T + Tr = Y – 100. Equilibrium on the demand side Y* solves the following equation Y = C + I + G + X – IM = 200 + 0.5(Y - 100) + 200 + 100 + 300 – 0.2Y Rearranging, we find Y* = (200 – 50 + 200 + 100 + 300) / (1 – (0.5 - 0.2)) = 1071 In general, Marginal Propensity to Import (MPI) is % of extra $1 of income that is spent on imports, e.g. suppose MPC = 0.9 and MPI = 0.1. This implies that C = 0.9DI + some constant and IM = 0.1Y. Out of each new dollar of income, $0.90 is spent, but of that $0.90, $0.10 is spent on foreign goods. So, Marginal Propensity to Consume Domestic Products MPC domestic = MPC - MPI = 0.90 - 0.10 = 0.8 only $ .80 of an extra $1 in income is spent on domestic goods. MPC domestic is the number we need to accurately calculate the multiplier Multiplier with imports = 1 / (1 – MPC domestic) = 1 / (1 - (MPC – MPI)) in our example, with MPI = .1: Multiplier with imports = 1 / ( 1- ( .9 - .1)) = 1 / (1- .8) = 1 / 0.2 = 5 Example from hw3 Suppose there are only two countries: the US and Mexico. Consider the following data: MPCMX = 0.4 (MPC in Mexico) MPIMX = 0.03 (so 3% of an additional $1 of income in Mexico is spent on the American goods)

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MPCUS = 0.6 (MPC in the US) MPIUS = 0.1 (so 10% of an additional $1 of income in the US is spent on the Mexican goods) a) Suppose Mexican government increases government spending by $1 billion. By how much does Mexican GDP grow? To solve this we use the Multiplier with imports. MMX = 1/(1 - (MPCMX - MPIMX)) = 1/(1-(0.4 – 0.03)) = 1.587 So in Mexico ΔY* = MMX · ΔG = 1.587 · $1 billion = $1.587 billion b) Calculate the increase in the American GDP induced by the increase in Mexican GDP. As we said...
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