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Answer to Question #44973 in Macroeconomics for Bob

Question #44973
Global Insight (GI) forecasting firm predicted that the Canadian economy will shrink by 1.4 percent on an annualized basis in the last quarter of 2008 and a further 1.2 percent in the first quarter of 2009. The firm sees substantial job losses as the recession takes hold.

a. a. What evidence does GI present to support the view that Canada had entered a recession?

b. Under what circumstances might the inflation rate not decrease during 2009?
Expert's answer
Assume that the production of commodity 1 uses 10 units of capital for each worker, so that K1 =10L1 , while the production of commodity 2
uses 2 units of capital for each worker, so that K2 =2L2 . The total supply of capital is 400 units and the total supply of labor is 100 units.
(a) Determine the amount of both inputs of production, that is, capital and labor, used in each commodity and the output levels.
According to the data above:
L1 + L2 = 100, K1 + K2 = 400.
As K1 =10L1 and K2 =2L2, so 10L1 + 2L2 = 400.
We have the system of equations:
L1 + L2 = 100
10L1 + 2L2 = 400
L2 = 100 - L1
10L1 + 200 - 2L1 = 400
L1 = 25, L2 = 75
So, K1 = 250, K2 = 150
So, the amounts of inputs for production of commodity 1 and 2 are (250;25) and (150;75).
(b) Now assume that the number of workers increases to 140 due to immigration, keeping total capital fixed at 400. Solve for the amount of capital and labor in
used in each commodity and for the output levels. 
Now we have another system:
L1 + L2 = 140
10L1 + 2L2 = 400
L2 = 140 - L1
10L1 + 280 - 2L1 = 400
L1 = 15, L2 = 125
So, K1 = 150, K2 = 250
So, the amounts of inputs for production of commodity 1 and 2 are (150;15) and (250;125).

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