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26 November, 10:50

An economy has full-employment output of 5000. Government purchases are 1000. Desired consumption and desired investment are given by:

Cd = 3600 - 2000r + 0.10Y

Id = 1200 - 4000r

Where Y is output and r is the expected real interest rate:

(a) Find the real interest rate that clears the goods market. Assume that output equals full-employment output.

(b) Calculate the amount of saving, investment, and consumption in equilibrium.

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  1. 26 November, 10:57
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    a. real interest rate is 0.217 or 21.7%.

    b. saving = 134, investment is 332, consumption is 3666.

    Explanation:

    a) Y = Cd + Id + Gd

    Where Y = output

    Cd = consumption

    Id = Investment purchases

    Gd=Government purchases

    Y = (3600 - 2000r + 0.10Y) + (1200 - 4000r) + 1000

    Y=5800-6000r+0.10Y

    0.9Y=5800-6000r

    At full employment Y=5000

    Putting the value of Y in the above equation

    0.9*5000=5800-6000r

    5800-4500=6000r

    r=0.217

    Therefore real interest rate is 0.217 or 21.7%.

    (b) Sd = Y - Cd - G

    where Sd is national saving

    Sd = Y - (3600 - 2000r + 0.1Y) - 1200

    Sd = 5000 - (3600 - 2000*0.217 + 0.1*5000) - 1200 = 5000-3600+434-500-1200 = 134

    Therefore, saving = 134

    Id = 1200-4000*0.217 = 332

    Therefore, investment is 332

    Cd = 3600-2000r+0.10Y=3600-434+500=3666

    Therefore, consumption is 3666.
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