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The goods market equilibrium condition is Y = C + I + G.

Economics

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3 parts
a

Y=10000−400rY = 10000 - 400r

b

Y=4000+400rY = 4000 + 400r

c
7000
7.5

Step-by-step solution

7 steps

Part a· 2 steps

Find IS Curve

  1. The goods market equilibrium condition is Y=C+I+GY = C + I + G.

    Substitute the given equations for CC, II, TT, and GG:

    C=1500+0.75(Y−T)C = 1500 + 0.75(Y-T) I=1000−100rI = 1000 - 100r T=0T = 0 G=0G = 0 Y=[1500+0.75(Y−0)]+[1000−100r]+0Y = [1500 + 0.75(Y-0)] + [1000 - 100r] + 0 Y=1500+0.75Y+1000−100rY = 1500 + 0.75Y + 1000 - 100r

  2. Combine constant terms and rearrange to solve for YY

    Y=2500+0.75Y−100rY = 2500 + 0.75Y - 100r Y−0.75Y=2500−100rY - 0.75Y = 2500 - 100r 0.25Y=2500−100r0.25Y = 2500 - 100r Y=25000.25−1000.25rY = \frac{2500}{0.25} - \frac{100}{0.25}r Y=10000−400rY = 10000 - 400r

    The IS curve is Y=10000−400r\boxed{Y = 10000 - 400r}.

Part b

Y=4000+400rY = 4000 + 400r

Find LM Curve

  1. The money market equilibrium condition is Ms=MdM_s = M_d.

    Substitute the given equations for Money Supply (MsM_s) and Money Demand (MdM_d):

    Ms=2000M_s = 2000 Md=0.5Y−200rM_d = 0.5Y - 200r 2000=0.5Y−200r2000 = 0.5Y - 200r

  2. Rearrange the equation to solve for YY

    0.5Y=2000+200r0.5Y = 2000 + 200r Y=20000.5+2000.5rY = \frac{2000}{0.5} + \frac{200}{0.5}r Y=4000+400rY = 4000 + 400r

    The LM curve is Y=4000+400r\boxed{Y = 4000 + 400r}.

Part c7000

Find equilibrium level of YY and rr

  1. Set the IS curve equation equal to the LM curve equation to find the equilibrium interest rate (rr)

    10000−400r=4000+400r10000 - 400r = 4000 + 400r

  2. Solve for rr

    10000−4000=400r+400r10000 - 4000 = 400r + 400r 6000=800r6000 = 800r r=6000800r = \frac{6000}{800} r=608r = \frac{60}{8} r=7.5r = 7.5

  3. Substitute the equilibrium value of rr into either the IS or LM equation to find the equilibrium output (YY).

    Using the LM equation:

    Y=4000+400rY = 4000 + 400r Y=4000+400(7.5)Y = 4000 + 400(7.5) Y=4000+3000Y = 4000 + 3000 Y=7000Y = 7000

    The equilibrium level of YY is 7000\boxed{7000} and the equilibrium level of rr is 7.5\boxed{7.5}.

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