ECO 200-810 Principles of Macroeconomics Spring 2001 Homework #4 due 3/30
answer key
  1. Consider the following model of the economy:
  2. Consumption function: C = 6000 + .8(Y-T)

    Investment function: I = 12,000

    Government spending: G = 17,000

    Net Exports: NX = -500

    Taxes: T = 15,000

    1. Calculate the equilibrium level of output/income in the economy. (Hint: remember to fill in taxes in the consumption function!)

    2. Y = C +I+G+NX
      Y = 6000 + .8(Y-15000) + 12000 + 17000 -500
      Y = 22,500 + .8Y
      Y = 112,500
       
    3. Determine the value of the government spending multiplier and the tax multiplier.

    4. multiplier for G:  1/(1-MPC) = 1/(1-.8) = 5
      multiplier for T:  MPC/(1-MPC) = .8/(1-.8) = 4
       
    5. Suppose the government is considering two proposals to balance the budget:
      1. increase T until T=G, OR
      2. decrease G until T=G
    Which policy will have a smaller impact on output? Explain your answer.
        using the multipliers:
        change in Y = 2000 x 4 = 8000  if taxes rise by 2000
        change in Y = 2000 x 5 = 10,000  if G falls by 2000

        so the tax hike has a smaller impact on output

  3. You are given the following simplified T-account for a bank:
Assets
Liabilities
Reserves $200

Loans $1000

Deposits $1200
The required reserve ratio is 5 percent.
    1. How much is the bank required to hold as reserves, given its deposits of $1200?

    2. (.05) x 1200 = 60
       
    3. How much are its excess reserves?

    4. excess reserves = total reserves - required reserves
      excess reserves = 200 - 60 = 140
       
    5. Suppose a depositor comes in and deposits $100 in cash. Show the banks new balance sheet below. Now how much are excess reserves?

    6. deposits rise to $1300
      reserves rise to $300
      loans stay at $1000

      excess reserves = 300 - (1300)(.05) = 300 -65 = 235
       

    7. Calculate the money multiplier

    8. = 1/reserve requirement = 1/.05 = 20
       
    9. Consider the $100 deposit made in (c). How much in new deposits can be created from this $100 deposit?

    10. new deposit creation = excess reserves x money multiplier
      new deposit creation = 95 x 20 = 1900
  1. Use the diagram below to answer the following questions:

  2. Ye is equilibrium output, while Yf is full employment output