Macroeconomics Extra Credit ($1,500 maximum)

Due Monday, November 2

 

This is just for extra credit.  You will receive a maximum of $500 per question for the stock market contest depending on the accuracy of your answers.  You should not copy someone’s work.  You should be able to do the algebra on your own.  If I ask you to do a similar problem and you are not able to you will be fined $5,000.  This assignment is not required. 

 

Below is the algebra for our model of the economy.  We can solve for the equilibrium level of GDP just like we did graphically.   

                                    (1)  AE = C + I + G + (X – IM)     Definition of AE

                                    (2) C =  + MPC x Y                Consumption Function   

                                    (3) I =                                    Investment

                                    (4) G =                                  Government Purchases

                                    (5) X =                                  Exports

                        (6) IM =                              Imports

                                    (7) Y = AD                                 Equilibrium Condition

 

(a)     Solve for the equilibrium level of GDP.  You do this by combining all of the equations.  First, try combining the first and last equations: If AE = C + I + G + (X – IM) and Y = AE in equilibrium, then Y = C + I + G + (X – IM) in equilibrium.  Next, substitute in the others equations.  (Substitute in  + MPC x Y for the C term and the bar terms for the other terms.)  Next, bring all of the Y terms to the left-hand side.  Factor out the Y and divide by the remainder so that only one GDP term is left by itself on the left.  This is the equilibrium level of GDP.  Write the right-hand side by separating out all the terms with bars from the rest of the equation.

 

(b) After solving for the equilibrium level of GDP, plug in the following numbers: = $200 billion, = $1,900 billion, = $2,400 billion, = $2,000 billion, I= $2,600 billion, and MPC = .75.  What is the equilibrium level of GDP?

 

(c) One key factor that has been left out of this algebraic model is the tax rate.  Consumption is really a function of your after-tax income, not your total income.  Thus, a more accurate model of the economy takes into account taxes.  We would write consumption as a function of income minus taxes:

 

(2a) C =  + MPC(Y – Taxes)

 

We would also need an equation to determine the level of taxes.  The main federal tax is the income tax.  The equation below says that taxes are a function of income: the tax rate (t) times the level of income (or Y).

 

            (2b) Taxes = t x Y

 

Replace this new equation for consumption into the model above and also add in the equation for taxes.  Solve for the equilibrium level of output in a similar fashion as you did in part (a).  Algebraically, what happens to the size of the multiplier?  (You can answer this by looking at the algebra, by thinking about taxes leaking out of the spending stream, or by plugging in reasonable numbers for the MPC and the tax rate, such as .75 for the MPC and a tax rate of .30.)