$$

Planned Expenditures: PE $=$ C $+$ I $+$ G $+$ NX

Consumption: C $=435+0\mathrm{.}76($Y$-$ T$)-11$ r

Net Tax Revenue: T $=125+0\mathrm{.}2$ Y

Gross Investment: I $=575-18$ r

Government Expenditures: G $=510$

Net Exports: NX $=345+80(1-$ $)-7$ r $-0\mathrm{.}1$ Y

Real Exchange Rate,$$ $=$ eP$/$Pus: $=1\mathrm{.}0292$

Fixed Real Interest rate for the PE$$Model: r$*=3\mathrm{.}871\%$

Real Transactions and Precautionary Demand for Money $=185+0\mathrm{.}16$ Y

Real Asset Demand for Money $=34-48$ r

Money Supply: M $=445$

Fixed Price for Keynesian Models: P $=1\mathrm{.}24$

Aggregate Demand: P $=9\mathrm{.}010096-0\mathrm{.}002547$ Y

Aggregate Supply: P $=-17\mathrm{.}098469+0\mathrm{.}006111$ Y

Natural Rate of Output: YN $=3,029\mathrm{.}153$

$$

$$

Enter your Answers to $3$ decimal places. Include the negative sign where appropriate.

$$

Section $1$: The Planned Expenditures $($PE$)$ Model

Derive the PE equation from the model provided above:

$$

Part $1$: What is the slope of the PE curve? $(4$marks$)$

Part $2$: What is the vertical intercept of the PE curve?$(4$marks$)$

Part $3$: Calculate the equilibrium ouput $($Ye$)$ for the PE model assuming the real interest rate is $3\mathrm{.}871\%.(4$ marks$)$

Part $4$: Calculate the Expenditures Multiplier for the PE model.$(2$ marks$)$

Part $5$: Calculate the autonomous Tax Multiplier for the PE model.$(2$marks$)$

Part $6$: Part $4$ above means a $180$ million dollar increase in government spending will increase equilibrium output in the PE model by approximately?$(2$marks$)$

Part $7$: How much autonomous tax cut would raise equilibrium output in the PE model by the same amount as the government expenditures increase raised it in Part $6$ above?$(3$ marks$)$

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Section $2$A: The IS$-$LM $$Model

Derive the IS and LM equations from the model provided above:$$

Part $8$: What is the slope of the IS curve?$(4$marks$)$

Part $9$: What is the vertical intercept of the IS curve?$(4$marks$)$

Part $10$: What is the Slope of the LM equation?$(4$marks$)$

Part $11$: What is the Vertical intercept of the LM equation?$(4$marks$)$

Part $12$: Solve for the equilibrium output in the IS$-$LM model:$(5$marks$)$

Part $13$: Solve for the equilibrium interest rate in the IS$-$LM model:$(3$ marks$)$

Part $14$:$$ Calculate the output gap $($YN$-$Ye$)$ in the IS$-$LM model?$(2$marks$)$

Part $15$: If the expenditures multiplier is $1\mathrm{.}634,$calculate the autonomous Tax Multiplier for the IS$-$LM$$model$.(2$marks$)$

Part $16$:$$ Calculate the change in government expenditures required to close the output gap? $(2$ marks$)$

Part $17$:$$Calculate the$$ change in autonomous taxes required to close the output gap?$(2$ marks$)$

$$

$$

Section $2$B: Effects of a Change in the Quantity of Money in the IS$-$LM $$Model

Suppose the Central Bank increases the Money Supply by $150.$ All other things equal:

Part $18$: Solve for the new IS$-$LM equilibrium output.$(6$marks$)$

Part $19$:$$Calculate the new IS$-$LM equilibrium interest rate. $(3$ marks$)$