# Consider the information below and answer the following questions: If AD is... Y=4(Ao-P/2) and...

## Question:

Consider the information below and answer the following questions:

If {eq}AD \text{ is}... Y=4(Ao-P/2) {/eq}

and

{eq}AS \ \text{is} ... Y=850, \ \text{for} \ P>287.5 \\ Ao=Co-\text{mpc} \ To+Io+Go+Xo-Mo=500 \\ \text{mpc}=0.3 {/eq}

a. The Equilibrium price level is _____,

b. The Equilibrium National Income is _____,

Suppose Government Spending increase by 60, given the change in government spending:

c. What is the new equilibrium price level?

d. What is the new equilibrium national income?

Starting again at initial equilibrium, suppose now lump-sum taxes are increased by 145.

e. What is the new equilibrium price level?

f. What is the new equilibrium national income?

## National income

The national income is the aggregate income of the country, for the final value of production produced by the country in terms of the factor income. The domestic factor income and factor income from abroad are included in the national income. The gross national product defines the national income.

## Answer and Explanation: 1

a.

The equilibrium price level:

{eq}\begin{align*} AD &= AS\\ 4\left( {{A_0} - \dfrac{P}{2}} \right) &= 850\\ 4\left( {500 - \dfrac{P}{2}} \right) &= 850\\ 2000 - P &= 1700\\ P &= 300 \end{align*}{/eq}

The equilibrium price is 300.

b.

The Equilibrium National Income (Y):

{eq}\begin{align*} Y &= 4\left( {{A_0} - \dfrac{P}{2}} \right)\\ Y &= 4\left( {500 - \dfrac{{300}}{2}} \right)\\ &= 2000 - 150\\ Y &= 1850 \end{align*}{/eq}

The Equilibrium National Income (Y) is 1850.

c.

If the government spending increased by 60, then Ao will increase by 60. Government spending Go is the being the component of Ao as given in the example. Hence the new Ao is 560.

The new equilibrium price level:

{eq}\begin{align*} AD &= AS\\ 4\left( {{A_0} - \dfrac{P}{2}} \right) &= 850\\ 4\left( {560 - \dfrac{P}{2}} \right) &= 850\\ 2240 - P &= 1700\\ P &= 540 \end{align*}{/eq}

The equilibrium price is 540.

d.

The new Equilibrium National Income (Y):

{eq}\begin{align*} Y &= 4\left( {{A_0} - \frac{P}{2}} \right)\\ Y &= 4\left( {560 - \frac{{540}}{2}} \right)\\ &= 2240 - 270\\ Y &= 1970 \end{align*}{/eq}

The Equilibrium National Income (Y) is 1970.

e.

Suppose now lump-sum taxes are increased by 145. As Tax To is a value to be decreased from Ao, and influenced by mpc, the actual tax value post mpc is: $mpc.To = 0.3 \times 145 = 43.5$ Thus the new value of Ao is ${A_0} = 500 - 43.5 = 456.5$. With this, the new equilibrium price level:

{eq}\begin{align*} AD &= AS\\ 4\left( {{A_0} - \dfrac{P}{2}} \right) &= 850\\ 4\left( {456.5 - \dfrac{P}{2}} \right) &= 850\\ 1826 - P &= 1700\\ P &= 126 \end{align*}{/eq}

The equilibrium price is 126.

f.

The new Equilibrium National Income (Y):

{eq}\begin{align*} Y &= 4\left( {{A_0} - \dfrac{P}{2}} \right)\\ Y &= 4\left( {486.5 - \dfrac{{126}}{2}} \right)\\ &= 1826 - 63\\ Y &= 1763 \end{align*}{/eq}

The new Equilibrium National Income (Y) is 1763.