Using this information from part $1$ to complete task $2,$

Task $($a$)$: The Economy$$s Equilibrium Real GDP $(($Y$))$

In equilibrium, aggregate expenditure $($AE$)$ equals total output$($Y$).$ The aggregate expenditure function includes autonomous spending $($A$)$ and the marginal propensity to spend $($z$).$ Autonomous spending combines consumption, investment, government spending, and exports. The marginal propensity to spend is determined by how disposable income influences consumption, adjusted for taxes and imports.

Autonomous Spending $($A$)$:

$[$A$=$c$+$I$+$G$+$X$=110+210+250+200=770]$

Marginal Propensity to Spend $($z$)$:

$[$z$=$MPC$(1$t$)$m$=0\mathrm{.}7(10\mathrm{.}3)0\mathrm{.}2=0\mathrm{.}490\mathrm{.}2=0\mathrm{.}29]$

Equilibrium Real GDP:

Using the formula:

$[$Y$=$A$1$z$]$

Substituting values:

$[$Y$=77010\mathrm{.}29=7700\mathrm{.}711,084\mathrm{.}51]$

Thus, the economy$$s equilibrium Real GDP is approximately $(1,084\mathrm{.}51).$

Explanation:

Task $($a$)$: Equilibrium Real GDP

The base Real GDP is figured by setting $($AEequal to output which is given by the formula $($Y$=$A$1$z$).$ Autonomous expenditure $(($A$))$ includes fixed expenditures while $($z$)$ is the marginal propensity to spend of the economy. This also gives the total picture of total economic output in the short$-$run.

Step $3$

Task $($b$)$: Calculating Key Variables at Equilibrium

When the economy is in equilibrium, we can calculate the levels of consumption $($C$),$ imports $($M$),$ net tax revenues $($T$),$ disposable income$($YD$),$and savings $($S$)$ using their respective relationships.

$1.$ Consumption $($C$)$:

$[$C$=$c$+$MPC$($Y$$T$)]$

First, calculate net tax revenues:

$[$T$=$t$$Y$=0\mathrm{.}31,084\mathrm{.}51325\mathrm{.}35]$

Then:

$[$C$=110+0\mathrm{.}7(1,084\mathrm{.}51325\mathrm{.}35)=110+0\mathrm{.}7759\mathrm{.}16641\mathrm{.}41]$

$2.$ Imports $($M$)$:

$[$M$=$m$$Y$=0\mathrm{.}21,084\mathrm{.}51216\mathrm{.}90]$

$3.$ Net Tax Revenues$($T$)$:

$[$T$=$t$$Y$=0\mathrm{.}31,084\mathrm{.}51325\mathrm{.}35]$

$4.$ Disposable Income $($YD$)$:

$[$YD$=$Y$$T$=1,084\mathrm{.}51325\mathrm{.}35759\mathrm{.}16]$

$5.$ Savings $(\backslash ($S$\backslash ))$:

$[$S$=$YD$$C$=759\mathrm{.}16641\mathrm{.}41117\mathrm{.}75]$

Explanation:

Task $($b$)$: Equilibrium Values

$1.$ Consumption $($C$)$: Consumption is obtained using the autonomous consumption plus that part of the disposable income spend by the households. It depicts relative household expenditure patterns in a state or period where no active changes are expected.

$2.$ Imports $($M$)$: They are associated with the national income and represent the interdependence between the production within the country and intent on imports of foreign products.

$3.$ Net Tax Revenues$($T$)$:The tax revenues in terms of the share in the GDP show the effectiveness of the government to mobilize income from the economic process.

$4.$ Disposable Income $($YD$)$: Purchasing power shows how much households have left to spend or save after taxes, it is called disposable income.

$5.$ Savings $($S$)$: Savings show how much of the disposable income is not spent at such represents the ability to invest in the future.

Step $4$

Task $($c$)$: The Multiplier of Expenditures $($k$)$

The multiplier measures how changes in autonomous spending affect the equilibrium GDP$.$ It is calculated using the formula:

$[$k$=11$z$]$

Substituting $($z$=0\mathrm{.}29)$:

$[$k$=110\mathrm{.}29=10\mathrm{.}711\mathrm{.}41]$

This indicates that for every unit increase in autonomous spending, equilibrium GDP increases by approximately $1\mathrm{.}41$ units.

Task $($d$)$: Impact of Changes in Government Spending and Exports

If government spending $(($G$))$ increases by $10\%$ and exports $(($X$))$decrease by $5\%,$ the change in autonomous spending $($A$)$ is calculated as:

$[$G$=0\mathrm{.}1$G$=0\mathrm{.}1250=25]$

$[$X$=0\mathrm{.}05$X$=0\mathrm{.}05200=10]$

$[$A$=$G$+$X$=2510=15]$

The resulting change in equilibrium GDP $(($Y$))$ is given by:

$[$Y$=$k$$A$=1\mathrm{.}411521\mathrm{.}15]$

Thus, the new equilibrium GDP is:

$[$Y$=$Y$+$Y$=1,084\mathrm{.}51+21\mathrm{.}151,105\mathrm{.}66]$

Task $2$: Let$$s predict what will happen to Canadian Real GDP in the short run if a crisis in Latin America make makes investors$$ sell their shares of Latin American firms and use their proceeds to buy shares of American firms, for which they first need to buy American dollars. The event makes the American dollar appreciate against other currencies, including CAD. In other words, it now takes more CAD to buy one USD. b$)$ Illustrate, using two graphs, what this phenomenon will mean for exports $(),$ imports $(),$ and net exports $().$ The first of these two graphs must show what happens to exports and imports. The second graph is for net exports.

Note: to get marks your axes and lines must be labelled properly, and all shifts and rotations must be properly depicted using dashed lines. $($Hint: if you$$re not sure how to graph these, avoid using Google and Chat GPT and instead read the slides or ask your professor, Google and Chat GPT want you to fail.$)$

a$)$ Explain how this event will affect the international relative prices of Canadian and American goods and services. $($i$.$e will Canadian G&S look cheaper, or more expensive to foreigners? How will American G&S look to Canadians?$)$

c$)$ Illustrate with another graph what this event will do to the $$function$.$