Answer to Question #166381 in Macroeconomics for Khushi

Question

The consumption function is C=250 +0.75Y) - 400r, and the investment function is given by I=1300 - 100r. Here Yo is disposable income and r is the real interest rate. Net taxes are T=1000. Government spending is G=1450. The economy is in the long run where real GDP is Y = 5000.

(A) Give a real-life example of a transaction that would count towards investment I.

(B) Derive the total savings function S.

(C) Find the equilibrium on the loanable funds market: find , S, and I at equilibrium

(D) The new president is concerned about the current budget deficit, and she orders to adjust G in such a way that the budget becomes balanced. Find the new equilibrium: find r. S. and I at the new equilibrium

Answer 1

$$solution$$

$GDP=Consumption+ investments+government\ expenditure+net \ exports\\ Y=C+I+G+NX\\ C=(250+0.75y)-400r\\ I=1300-100r\\ Yo=disposable \ income\\ r=real \ intrest\ rates\\ net\ taxes=1000\\ G=1450\\ real \ gdp=5000\\$

quiz A

investment -refers to purchases of physical plants and equipment, primarily by businesses. For example, if Starbucks builds a new store for one million dollars ( $ 1 million)or Amazon buys robots worth 100 million dollars($100 million) to enable sorting of parcels , these expenditures are counted under business investment.

quiz B

Total saving function/ saving function (or propensity to save) relates the level of saving to the level of income. It is the desire or tendency of the households to save at a given level of income. Thus, saving ($s$ ) is a function ($f$ ) of income ($y$ ).

$s=f(Y)\\ s=Y-C\\ c=C+bY\\ s=Y-C\\ s=Y-(C+bY)\\ s=Y-C-bY\\ s=-C+(1-b)Y\\$

NB: $C=bY$

$s=-250+(1-0.75)\\$

-250  is dissaving (or autonomous saving that needs to take place to finance autonomous consumption). As income increases, 0.25 (= 1 – 0.75) or 25% of additional income is saved.

quiz c

Loanable funds ,$S\ and \ I \ at\ eqilibrium$

The loanable funds market illustrates the interaction of borrowers and savers in the economy. It is a variation of a market model, but what is being “bought” and “sold” is money that has been saved. Borrowers demand loanable funds and savers supply loanable funds.

The market is in equilibrium when the real interest rate has adjusted so that the amount of borrowing is equal to the amount of saving.

$s=r$

$-250+(1-0.75y)=6.66\\ -250+0.25y=6.66\\ 0.25y=6.66+250\\ 0.25y=256.66\\ y=1026.64$

quiz D

$5000=(250)-400r+1300-100r+1450+1000\\ 5000=250+1300+1450+1000+400r-100r\\ 5000=3000+300r\\ 2000=300r\\ r=\frac{2000}{300}\\ r=6.66$

$I=1300-(100\times6.66)\\ I=1300-666\\ I=634$

$S=-250+({1-0.75 \times 1026.24})\\ S=-250+(1-769.68)\\ S=-250+1-769.68\\ S=-1018.68$