Economics 102 Fall 2007 Homework 4 Answer Key
1.
You are given the following information about aggregate expenditures and output as
well as the table below describing investment and savings behavior for a small open
economy with a balanced budget.
GDP = 50,000
C = 25,000
X = 8,000
M = 12,000
a.
Assume a linear relationship, and find the demand equation for the loanable funds
market.
We have two points of (I,i), so we can find the slope equal to
m = (i
2
– i
1
) / (I
2
– I
1
) = (8 – 3) / (7,900 – 21,900) =
 5/14,000 =  1/2,800
Then we can plug into the slope intercept form, i = mI + b
8 =  1/2,800 * 7,900 + b
8 =  79/28 + b
b = 303/28
i =  1/2800 * I + 303/28
or if we rearrange we get the linear relationship of
I = 30,300 – 2,800 * i
double check to make sure both points work
8 =  1/2800 * 7,900 + 303/28= 79/28 + 303/28
Checks
3 =  1/2800 * 21,900 + 303/28= 219/28 + 303/28
Checks
b.
Assume a linear relationship, and find the supply equation for the loanable funds
market. (Note: Check capital inflows (KI))
We have two points of (S
p
,i), so we can find the slope equal to
m = (i
2
– i
1
) / (S
p2
– S
p1
) = (8 – 3) / (30,000 – 15,000) = 5/15,000 = 1/3000
Then we can plug into the slope intercept form, i = mI + b
8 =
1/3000 * 30,000 + b
8 = 10 + b
b =  2
i =
1/3000 * S
p
 2
i
I
S
p
8
7,900
30,000
3
21,900
15,000
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or if we rearrange we get the linear relationship of
S
p
= 3000*i + 6000
double check to make sure both points work
8 =
1/3000 * 30,000  2 = 10 – 2
Checks
3 = 1/3000 * 15,000 2
= 5 – 2
Checks
This however is only the private savings function, which is only part of the loanable funds
supply curve as we have capital inflows equal to KI = M – X = 12,000 – 8,000 = 4,000,
which we know is horizontally added to the private savings function we just found.
S
p
= 3000i + 10,000 or i = 1/3000 * S
p
– 10/3
c.
What is the equilibrium investment spending in this economy?
Set supply equal to demand in the loanable Funds Market which implies I = S
p
Demand
: (Private Investment)
I = 30,300 – 2,800 * i
Supply
: (Private Savings plus Kapital Inflows)
S
p
= 3,000i + 10,000
30,300 – 2,800 * i = I = S
p
= 3,000 * i + 10,000
20,300 = 5,800*i
i = 203/ 58 = 3.5
I = 20,500 =
30,300– 2,800*3.5 = 30,300– 9,800
d.
What is private savings in this economy?
Use the information above, from parts c and b to calculate from the private savings
function, or use the fact that private savings is equal to total investment less capital
inflows.
S
p
= 16,500
= 3000*i + 6000 = 3,000 * 3.5 + 6,000
= 20,500 – 4,000
e.
What is government expenditure for this economy?
We know that Y = C + S
p
+ (TTR) and that the budget is balanced, or G = (TTR),
implying
G = Y – C – S
p
= 50,000 – 25,000 – 16,500 =
8,500 = G
Alternatively, we could have calculated government expenditure from the GDP
relationship, Y = C + I + G+ X – M, implying
G = Y – C – I – X + M = 50,000 – 25,000 – 20,500 – 8,000 + 12,000 = 8,500
2.
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 Spring '08
 Drozd
 Economics, Macroeconomics, Supply And Demand, Public Finance, capital inflows, gross domestic product, loanable funds market, private savings

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