Econ 302
Spring 2008
Homework #2 Answer Key
1. For real interest rates of .01, .03, .05, and .07 calculate Cd, Id, and Snd.
The formula for national savings is Snd = Y – C – G. Using the formula for C and the values for
Y and G, we have Snd = 12 + 504  r r Cd Id Snd
.01
.03
.05
.07
43
33
23
13
46
38
30
22
17
27
37
47
2. Plot on a graph the Snd and Id curves, find the real interest rate that creates a goods market equilibrium if this is a closed economy.
Calculation by formula: set desired investment equal to desired national savings, solve for r. r will equal 38/904 or .042 or 4.2%.
Interest rate
.07
.05
.03
.01
S
I
10 20 30 40 50 S, I
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3. At r = .02, desired national savings = 22, desired investment = 42, so CA balance equals minus 20.
4. Result: desired national savings shifts to the left by 6 (savings falls by 10 because of the rise in G, but rises by 4 because of the effect of the higher future taxes on consumption). New
CA balance would be minus 26.
5. Result: because consumers reacted in question 4 to the future taxes needed to pay for the government spending, the result is not different if the taxes are collected now. Same answer as question 4.
6. No impact on the diagram (compared to question 1), since consumers will assume the current taxes substitute for the future taxes necessary to pay for the government’s current borrowing.
7. Desired savings shifts to the left because consumers expect the present value of taxes to rise because of the higher (future) government spending.
Part II
1. y = k ^(1/3), where y is output per person, k is capital per person, and “^” means the number following is an exponent.
2. Plot on a graph the amount of output per person, the amount of savings per person, and the amount of investment per person necessary to maintain a constant amount of capital per person.
Answer: Conventional Solow diagram.
3. Steady-state output occurs when the country invests just enough to offset the forces that would otherwise reduce capital per person (population growth and depreciation of capital).
4.
5. s  f(k) = (n+d)  k
0.2
 k^(1/3) = (.02+.08)  k
2 = k^(2/3)
Steady-state k = 2^(3/2) or k steady-state = square root of 8 or 2.8.
Steady-state y = 2^(1/2) or 1.4
Steady-state consumption is 0.8
 y-steady-state = 1.1
Result: s  f(k) line shifts outward, intersects (n+d)  k at a higher value of k.
New value of k-steady-state = 2.4^(3/2) = 3.7
New y-steady-state = 2.4^(1/2) = 1.5
New c-steady-state = 1.2
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