The country of Honiglandia is always in long-run equilibrium; the 𝑚𝑝𝑐 = 0.6 and planned investment
decreases by 30 for every one percentage point increase in the real interest rate (i.e., 𝑑 in the investment
function equals 30). Assume that 𝑐 = 10.
Suppose taxes and government purchase both increase by 200 (i.e., ∆𝑇 = ∆𝐺 = 200).
1. Calculate the change in the following quantities holding 𝑟 constant:
a) Consumption.
𝐶 = 𝐶̅ + 𝑚𝑝𝑐(𝑌 − 𝑇) − 𝑐𝑟
∆𝐶 = 𝑚𝑝𝑐(−∆𝑇) = .6(−200) = −120
Note that without knowing what 𝑌, 𝑟, 𝑇, 𝐶̅ are, we can’t calculate the specific value for
𝐶. But that’s okay, we just want to know how much 𝐶 changes.
b) 𝑆 (national saving)
𝑆 = 𝑆𝑝 + 𝑇 − 𝐺
𝑆 = (𝑌 − 𝑇) − 𝐶 + 𝑇 − 𝐺
𝑆 = (𝑌 − 𝑇) − [𝐶̅ + 𝑚𝑝𝑐(𝑌 − 𝑇) − 𝑐𝑟] + 𝑇 − 𝐺
∆𝑆 = −∆𝑇 − [𝑚𝑝𝑐(−∆𝑇)] + ∆𝑇 − ∆𝐺 = −100 + .6 ∗ 100 + 100 − 100 = −80
So the 𝑆 curve shifts to the left by 80. We know it’s a shift because we’re calculating the change
in 𝑆 for a given 𝑟.
2. Calculate the change in the equilibrium 𝑟, 𝑆, 𝐼:
We know that in equilibrium, 𝑆 = 𝐼(𝑟) so ∆𝑆 = ∆𝐼(𝑟) (we started in equilibrium where 𝑆 = 𝐼 and
end in equilibrium where 𝑆 = 𝐼, so 𝑆 and 𝐼 must change by the same amount).
The complication now is that due to the shift in 𝑆 from part 1, 𝑟 will change and so we also need
to consider the effects of changes in 𝑟 on 𝑆 and 𝐼.
∆𝑆 = ∆𝐼(𝑟)
−∆𝑇 − [𝑚𝑝𝑐(−∆𝑇) − 𝒄∆𝒓] + ∆𝑇 − ∆𝐺 = −𝒅∆𝒓
−80 + 10∆𝑟 = −30∆𝑟
 ∆𝑟 = 2
Then you can calculate the changes in the equilibrium levels for 𝑆 and by just plugging in ∆𝑟 = 2.
∆𝑆 = −80 + 10∆𝑟 = −80 + 20 = −60
∆𝐼 = −30∆𝑟 = −60
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Here is what has happened graphically.
The savings line shifts left by 80. But this induces a rise in 𝑟 that increases 𝑆. So in the
end, 𝑆 and 𝐼 only fall by 60.
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