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Unformatted text preview: Population growth rate is constant (nt = n). 3 Suppose that n = 10%. Then, if today we have 100 people, tomorrow,
Lt+1 = (1 + n) × Lt = 1.1 × 100 = 110
Our last assumption is going to be,
Assumption 4. The level of technology (recipes) is going to be constant over time. So, At = A.
And we are done characterizing the supply side of the economy!!!! Take a deep breath, and smile! 4 2.2 The Demand Side of the Economy Remember from last week that,
Y t = C t + I t + Gt + N X t
Assumption 5. We are going to assume a closed economy with no government. That is, we are going to set Gt = 0 and N Xt = 0.
Also, remember from last week that consumption is what households buy, and investment is the physical capital that
ﬁrms buy in order to produce GDP in the future. Then, in our model,
Yt = Ct + It (2.1) Investment
The ﬁrst question that we should ask ourselves is what investment is. Think of an example. Suppose that today you
have 100 lightbulbs in a classroom. But, tomorrow, you want to have 120 (maybe because you need more light to check
which students are using Facebook during the recitation). How many should you buy? If you say 20, then you are
wrong. Why? Because it is quite likely that today, some of the lightbulbs will break. Suppose that every day, 10% of the
lightbulbs break. So, today you have 100, but, at the end of the day, you will have 90. So, you will have to buy 20 + 10
= 30 lightbulbs. 20 is the difference between the lightbulbs that you want to have tomorrow minus the amount that you
have today and 10 is the amount of lightbulbs that you have to replace due to depreciation. Therefore, the total amount of
investment in lightbulbs is given by:
It = (Kt+1 − Kt ) + δ Kt = ∆K + δ K (2.2) where δ stands for the depreciation rate (for example, a reasonable value is 10%).
Then, plug equation 2.2 into 2.1 to get,
Y = C + ∆K + δ K (2.3) Consumption
How much are people going to consume every period? Well, we can just think of how much I want to save. That is, I will
save what I don’t consume, right? So, what determines savings? The interest rate, the value of your assets, your wage...
This implies that at every period of time, I will decide which is my savings rate. However, we are going to consider a
constant savings rate (in fact, over the long run, the savings rate in the US is fairly constant).
Assumption 6. The savings rate, s, is going to be constant in the model.
If I produce 1000 cheesecakes, and the savings rate is s = 0.3 (30%), I am saving 300 cheesecakes, and I will consume 700.
Therefore,
C = (1 − s) × Y
Plug this result into our previous equation, 2.3, to get: Y = Y − Y + sY = sY = (1 − s)Y + ∆K + δ K
∆K + δ K
∆K + δ K or,
∆K = sY − δ K
And we are almost done :)
5 (2.4) 2.3 Putting all pieces together! We already k...
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 Spring '10
 Xaviersalaimartin

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