<p>The first constraint:</p>
<p><span class="math-container">$C_t + K_{t+1} = Y_t +(1-\delta)K_t$</span></p>
<p>Has all variables included in real terms. Here <span class="math-container">$C_t$</span> is real consumption (that is consumption adjusted for inflation), <span class="math-container">$K_t$</span> real capital and <span class="math-container">$Y_t$</span> real income.</p>
<p>The second constraint:</p>
<p><span class="math-container">$P_tC_t+Q_tB_t =B_{t-1}+W_tN_t -T_t$</span></p>
<p>Has <span class="math-container">$P_t$</span> in front of the <span class="math-container">$C$</span> because it describes nominal consumption (that is consumption not adjusted for inflation). Nominal consumption is <span class="math-container">$nC= P_t C_t$</span>.</p>
<p>There is no hard rule about whether to write equation in nominal terms or real terms. You will usually see equations written in nominal terms in models where financial sector is introduced and where nominal frictions play some role. The second constraint clearly looks at some investment decision into something like bonds. In  such case it makes sense to express things in nominal terms as inflation (change in <span class="math-container">$P$</span>) will have important implications on optimal saving behavior. If you are building model of long run growth without some complex financial sector inflation will not play big role so you can abstract from it and express everything in real terms. However, again there are no hard rules the above just shows example of how people would think about it.</p>

CC BY-SA 4.0
2023-01-23T12:59:32.313Z
2023-01-23T12:59:32.313Z
1muflon1
<p>I am confused with basic concept, budget constraint.</p>
<p>I thought that the budget constraint should be look like <span class="math-container">$C_t + K_{t+1} = Y_t +(1-\delta)K_t$</span>. It does not include the price variable <span class="math-container">$P_t$</span> in front of other variables.</p>
<p>However, when I read Gali’s book, the budget constraint is written as <span class="math-container">$P_tC_t+Q_tB_t =B_{t-1}+W_tN_t -T_t$</span>. Here, <span class="math-container">$P_t$</span> is put in front of <span class="math-container">$C_t$</span>.</p>
<p>I don’t know exactly why they are different, and I want to know when and how to use the budget constraint correctly.</p>

CC BY-SA 4.0
2023-01-23T12:18:35.920Z
Please define the variables. What do $P_t, C_t, K_t, Q_t$ etc mean? Of course different agents in different models would have different budget constraints
Ishan Kashyap Hazarika
<macroeconomics>
$P_tC_t$ or $C_t$ in budget constraint?
OhRoBo
# $P_tC_t$ or $C_t$ in budget constraint?

(Asked by: username_0 on 2023-01-23)

I am confused with basic concept, budget constraint.

I thought that the budget constraint should be look like $C\_t + K\_{t+1} = Y\_t +(1-\delta)K\_t$. It does not include the price variable $P\_t$ in front of other variables.

However, when I read Gali’s book, the budget constraint is written as $P\_tC\_t+Q\_tB\_t =B\_{t-1}+W\_tN\_t -T\_t$. Here, $P\_t$ is put in front of $C\_t$.

I don’t know exactly why they are different, and I want to know when and how to use the budget constraint correctly.

**Tags:** macroeconomics
> **Comments:**
> **username_1**: Please define the variables. What do $P_t, C_t, K_t, Q_t$ etc mean? Of course different agents in different models would have different budget constraints  

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## 1 answers

### Answer by username_2 on 2023-01-23. Score: 2

The first constraint:

$C\_t + K\_{t+1} = Y\_t +(1-\delta)K\_t$

Has all variables included in real terms. Here $C\_t$ is real consumption (that is consumption adjusted for inflation), $K\_t$ real capital and $Y\_t$ real income.

The second constraint:

$P\_tC\_t+Q\_tB\_t =B\_{t-1}+W\_tN\_t -T\_t$

Has $P\_t$ in front of the $C$ because it describes nominal consumption (that is consumption not adjusted for inflation). Nominal consumption is $nC= P\_t C\_t$.

There is no hard rule about whether to write equation in nominal terms or real terms. You will usually see equations written in nominal terms in models where financial sector is introduced and where nominal frictions play some role. The second constraint clearly looks at some investment decision into something like bonds. In such case it makes sense to express things in nominal terms as inflation (change in $P$) will have important implications on optimal saving behavior. If you are building model of long run growth without some complex financial sector inflation will not play big role so you can abstract from it and express everything in real terms. However, again there are no hard rules the above just shows example of how people would think about it.


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