<p>This is a question posed in Blanchard's book on Macroeconomics.</p>
<p>The question is simple. Consider an economy with a central bank (CB) and private banks. The demand for CB money is then determined by both the demand for currency <span class="math-container">$CU^d = cM^d$</span> by people where <span class="math-container">$c\in[0,1]$</span>, and the demand for reserve by the private banks <span class="math-container">$R^d=\theta D^d=\theta(1-c)M^d$</span> where <span class="math-container">$D^d$</span> is the demand for deposits by people so given by the fraction <span class="math-container">$1-c$</span> of the total demand for money. Now call <span class="math-container">$H^d$</span> the demand for CB money. Then <span class="math-container">$H^d=[c+\theta(1-c)]YL(i)$</span>.</p>
<p>Suppose now that the number of ATM's provided by the private banks increases which makes it easier for people to deposit money. What happens to the demand for CB money?</p>
<blockquote>
<p>My solution. The dependence of <span class="math-container">$H^d$</span> on the fraction of money in deposits is <span class="math-container">$$\dfrac{\partial H^d}{\partial (1-c)} = (\theta-1)YL(i)$$</span> which is a constant in <span class="math-container">$c$</span>. So we can assume the demand for CB money is linear in <span class="math-container">$c$</span>. If we assume that <span class="math-container">$\theta\in[0,1]$</span> then <span class="math-container">$\theta-1\in[-1,0]$</span> so <span class="math-container">$H^d$</span> depends negatively on <span class="math-container">$c$</span>. If <span class="math-container">$c$</span> goes up, then <span class="math-container">$H^d$</span> goes down. (We also assumed <span class="math-container">$M^d&gt;0$</span>.)</p>
</blockquote>

CC BY-SA 4.0
2021-11-23T18:15:15.423Z
Are you looking for a solution verification?
Herr K.
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2021-11-23T23:10:48.087Z
@HerrK. yes, I am. That, or if possible/necessary, comments on the solution.
Stijn D'hondt
<macroeconomics><central-banking>
The influence of an increase in ATM's on the demand for central bank money
Stijn D'hondt
# The influence of an increase in ATM's on the demand for central bank money

(Asked by: username_0 on 2021-11-23)

This is a question posed in Blanchard's book on Macroeconomics.

The question is simple. Consider an economy with a central bank (CB) and private banks. The demand for CB money is then determined by both the demand for currency $CU^d = cM^d$ by people where $c\in[0,1]$, and the demand for reserve by the private banks $R^d=\theta D^d=\theta(1-c)M^d$ where $D^d$ is the demand for deposits by people so given by the fraction $1-c$ of the total demand for money. Now call $H^d$ the demand for CB money. Then $H^d=[c+\theta(1-c)]YL(i)$.

Suppose now that the number of ATM's provided by the private banks increases which makes it easier for people to deposit money. What happens to the demand for CB money?

> My solution. The dependence of $H^d$ on the fraction of money in deposits is $$\dfrac{\partial H^d}{\partial (1-c)} = (\theta-1)YL(i)$$ which is a constant in $c$. So we can assume the demand for CB money is linear in $c$. If we assume that $\theta\in[0,1]$ then $\theta-1\in[-1,0]$ so $H^d$ depends negatively on $c$. If $c$ goes up, then $H^d$ goes down. (We also assumed $M^d>0$.)

**Tags:** macroeconomics, central-banking

> **Comments:**
> **username_1**: Are you looking for a solution verification?  
> **username_0**: @HerrK. yes, I am. That, or if possible/necessary, comments on the solution.  

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