<p>The answer would depend on a lot of factors, such as what is the government money spent on, what is the tax regime etc. For starters, let us look at what would happen in different time scales. We can use a simple textbook IS-LM-AS model with three equations:</p>
<p><span class="math-container">$$Y = C(Y-T) + I(r) + G$$</span>
<span class="math-container">$$M^s(H, P) = M^d(Y, r)$$</span>
<span class="math-container">$$Y = S(P)$$</span></p>
<p>The first equation is the IS equation. The total income in the economy (LHS) is equal to the total expenditure, which is the  sum of consumption <span class="math-container">$C$</span>, investment <span class="math-container">$I$</span> and government spending <span class="math-container">$G$</span>. <span class="math-container">$C$</span> rises with disposable income <span class="math-container">$Y-T$</span> where <span class="math-container">$T$</span> is tax, but not as much as income as people save part of it. Therefore <span class="math-container">$0 &lt; \partial C/ \partial (Y-T) &lt; 1$</span>. <span class="math-container">$I$</span> falls with the interest rate <span class="math-container">$r$</span>, as a higher interest rate means more difficulty getting funds. In the LM equation, real money supply <span class="math-container">$M^s$</span> increases with hard money <span class="math-container">$H$</span> as there is more money in people's hands and falls with price level <span class="math-container">$P$</span> as each note buys less when price is high. Money demand <span class="math-container">$M^d$</span> rises with <span class="math-container">$Y$</span> as higher income households would need more money to accommodate higher spending, assuming constant velocity. <span class="math-container">$M^d$</span> falls with <span class="math-container">$r$</span> as bond prices are inversely related to <span class="math-container">$r$</span>, so with high <span class="math-container">$r$</span> and low pond prices, people would hold bonds instead of money. Finally, the AS curve states that total supply <span class="math-container">$S$</span> is related to <span class="math-container">$P$</span>. The result will depend on the nature of this relation.</p>
<p>We have <span class="math-container">$Y$</span>, <span class="math-container">$r$</span> and <span class="math-container">$P$</span> as endogenous variables. Rest are all exogenous.  To avoid notational clutter, I will write <span class="math-container">$A_B$</span> for the derivative of <span class="math-container">$A$</span> with respect to <span class="math-container">$B$</span>. For example, <span class="math-container">$Y_G$</span> is the derivative of <span class="math-container">$Y$</span> with respect to <span class="math-container">$G$</span>. Differentiating both sides of all the three equations and solving for <span class="math-container">$Y_G$</span>, we get,</p>
<p><span class="math-container">$$Y_G = \frac{M^d_r S_p}{S_P (1-C_{Y-T})M^d_r + S_p M^d_Y I_r - M^s_P I_r}$$</span></p>
<p>A similar exercise for <span class="math-container">$Y_T$</span> yields</p>
<p><span class="math-container">$$Y_T = \frac{- C_{Y-T} M^d_r S_p}{S_P (1-C_{Y-T})M^d_r + S_p M^d_Y I_r - M^s_P I_r}$$</span></p>
<p>Suppose the government spending has changed by <span class="math-container">$\Delta G$</span>. The <span class="math-container">$Y$</span> changes approximately by <span class="math-container">$Y_G \Delta G$</span>. Suppose <span class="math-container">$T$</span> has changed by <span class="math-container">$\Delta T$</span>, then <span class="math-container">$Y$</span> changes by approximately <span class="math-container">$Y_T \Delta T$</span>. In your question, the government has reduced spending <em>exactly</em> as much as it has reduced taxes. Therefore, <span class="math-container">$\Delta T = \Delta G$</span>. Using this, the total change in <span class="math-container">$Y$</span> is approximately</p>
<p><span class="math-container">$$(Y_G + Y_T) \Delta G$$</span></p>
<p><span class="math-container">$$ = \frac{(1 - C_{Y-T}) M^d_r S_p}{S_P (1-C_{Y-T})M^d_r + S_p M^d_Y I_r - M^s_P I_r} \Delta G$$</span></p>
<p>The interesting thing to note is, <span class="math-container">$Y_T = - C_{Y-T} Y_G$</span>. Why is it so? Looking at the processes helps. When the government spends an additional penny, that spending directly gets added to <span class="math-container">$Y$</span> in the first step. Once that penny reaches the people, they spend <span class="math-container">$C_{Y-T}$</span> of it, which also gets added to <span class="math-container">$Y$</span>. But this additional <span class="math-container">$C_{Y-T}$</span> further prompts additional spending and so on. But in the case of raising <span class="math-container">$T$</span>, the raise in T does not directly count as a fall in <span class="math-container">$Y$</span>. Raising <span class="math-container">$T$</span> leads to falling expenditure, which in the first round only amounts to a fall of <span class="math-container">$C_{Y-T}$</span> in <span class="math-container">$Y$</span>. This fall reduces expenditure further and so on. Therefore, the first round effect of changing <span class="math-container">$T$</span> is <span class="math-container">$C_{Y-T}$</span> times of the first round effect of changing <span class="math-container">$G$</span> and the rest of the process is same.</p>
<p><em><strong>As <span class="math-container">$0 &lt; C_{Y-T} &lt; 1$</span>, this means that changing <span class="math-container">$T$</span> and <span class="math-container">$G$</span> by the same amount would lead to the two having effects opposite in direction, but the effect of <span class="math-container">$G$</span> would be higher. Overall, the direction would be the same as a change in <span class="math-container">$G$</span> only.</strong></em></p>
<p><strong>Reducing <span class="math-container">$G$</span> and reducing <span class="math-container">$T$</span> equally would have the same direction of effect as reducing <span class="math-container">$G$</span> and doing nothing to <span class="math-container">$T$</span>.</strong></p>
<p>The LM and AS curves add more nuance but the result remains more or less the same. With price stickiness, in the short run the price level is a constant. Therefore, the <span class="math-container">$AS$</span> curve is horizontal and <span class="math-container">$S_P = \infty$</span>. In the equation above, as we do <span class="math-container">$ \lim_{P \rightarrow \infty} $</span>, we get</p>
<p><span class="math-container">$$(Y_G + Y_T) \Delta G = \frac{(1 - C_{Y-T}) M^d_r}{(1-C_{Y-T})M^d_r + M^d_Y I_r} \Delta G$$</span></p>
<p>You can check that this is an overall negative quantity. You can check that if <span class="math-container">$I_r = 0$</span>, <span class="math-container">$\Delta Y$</span> would have been exactly equal to <span class="math-container">$\Delta G$</span>. But with <span class="math-container">$I_r &lt; 0$</span>, additional government spending eats up part of investment by raising interest rates, dampening the effect.</p>
<p>As <span class="math-container">$S_P$</span> reduces in the medium run, <span class="math-container">$S_P$</span> still remains positive. Oversimplifying, this is because higher <span class="math-container">$P$</span> means lower real wage, higher employment and therefore higher supply. With a positive <span class="math-container">$S_P$</span>, it is easy to check that <span class="math-container">$(Y_G + Y_T) \Delta G$</span> is less fall in income than the short run, but still negative.</p>
<p>In the long run, <span class="math-container">$S_P$</span> becomes zero, and the income becomes independent of price level. Here, <span class="math-container">$(Y_G + Y_T) \Delta G = 0$</span>, which was your hunch.</p>
<p>Therefore, refining the previous statement:</p>
<p><strong>Reducing <span class="math-container">$G$</span> and reducing <span class="math-container">$T$</span> equally would have the same direction of effect as reducing <span class="math-container">$G$</span> and doing nothing to <span class="math-container">$T$</span>:</strong></p>
<ol>
<li>Reducing the income in the short run</li>
<li>Reducing the income but a little less in the medium run</li>
<li>Having no effect in the long run</li>
</ol>
<p>The above simplifies a lot of things however. We had a lump sum tax. Different tax regimes would give different results, but as long as higher tax reduces disposable income, the direction of the results would remain the same. We have considered government spending affecting consumption directly only. Government expenditure in the form of investment subsidies might have different effect. Finally, the nature of expenditure cut also would affect the results. In our model, the long run AS income is exogenous: but it is very likely that it is not exogenous in the real world. Reduction in government spending on key sectors like infrastructure might negatively affect it.</p>

CC BY-SA 4.0
2024-06-05T18:28:11.330Z
2024-06-05T19:22:24.477Z
2024-06-05T19:22:24.477Z
Ishan Kashyap Hazarika
<blockquote>
<p>So would it result in a net zero change to the economy?  Or would there be other effects which come into play?</p>
</blockquote>
<p>No,</p>
<ol>
<li>With non distortionary tax there would be almost no change to the economy, but there would still be short run change in aggregate gross income.</li>
<li>You are talking about income tax which is distortionary and will create multiple changes to the economy.</li>
</ol>
<p>Your reasoning would be (almost) correct if instead of income taxes you would use non-distortionary lump sum taxes. For non-distortionary tax (e.g. lump-sum tax), for balanced fiscal change this would be true.</p>
<p>In that case (for simplified closed economy with fixed level of investment) change in income <span class="math-container">$y$</span> equals change in consumption <span class="math-container">$c$</span>, snd change in government spending <span class="math-container">$g$</span>, so <span class="math-container">$dy = dc + dg$</span>. Since change in disposable income is <span class="math-container">$dy_d = dy -dt$</span> and since change in consumption is also equivalent to change in disposable income multiplied by marginal propensity to consume (m) <span class="math-container">$dc=m \cdot dy_d$</span>, if we combine all this expressions and solve for <span class="math-container">$dc$</span> we get that:</p>
<p><span class="math-container">$$dc= \frac{m}{1-m}(dg -dt) \implies dc=0.$$</span></p>
<p>So for balanced fiscal change <span class="math-container">$dg=dt$</span> there is no change in consumption. Moreover, by extension <span class="math-container">$dc \implies dy_d=0$</span>. Hence there is also no change in disposable income. However, you can't say that there is absolutely no change whatsoever. When we solve for <span class="math-container">$dy$</span> we get;</p>
<p><span class="math-container">$$dy = dg - \frac{m}{1-m} dt.$$</span></p>
<p>So for balanced budget <span class="math-container">$dy=1$</span>. Hence there is some change. There is no fiscal multiplier that would scale economy up or down, but economy will shrink. Now you might wonder why, if people's consumption and disposable income didn't change, it might look like government appears and disappears as if from ether. The reason for this is that this model abstracts from supply side of an economy. In background, when government disappears it frees capital (e.g. hospitals, gov buildings and real estate etc). As this resources get absorbed into private economy <span class="math-container">$y_d$</span> would increase to perfectly offset the decrease in <span class="math-container">$y$</span>. However, while some government facilities (e.g. hospitals) can be absorbed quickly into private economy, others like military installations may take years. Hence, at least in short-run economy should experience drop in output. Not because there is less consumption, or because (private) people have lower disposable income, but because factors that are tied in government sector can't be instantly absorbed by private economy (in fact this is what is explained in the answer by Ishan Kashyap Hazarika in greater detail as he also models supply side).</p>
<p>But income taxes change this problem drastically because income taxes also change people's incentive to work and hence they do not only affect disposable income (<span class="math-container">$y_d$</span>) but also gross income <span class="math-container">$y$</span>. The change is not necessarily a priory negative. Income tax has both substitution effect, as it makes leisure more attractive, but it also has wealth effect which can encourage work, as poor person can less afford to enjoy leisure time due to lower income (You can see deeper discussion of this in Hindriks and Myles, Intermediate Public Economics Ch 16).  Hence this has to be estimated empirically.  Empirical studies generally show that labor supply most often responds negatively to higher income taxes in EU and US, even though the effect is sometimes small and positive effects are also sometimes shown in the data (<a href="https://deliverypdf.ssrn.com/delivery.php?ID=769100067111073023004093027003089101037063061035027036094000018010069012000067008083123123053005045081081097064097107094001098100007086102121116127071081099007073005026104075021&amp;EXT=pdf&amp;INDEX=TRUE" rel="nofollow noreferrer">Bargain, Orsini, &amp; Peichl, 2011</a>). In turn this results in lower gross income  compared to counterfactual without taxes. Moreover, so far we only discussed labor taxes, but considerable portion of income comes also from employing capital and supply of capital is known to be way more elastic than supply of labor, hence this further lowers income ceteris paribus.</p>
<p>If we adjust for the fact that income taxes have negative effect on gross output then we will have <span class="math-container">$dy = dc + dg - \delta(t)$</span> where <span class="math-container">$\delta$</span> is the deadweight loss caused by distortionary income tax. Moreover, linear income tax (which is what I suppose you mean by tax that is neither progressive or regressive, since typically laymen call taxes progressive/regressive depending on how rate changes with income) also enters now the problem as a scalar of <span class="math-container">$y$</span> hence <span class="math-container">$dy_d = (1-t)dy$</span> and under your assumption that any change in taxes will be offset by lower government spending we also now get that <span class="math-container">$dg = tdy$</span>.</p>
<p>Now when we solve the model for consumption with these changes we get;</p>
<p><span class="math-container">$$dc= - \frac{m}{1-m} \delta(t)$$</span></p>
<p>And for income we get;</p>
<p><span class="math-container">$$dy = - \frac{1}{(1-t)(1-m)} \delta(t)$$</span></p>
<p>In this case lowering the taxes increases income and consumption.</p>
<p>There are further nuances;</p>
<p>A) we assumed everyone is equal in the model above. In real life people can have different marginal propensities to consume. In that case it matters who the taxes take income away from and how government spends the income.</p>
<p>B) we abstracted away from investment which also affects income. In the same way as different people have different marginal propensity to consume different people have different marginal propensity to save and invest. This partially, but not necessarily cancels out the effect mentioned in A.</p>
<p>C) Private economy can't always provide some goods in sufficient quantity. This is especially true for non-rivalrous and non-excludable goods, we in economics even call these public goods. For example, due to free rider problem it is very likely that a private army would be underfunded, even with the same preferences. This would lead to lower output.</p>
<p>D) Government can't efficiently provide some goods. For example, historically governments are worse at providing private (excludable and rivalrous) goods. If reduction in government spending comes from less spending on providing private goods it would further increase income offsetting the C.</p>
<p>There are more nuances, but I think this already well illustrates the complexity of the problem.</p>
<p>Main point is that it is extremely unlikely there would be no change if we deal with distortionary taxes as opposed to non-distortionary taxation.</p>
<p>Moreover, there are further complexities. Overall income and consumption depend both on distribution of income and also on what type of activities is the government funding.</p>

CC BY-SA 4.0
2024-06-05T18:54:04.437Z
2024-06-05T18:54:04.437Z
1muflon1
<p>The first-order effect, as you say, would simply be a transfer from the Government to Households. Consequently, the largest impact will be distributional, which as you say shouldn't have a large effect on the aggregate economy.</p>
<p>However, there are a few additional effects that will impact the economy at large.</p>
<ol>
<li>What is the relative Marginal Propensity to Consume of those receiving the tax income versus the Government?</li>
</ol>
<p>If the government spends or invests a different proportion of the tax take to those who pay it, you'd expect both supply and demand responses (even if the tax is neither regressive nor progressive, as you specify).</p>
<p>If Consumers spend a higher proportion of the marginal income than the government would, then we would expect a short-run (demand side) expansion in GDP, but a decline in savings (and thus, probably, investment).</p>
<p>This depends crucially on two factors - who gets the money and what the government was spending it on before.</p>
<p>Furthermore, there are some kinds of investment which can realistically <em>only</em> be provided by the state (e.g maintenance of the road network, defence etc.). A decline in investment in expenditure of this kind can be expected to cause a long-run decline in GDP due to a weakening of the Supply side of the economy.</p>
<ol start="2">
<li>Income taxes are distortionary.</li>
</ol>
<p>On the other hand, income taxes are distortionary. Cp, cutting income taxes will encourage labour supply (and other productive activities), expanding the economy relative to prior to the cut. Therefore a shift from government expenditure to tax cuts could stimulate the economy somewhat.</p>

CC BY-SA 4.0
2024-06-05T09:02:54.190Z
2024-06-05T09:02:54.190Z
matthewoulton
<p>Let's say a government comes out with a new budget. This budget decreases income taxes in a more or less neutral way (neither progressive or regressive). However they also decrease government spending (education, healthcare, defense etc) by the same (estimated) dollar amount.</p>
<p>Lower taxes theoretically<code>*</code> should increase take home (disposable) income, which should then result in more consumer spending, which should boost the economy.</p>
<p>However since the budget is decreasing its spending, that (in my mind, and what I want to explore and understanding better) seems like it would have the exact opposite effect. (E.g., over all health care/ defense worker disposable income would be less, less consumer spending, slowing of the economy,etc, etc).</p>
<p><strong>So would it result in a net zero change to the economy?</strong>
<strong>Or would there be other effects which come into play?</strong></p>
<p><code>*</code> According to the budget announcement PR person.</p>

<macroeconomics><government-spending><optimal-taxation><services>
Net effect of govt spending and tax cuts
DarcyThomas
# Net effect of govt spending and tax cuts

(Asked by: username_0 on 2024-06-05)

Let's say a government comes out with a new budget. This budget decreases income taxes in a more or less neutral way (neither progressive or regressive). However they also decrease government spending (education, healthcare, defense etc) by the same (estimated) dollar amount.

Lower taxes theoretically`*` should increase take home (disposable) income, which should then result in more consumer spending, which should boost the economy.

However since the budget is decreasing its spending, that (in my mind, and what I want to explore and understanding better) seems like it would have the exact opposite effect. (E.g., over all health care/ defense worker disposable income would be less, less consumer spending, slowing of the economy,etc, etc).

**So would it result in a net zero change to the economy?**
**Or would there be other effects which come into play?**

`*` According to the budget announcement PR person.

**Tags:** macroeconomics, government-spending, optimal-taxation, services


---

## 3 answers

### Answer by username_1 on 2024-06-05. Score: 3

The answer would depend on a lot of factors, such as what is the government money spent on, what is the tax regime etc. For starters, let us look at what would happen in different time scales. We can use a simple textbook IS-LM-AS model with three equations:

$$Y = C(Y-T) + I(r) + G$$
$$M^s(H, P) = M^d(Y, r)$$
$$Y = S(P)$$

The first equation is the IS equation. The total income in the economy (LHS) is equal to the total expenditure, which is the sum of consumption $C$, investment $I$ and government spending $G$. $C$ rises with disposable income $Y-T$ where $T$ is tax, but not as much as income as people save part of it. Therefore $0 < \partial C/ \partial (Y-T) < 1$. $I$ falls with the interest rate $r$, as a higher interest rate means more difficulty getting funds. In the LM equation, real money supply $M^s$ increases with hard money $H$ as there is more money in people's hands and falls with price level $P$ as each note buys less when price is high. Money demand $M^d$ rises with $Y$ as higher income households would need more money to accommodate higher spending, assuming constant velocity. $M^d$ falls with $r$ as bond prices are inversely related to $r$, so with high $r$ and low pond prices, people would hold bonds instead of money. Finally, the AS curve states that total supply $S$ is related to $P$. The result will depend on the nature of this relation.

We have $Y$, $r$ and $P$ as endogenous variables. Rest are all exogenous. To avoid notational clutter, I will write $A\_B$ for the derivative of $A$ with respect to $B$. For example, $Y\_G$ is the derivative of $Y$ with respect to $G$. Differentiating both sides of all the three equations and solving for $Y\_G$, we get,

$$Y\_G = \frac{M^d\_r S\_p}{S\_P (1-C\_{Y-T})M^d\_r + S\_p M^d\_Y I\_r - M^s\_P I\_r}$$

A similar exercise for $Y\_T$ yields

$$Y\_T = \frac{- C\_{Y-T} M^d\_r S\_p}{S\_P (1-C\_{Y-T})M^d\_r + S\_p M^d\_Y I\_r - M^s\_P I\_r}$$

Suppose the government spending has changed by $\Delta G$. The $Y$ changes approximately by $Y\_G \Delta G$. Suppose $T$ has changed by $\Delta T$, then $Y$ changes by approximately $Y\_T \Delta T$. In your question, the government has reduced spending *exactly* as much as it has reduced taxes. Therefore, $\Delta T = \Delta G$. Using this, the total change in $Y$ is approximately

$$(Y\_G + Y\_T) \Delta G$$

$$ = \frac{(1 - C\_{Y-T}) M^d\_r S\_p}{S\_P (1-C\_{Y-T})M^d\_r + S\_p M^d\_Y I\_r - M^s\_P I\_r} \Delta G$$

The interesting thing to note is, $Y\_T = - C\_{Y-T} Y\_G$. Why is it so? Looking at the processes helps. When the government spends an additional penny, that spending directly gets added to $Y$ in the first step. Once that penny reaches the people, they spend $C\_{Y-T}$ of it, which also gets added to $Y$. But this additional $C\_{Y-T}$ further prompts additional spending and so on. But in the case of raising $T$, the raise in T does not directly count as a fall in $Y$. Raising $T$ leads to falling expenditure, which in the first round only amounts to a fall of $C\_{Y-T}$ in $Y$. This fall reduces expenditure further and so on. Therefore, the first round effect of changing $T$ is $C\_{Y-T}$ times of the first round effect of changing $G$ and the rest of the process is same.

***As $0 < C\_{Y-T} < 1$, this means that changing $T$ and $G$ by the same amount would lead to the two having effects opposite in direction, but the effect of $G$ would be higher. Overall, the direction would be the same as a change in $G$ only.***

**Reducing $G$ and reducing $T$ equally would have the same direction of effect as reducing $G$ and doing nothing to $T$.**

The LM and AS curves add more nuance but the result remains more or less the same. With price stickiness, in the short run the price level is a constant. Therefore, the $AS$ curve is horizontal and $S\_P = \infty$. In the equation above, as we do $ \lim\_{P \rightarrow \infty} $, we get

$$(Y\_G + Y\_T) \Delta G = \frac{(1 - C\_{Y-T}) M^d\_r}{(1-C\_{Y-T})M^d\_r + M^d\_Y I\_r} \Delta G$$

You can check that this is an overall negative quantity. You can check that if $I\_r = 0$, $\Delta Y$ would have been exactly equal to $\Delta G$. But with $I\_r < 0$, additional government spending eats up part of investment by raising interest rates, dampening the effect.

As $S\_P$ reduces in the medium run, $S\_P$ still remains positive. Oversimplifying, this is because higher $P$ means lower real wage, higher employment and therefore higher supply. With a positive $S\_P$, it is easy to check that $(Y\_G + Y\_T) \Delta G$ is less fall in income than the short run, but still negative.

In the long run, $S\_P$ becomes zero, and the income becomes independent of price level. Here, $(Y\_G + Y\_T) \Delta G = 0$, which was your hunch.

Therefore, refining the previous statement:

**Reducing $G$ and reducing $T$ equally would have the same direction of effect as reducing $G$ and doing nothing to $T$:**

1. Reducing the income in the short run
2. Reducing the income but a little less in the medium run
3. Having no effect in the long run

The above simplifies a lot of things however. We had a lump sum tax. Different tax regimes would give different results, but as long as higher tax reduces disposable income, the direction of the results would remain the same. We have considered government spending affecting consumption directly only. Government expenditure in the form of investment subsidies might have different effect. Finally, the nature of expenditure cut also would affect the results. In our model, the long run AS income is exogenous: but it is very likely that it is not exogenous in the real world. Reduction in government spending on key sectors like infrastructure might negatively affect it.


---

### Answer by username_2 on 2024-06-05. Score: 2

> So would it result in a net zero change to the economy? Or would there be other effects which come into play?

No,

1. With non distortionary tax there would be almost no change to the economy, but there would still be short run change in aggregate gross income.
2. You are talking about income tax which is distortionary and will create multiple changes to the economy.

Your reasoning would be (almost) correct if instead of income taxes you would use non-distortionary lump sum taxes. For non-distortionary tax (e.g. lump-sum tax), for balanced fiscal change this would be true.

In that case (for simplified closed economy with fixed level of investment) change in income $y$ equals change in consumption $c$, snd change in government spending $g$, so $dy = dc + dg$. Since change in disposable income is $dy\_d = dy -dt$ and since change in consumption is also equivalent to change in disposable income multiplied by marginal propensity to consume (m) $dc=m \cdot dy\_d$, if we combine all this expressions and solve for $dc$ we get that:

$$dc= \frac{m}{1-m}(dg -dt) \implies dc=0.$$

So for balanced fiscal change $dg=dt$ there is no change in consumption. Moreover, by extension $dc \implies dy\_d=0$. Hence there is also no change in disposable income. However, you can't say that there is absolutely no change whatsoever. When we solve for $dy$ we get;

$$dy = dg - \frac{m}{1-m} dt.$$

So for balanced budget $dy=1$. Hence there is some change. There is no fiscal multiplier that would scale economy up or down, but economy will shrink. Now you might wonder why, if people's consumption and disposable income didn't change, it might look like government appears and disappears as if from ether. The reason for this is that this model abstracts from supply side of an economy. In background, when government disappears it frees capital (e.g. hospitals, gov buildings and real estate etc). As this resources get absorbed into private economy $y\_d$ would increase to perfectly offset the decrease in $y$. However, while some government facilities (e.g. hospitals) can be absorbed quickly into private economy, others like military installations may take years. Hence, at least in short-run economy should experience drop in output. Not because there is less consumption, or because (private) people have lower disposable income, but because factors that are tied in government sector can't be instantly absorbed by private economy (in fact this is what is explained in the answer by username_1 in greater detail as he also models supply side).

But income taxes change this problem drastically because income taxes also change people's incentive to work and hence they do not only affect disposable income ($y\_d$) but also gross income $y$. The change is not necessarily a priory negative. Income tax has both substitution effect, as it makes leisure more attractive, but it also has wealth effect which can encourage work, as poor person can less afford to enjoy leisure time due to lower income (You can see deeper discussion of this in Hindriks and Myles, Intermediate Public Economics Ch 16). Hence this has to be estimated empirically. Empirical studies generally show that labor supply most often responds negatively to higher income taxes in EU and US, even though the effect is sometimes small and positive effects are also sometimes shown in the data ([Bargain, Orsini, & Peichl, 2011](https://deliverypdf.ssrn.com/delivery.php?ID=769100067111073023004093027003089101037063061035027036094000018010069012000067008083123123053005045081081097064097107094001098100007086102121116127071081099007073005026104075021&EXT=pdf&INDEX=TRUE)). In turn this results in lower gross income compared to counterfactual without taxes. Moreover, so far we only discussed labor taxes, but considerable portion of income comes also from employing capital and supply of capital is known to be way more elastic than supply of labor, hence this further lowers income ceteris paribus.

If we adjust for the fact that income taxes have negative effect on gross output then we will have $dy = dc + dg - \delta(t)$ where $\delta$ is the deadweight loss caused by distortionary income tax. Moreover, linear income tax (which is what I suppose you mean by tax that is neither progressive or regressive, since typically laymen call taxes progressive/regressive depending on how rate changes with income) also enters now the problem as a scalar of $y$ hence $dy\_d = (1-t)dy$ and under your assumption that any change in taxes will be offset by lower government spending we also now get that $dg = tdy$.

Now when we solve the model for consumption with these changes we get;

$$dc= - \frac{m}{1-m} \delta(t)$$

And for income we get;

$$dy = - \frac{1}{(1-t)(1-m)} \delta(t)$$

In this case lowering the taxes increases income and consumption.

There are further nuances;

A) we assumed everyone is equal in the model above. In real life people can have different marginal propensities to consume. In that case it matters who the taxes take income away from and how government spends the income.

B) we abstracted away from investment which also affects income. In the same way as different people have different marginal propensity to consume different people have different marginal propensity to save and invest. This partially, but not necessarily cancels out the effect mentioned in A.

C) Private economy can't always provide some goods in sufficient quantity. This is especially true for non-rivalrous and non-excludable goods, we in economics even call these public goods. For example, due to free rider problem it is very likely that a private army would be underfunded, even with the same preferences. This would lead to lower output.

D) Government can't efficiently provide some goods. For example, historically governments are worse at providing private (excludable and rivalrous) goods. If reduction in government spending comes from less spending on providing private goods it would further increase income offsetting the C.

There are more nuances, but I think this already well illustrates the complexity of the problem.

Main point is that it is extremely unlikely there would be no change if we deal with distortionary taxes as opposed to non-distortionary taxation.

Moreover, there are further complexities. Overall income and consumption depend both on distribution of income and also on what type of activities is the government funding.


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### Answer by username_3 on 2024-06-05. Score: 1

The first-order effect, as you say, would simply be a transfer from the Government to Households. Consequently, the largest impact will be distributional, which as you say shouldn't have a large effect on the aggregate economy.

However, there are a few additional effects that will impact the economy at large.

1. What is the relative Marginal Propensity to Consume of those receiving the tax income versus the Government?

If the government spends or invests a different proportion of the tax take to those who pay it, you'd expect both supply and demand responses (even if the tax is neither regressive nor progressive, as you specify).

If Consumers spend a higher proportion of the marginal income than the government would, then we would expect a short-run (demand side) expansion in GDP, but a decline in savings (and thus, probably, investment).

This depends crucially on two factors - who gets the money and what the government was spending it on before.

Furthermore, there are some kinds of investment which can realistically *only* be provided by the state (e.g maintenance of the road network, defence etc.). A decline in investment in expenditure of this kind can be expected to cause a long-run decline in GDP due to a weakening of the Supply side of the economy.

2. Income taxes are distortionary.

On the other hand, income taxes are distortionary. Cp, cutting income taxes will encourage labour supply (and other productive activities), expanding the economy relative to prior to the cut. Therefore a shift from government expenditure to tax cuts could stimulate the economy somewhat.


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