<p>Diminishing marginal utility is an ordinal property which has no effect whatsoever on the specification of demand functions. While <span class="math-container">$u(x,y)=x^{1/2}y^{2/3}$</span> exhibits diminishing marginal utility (in both <span class="math-container">$x$</span> and <span class="math-container">$y$</span>), <span class="math-container">$v(x,y)=(u(x,y))^{10}$</span> has increasing marginal utility, but both utility functions yield the same demand system.</p>
<p>A related discussion is available here:
<a href="https://economics.stackexchange.com/questions/51569/diminishing-marginal-utility-role-in-downward-sloping-demand-curve/51666#51666">Diminishing marginal utility role in downward sloping demand curve</a></p>
<p>A generalization to take into account habits and the influence of past consumption could be provided by the utility function <span class="math-container">$U(x_t,y_t,x_{t-1},y_{t-1})$</span> which generates a demand system depending upon <span class="math-container">$x_{t-1},y_{t-1}$</span>, and the cross derivative of <span class="math-container">$U$</span> wrt <span class="math-container">$x_t$</span>, and <span class="math-container">$x_{t-1}$</span> may correspond to what you are looking for, but this is not really related to &quot;diminishing marginal utility&quot; as <span class="math-container">$x_t$</span>, and <span class="math-container">$x_{t-1}$</span> are indexed by different periods, they are not strictly speaking the same commodity.</p>

CC BY-SA 4.0
2022-12-27T19:59:54.683Z
2022-12-27T20:07:58.750Z
2022-12-27T20:07:58.750Z
Bertrand
<blockquote>
<p>as they consume more, they get less and less utility from consumption and therefore at a certain point no longer want to consume</p>
</blockquote>
<p>A series/function can converge to zero without becoming negative; thus decreasing marginal utility does not in itself imply satiation.</p>

CC BY-SA 4.0
2022-12-26T19:48:28.777Z
2022-12-26T19:48:28.777Z
Giskard
<p>So the cobbs douglas demand system indicates that  the consumption of the capitalist class can be modeled as C=(1+r)K where r represents net profit for that time period, K represents capital stock of that time period and C represents consumption</p>
<p>What I want to know is, how do you properly incorporate the law of diminishing marginal utility into this?</p>
<p>So let's say the capitalist class has a constant population, or at least very little growth. An increase in production from one period to the next means more goods are produced. These goods will be consumed by both the laboring class, who spends the whole wage, and the capitalist class who spends a portion of profit on consumption. However, as the capitalist class consumes more, shouldn't individuals within that class experience decreasing marginal utility for general levels of consumption? As the class has a constant population, wouldn't that mean consumption would eventually drop off? So like, as they consume more, they get less and less utility from consumption and therefore at a certain point no longer want to consume?</p>
<p>I don't see that in the consumption function, as it does not account for past consumption.</p>
<p>Am I missing something? Where is diminishing marginal utility incorporated in the cobbs douglas demand system?</p>

<macroeconomics><consumption>
How does the Cobbs-Douglas Demand system account for diminishing marginal utility?
Robotic_Cow
# How does the Cobbs-Douglas Demand system account for diminishing marginal utility?

(Asked by: username_0 on 2022-12-26)

So the cobbs douglas demand system indicates that the consumption of the capitalist class can be modeled as C=(1+r)K where r represents net profit for that time period, K represents capital stock of that time period and C represents consumption

What I want to know is, how do you properly incorporate the law of diminishing marginal utility into this?

So let's say the capitalist class has a constant population, or at least very little growth. An increase in production from one period to the next means more goods are produced. These goods will be consumed by both the laboring class, who spends the whole wage, and the capitalist class who spends a portion of profit on consumption. However, as the capitalist class consumes more, shouldn't individuals within that class experience decreasing marginal utility for general levels of consumption? As the class has a constant population, wouldn't that mean consumption would eventually drop off? So like, as they consume more, they get less and less utility from consumption and therefore at a certain point no longer want to consume?

I don't see that in the consumption function, as it does not account for past consumption.

Am I missing something? Where is diminishing marginal utility incorporated in the cobbs douglas demand system?

**Tags:** macroeconomics, consumption

---

## 2 answers

### Answer by username_1 on 2022-12-27. Score: 1 | Accepted answer

Diminishing marginal utility is an ordinal property which has no effect whatsoever on the specification of demand functions. While $u(x,y)=x^{1/2}y^{2/3}$ exhibits diminishing marginal utility (in both $x$ and $y$), $v(x,y)=(u(x,y))^{10}$ has increasing marginal utility, but both utility functions yield the same demand system.

A related discussion is available here:
[Diminishing marginal utility role in downward sloping demand curve](https://economics.stackexchange.com/questions/51569/diminishing-marginal-utility-role-in-downward-sloping-demand-curve/51666#51666)

A generalization to take into account habits and the influence of past consumption could be provided by the utility function $U(x\_t,y\_t,x\_{t-1},y\_{t-1})$ which generates a demand system depending upon $x\_{t-1},y\_{t-1}$, and the cross derivative of $U$ wrt $x\_t$, and $x\_{t-1}$ may correspond to what you are looking for, but this is not really related to "diminishing marginal utility" as $x\_t$, and $x\_{t-1}$ are indexed by different periods, they are not strictly speaking the same commodity.


---

### Answer by username_2 on 2022-12-26. Score: 1

> as they consume more, they get less and less utility from consumption and therefore at a certain point no longer want to consume

A series/function can converge to zero without becoming negative; thus decreasing marginal utility does not in itself imply satiation.


---

