<p>Your second answer is correct. The problem your first approach has, is that you assume that you may only buy a discrete amount of goods. However, your demand curve is continuous and the usual assumption in microeconomics is that you can consume any amount of this good, for instance $1.478926574$ units. Thus, your first calculation for the surplus is not correct, the correct way to do it is</p>

<p>$$CS = \int_{5}^{10} (10-p) \mathcal{d}p = 10p-\dfrac{p^{2}}{2}|^{10}_{5} = 100-50-50+12.5=12.5$$</p>

<p>This result is equal to the second calculation of yours simply by the fact that it is a triangle. If demand wouldn't be linear, you'd have to use the integral form to calculate CS.</p>

CC BY-SA 4.0
2018-05-05T13:41:13.063Z
thank you for your answer, so that is the fundamental difference. Could you maybe try to explain why surplus should be smaller in the case of continuous consumption?
user18214
CC BY-SA 4.0
2018-05-05T14:46:14.003Z
Just draw the graphs, for discrete consumption and for continuous consumption. The demand function in your case always cuts off 0.5 of your CS below the bars you constructed. Note: through your calculations you already assumed how the discrete demand looks like. The first bar is equal to $p=10$ for values between $0$ and $1$ on your $q$-axis, $p = 9$ for $q$ between $1$ and $2$, and so on.
saguru
CC BY-SA 4.0
2018-05-05T14:48:28.927Z
so for discrete demand you're getting $0.5$ CS more per unit, which equals $2.5$ for $q=5$.
saguru
CC BY-SA 4.0
2018-05-05T15:38:25.400Z
you're very welcome
saguru
CC BY-SA 4.0
2018-05-05T12:49:15.923Z
2018-05-05T12:49:15.923Z
saguru
<p>let's say we have a consumer with a demand curve <span class="math-container">$q^d(p)=10-p$</span> and the good its price is <span class="math-container">$5$</span>. So the consumer will consume 5 units. The surplus of the consumer would then be equal to <span class="math-container">$(10-5)+(9-5)+(8-5)+(7-5)+(6-5) = 5+4+3+2+1 = 15$</span>. However, when solving this in the conventional manner it gives me <span class="math-container">$(10-5)\times 5/2 = 12.5$</span></p>
<p>What am I doing wrong? Or is surplus just an approximation?</p>

<microeconomics>
is surplus just an approximation?
user18214
# is surplus just an approximation?

(Asked by: username_0 on 2018-05-05)

let's say we have a consumer with a demand curve $q^d(p)=10-p$ and the good its price is $5$. So the consumer will consume 5 units. The surplus of the consumer would then be equal to $(10-5)+(9-5)+(8-5)+(7-5)+(6-5) = 5+4+3+2+1 = 15$. However, when solving this in the conventional manner it gives me $(10-5)\times 5/2 = 12.5$

What am I doing wrong? Or is surplus just an approximation?

**Tags:** microeconomics

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## 1 answers

### Answer by username_1 on 2018-05-05. Score: 5 | Accepted answer

Your second answer is correct. The problem your first approach has, is that you assume that you may only buy a discrete amount of goods. However, your demand curve is continuous and the usual assumption in microeconomics is that you can consume any amount of this good, for instance $1.478926574$ units. Thus, your first calculation for the surplus is not correct, the correct way to do it is

$$CS = \int\_{5}^{10} (10-p) \mathcal{d}p = 10p-\dfrac{p^{2}}{2}|^{10}\_{5} = 100-50-50+12.5=12.5$$

This result is equal to the second calculation of yours simply by the fact that it is a triangle. If demand wouldn't be linear, you'd have to use the integral form to calculate CS.

> **Comments:**
> **username_0**: thank you for your answer, so that is the fundamental difference. Could you maybe try to explain why surplus should be smaller in the case of continuous consumption?  
> **username_1**: Just draw the graphs, for discrete consumption and for continuous consumption. The demand function in your case always cuts off 0.5 of your CS below the bars you constructed. Note: through your calculations you already assumed how the discrete demand looks like. The first bar is equal to $p=10$ for values between $0$ and $1$ on your $q$-axis, $p = 9$ for $q$ between $1$ and $2$, and so on.  
> **username_1**: so for discrete demand you're getting $0.5$ CS more per unit, which equals $2.5$ for $q=5$.  
> **username_1**: you're very welcome  

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