<p>Equating supply and demand we obtain the equilibrium</p>

<p>$$P^* = 75, Q^*=100$$</p>

<p>The corresponding diagram is
<img src="https://i.sstatic.net/mxrp8.png" alt="enter image description here"></p>

<p><strong>Consumer Surplus</strong> is the area of triangle $B-E-C$ so</p>

<p>$$CS = \frac 12 \cdot (100-75)\cdot 100 = 1250$$</p>

<p><strong>Producer Surplus</strong> is the area of the triangle $B-E-A$ so</p>

<p>$$PS = \frac 12 \cdot (75-20)\cdot 100 = 2750$$</p>

CC BY-SA 3.0
2015-04-09T13:44:37.810Z
2015-04-09T13:49:39.793Z
2015-04-09T13:49:39.793Z
Alecos Papadopoulos
<p>Inverse function of market demand for certain good is equal to $P=100-0.25Q$, inverse supply function is $P=20+0.55Q$. Calculate equilibrium price and quantity. Furthermore calculate consumer and producer surplus.</p>

<p>Equlibrium price and quantity i think i know how to calculate:
$$20+0.55Q=100-0.25Q$$
and this will be the quantity whereas the price will be (substituting Q with value calculated above): 
20+0.55Q=P
am i correct with this?
I am lost with consumer/producer surplus need more help. 
edit: I have and idea about consumer/producer surplus:
consumer:
$0.5 \times 100 \times 25=1250$ and producer $100 \times 55 \times 0.5=2750$
is this correct?</p>

CC BY-SA 3.0
2015-04-08T19:56:21.150Z
When you are lucky enough to deal with affine/linear functions, it is a pity not to draw diagrams, to see for your eyes consumer and producer surplus, before calculating numerical values.
Alecos Papadopoulos
CC BY-SA 3.0
2015-04-09T11:30:56.053Z
but am i right or wrong with my solutions?
Krowskir
CC BY-SA 3.0
2015-04-09T12:37:33.227Z
The price and quantity are obviously correct. For the surpluses I don't know -draw the diagrams and you will figure it out.
Alecos Papadopoulos
CC BY-SA 3.0
2015-04-09T13:09:18.953Z
I have the diagram and what i have calculated is the area of those two triangles that on the graph should represent consumer and producer surplus. Nevertheless thank you for your answer.
Krowskir
<microeconomics><general-equilibrium><producer-theory><consumer-surplus><producer-surplus>
Equilibrium price and quantity - consumer and producer surplus
Krowskir
# Equilibrium price and quantity - consumer and producer surplus

(Asked by: username_0 on 2015-04-08)

Inverse function of market demand for certain good is equal to $P=100-0.25Q$, inverse supply function is $P=20+0.55Q$. Calculate equilibrium price and quantity. Furthermore calculate consumer and producer surplus.

Equlibrium price and quantity i think i know how to calculate:
$$20+0.55Q=100-0.25Q$$
and this will be the quantity whereas the price will be (substituting Q with value calculated above):
20+0.55Q=P
am i correct with this?
I am lost with consumer/producer surplus need more help.
edit: I have and idea about consumer/producer surplus:
consumer:
$0.5 \times 100 \times 25=1250$ and producer $100 \times 55 \times 0.5=2750$
is this correct?

**Tags:** microeconomics, general-equilibrium, producer-theory, consumer-surplus, producer-surplus

> **Comments:**
> **username_1**: When you are lucky enough to deal with affine/linear functions, it is a pity not to draw diagrams, to see for your eyes consumer and producer surplus, before calculating numerical values.  
> **username_0**: but am i right or wrong with my solutions?  
> **username_1**: The price and quantity are obviously correct. For the surpluses I don't know -draw the diagrams and you will figure it out.  
> **username_0**: I have the diagram and what i have calculated is the area of those two triangles that on the graph should represent consumer and producer surplus. Nevertheless thank you for your answer.  

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## 1 answers

### Answer by username_1 on 2015-04-09. Score: 1 | Accepted answer

Equating supply and demand we obtain the equilibrium

$$P^\* = 75, Q^\*=100$$

The corresponding diagram is
![enter image description here](https://i.sstatic.net/mxrp8.png)

**Consumer Surplus** is the area of triangle $B-E-C$ so

$$CS = \frac 12 \cdot (100-75)\cdot 100 = 1250$$

**Producer Surplus** is the area of the triangle $B-E-A$ so

$$PS = \frac 12 \cdot (75-20)\cdot 100 = 2750$$


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