### Example: In a hypothetical market

Demand is given by: $P=100-2{Q}_{d}$

Supply is given by: $P=10+{Q}_{s}$

- What is the competitive market equilibrium, the consumer surplus and the producer surplus?
- Given the data from Question 1, how much wealth will a consumer make if his willingness to pay is 70? 40? 30?
- Given the data from Question 1, how much wealth will a producer make if his willingness to accept is 70? 40? 30?

### Part 1)

At equilibrium, supply equals demand (both quantity and price). So, first, we need to equate the supply and demand functions and find the equilibrium price and quantity $(Q*,P*)$ .

$$P=100-2{Q}_{d}$$

$$P=10+{Q}_{s}$$

Then,

$$100-2{Q}_{d}=10+{Q}_{s}$$At equilibrium

$${Q}_{d}={Q}_{s}$$

$$100-10=Q+2Q$$$$90=3Q$$

Then, equilibrium quantity will be $Q*=\frac{90}{3}=30$

By plugging equilibrium quantity ($Q*$ ) in one of the supply or demand equations (doesn’t matter which one, we should get the same answer), we will find the equilibrium price ($P*$ ):

$${P}_{d}=100-2{Q}_{d}$$

$$P*=100-2\left(30\right)=40$$

The next step will be calculating the CS and PS at market equilibrium $(Q*,P*)$ :

$$CS=\frac{\left(100-40\right)\left(30-0\right)}{2}=900$$ $$PS=\frac{\left(40-10\right)\left(30-0\right)}{2}=450$$And total wealth created by the market

$$\text{TotalWealth}=CS+PS=900+450=1350$$Note for review: Here are the steps in calculating the equlibrium, consumer surplus, and producer surplus:

- P* and Q* can be calculated by solving the supply and demand system of equations for P and Q, which give P* = 40 and Q* = 30
- Consumer surplus is the area of triangle above the P* and below the demand curve (yellow triangle): area = base times height/2
- base of this triangle = Q* = 30
- height = P
_{1}- P*

P_{1}is the intercept of demand function. So, we can find P_{1}by plugging Q = 0 into the demand function.

P_{1}= 100 - 2*0 = 100

Then, height = 100 - 40 = 60 - Consumer Surplus = area of yellow triangle = base * height/2 = (30 * 60)/2 = 900

- Producer surplus, is the area of triangle below the P* and above the supply curve (red triangle): area = base times height/2
- base of the red triangle = Q* = 30
- height of the red triangle = P* - P
_{2} - P
_{2}is the intercept of the supply curve. So, we just need to plug Q = 0 into the supply function to find the P_{2}.

P_{2}= 10 + 1*0 = 10

So, height of the red triangle = P* - P2 = 40 - 10 = 30 - Producer Surplus = area of red triangle = base * height/2 = (30*30)/2 = 450

### Part 2)

$\text{Maximum willingness to pay}=70$ : the consumer will make $70-40=30$

$\text{Maximum willingness to pay}=40$ : the consumer will make $40-40=0$

$\text{Maximum willingness to pay}=30$ : the consumer will not buy the good because willingness to pay > price

### Part 3)

$\text{Minimum willingness to accept}=70$ : the producer will not sell the good because willingness to accept < price

$\text{Minimum willingness to accept}=40$ : the producer will make $40-40=0$

$\text{Minimum willingness to accept}=30$ : the producer will make $40-30=10$

#### Practice Exercise

Assume In a hypothetical market demand and supply functions for a good are

Demand: $P=60-5{Q}_{d}$

Supply: $P=20+{\mathrm{3Q}}_{s}$

Calculate the competitive market equilibrium, consumer surplus, producer surplus, and total wealth created by the market.

### Take Aways

After working through the material on this page and reading the associated textbook content, you should be able to confidently:

- calculate the consumer surplus created by a single trade and by a market;
- calculate the producer surplus created by a single trade and by a market;
- calculate the total wealth created by a single trade and by a market;
- understand why a buyer decides to enter the market (or not);
- understand why a seller decides to enter the market (or not);
- understand why there are no trades to the right of the equilibrium.