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Definition of Market equilibrium demand and supply graph consumer producer surplus

 “In this section, we have covered a few topics including demand and supply curves equations, market equilibrium, demand and supply curves graphs, consumer and producer surplus and social surplus.”

full topic market equilibrium


Supply Curve Equation:

Supply Equation = Q(s) = -a +b (P).

Supply Equation = S (Q) = P(s) = a +b (Q).

Where a is the intercept, b is the slope of supply curve, Q and P represent Quantity and price respectively.

Demand Curve Equation:

Demand Equation = Q (d) = a - b (P).

Demand Equation = D (Q) = P (d) = a -b (Q).

Where a is the intercept, b is the slope of the demand curve, Q and P represent Quantity and price respectively.

What is Market Equilibrium?

Let’s suppose we have demand and supply equations as given below respectively;

Demand Equation = d(q) = P = -0.8q+150                        (1)

Supply equations= S(q) = P = 5.2q                          (2)

Where “q” is the quantity and “p” is the price.

Equilibrium point/Market Equilibrium is the point where d(q) and S(q) becomes equal.

Equation (1) = Equation (2)

d(q) = S(q)

-0.8q+150 = 5.2q

5.2q+0.8q = 150

6q = 150

q = 150/6 = 25

put q = 25 in equation (2)

Eq (2)               P = 5.2 (25) = 130

Market equilibrium point is (25 , 130).

How to find and calculate market Equilibrium price and quantity on graph?


Demand and Supply Graphs Curves:

We can draw demand and supply curves in the event that we have either demand and supply equations or a table of quantities and prices for both curves. Here below we mapped demand and supply curves through demand and supply equations that we supposed above to find market equilibrium. You can see below that we found out prices for a different number of quantities from the demand and supply equations and wrote them in tables. Then, the points in both tables are plotted on the graphs to draw the curves. The more the points i.e. (quantities, price), the more curves will accurate. But if we have already been given a table of quantities and prices for both curves, it will be easier for us to draw demand and supply curves.

 

Demand Curve:

Demand Equation = d(q) = P = -0.8q+150

QUANTITY (q)

PRICE(P)

0

150

25

130

50

110

75

90

150

30

175

10



Supply Curve:

Supply equations= S(q) = P = 5.2q

QUANTITY(q)

PRICE(P)

0

0

1

5.2

25

130

50

260


How to identify Supply and Demand Tables and How to draw demand and supply curves through the table:

Suppose we have been given two tables and we are asked to explain which table represents demand and which one supply and also to draw demand and supply curves after you identified and explained which the table represents what. First of all, in order to draw, you must understand which the table represents demand and which one supply. Now, how will you identify?

 Let's understand it with the help of an example. Suppose we have two tables as given below;



The first table represents demand because it is clear form this table that a decrease in price increases the quantity of a product or the table shows an inverse relationship between the quantity and price. More it will become clear through a chart that will show an inverse relation between quantity and price for a product.

Similarly, the second table represents the supply because there is a direct relationship between quantity and price. Quantity increases with an increase in price. It will be proved through the chart that will show the direct relationship between quantity and price.

Now we can draw demand and supply curves, which are for the above tables are as follows respectively;



How to find  market equilibrium through demand and supply tables:

Let's say we have a demand table;



And supply table;




If we are provided by the demand and supply the table then we may be able to find market equilibrium through the given demand and supply tables. For example from the above demand and supply tables, we can find market equilibrium. The market equilibrium will be the point that is present in both demand and supply tables which is in this case (400,40). But this is not applicable on all demand and supply tables. We may have given market equilibrium in the table and if not then plot both curves on the same graph and see where both curves meet.

Consumer Surplus:

“It is the area of the region above the equilibrium price and below the demand curve.”

Producer Surplus:

“It is the area of the region above the supply curve and below the equilibrium price.”

In the below table, the area similar to the shape of a triangle which contains an arrow CS is consumer surplus while the area similar to the shape of a triangle which contains arrow PS is producer surplus.




How to Find Consumer and Producer Surplus?

CASE 1:

In the simple case where demand and supply curves are actually not curves but straight lines as showing in the below graph titled market equilibrium. We can find consumer and producer surplus by simply calculating the area of triangles showing the consumer and producer surplus as shown in the below graph through the yellow and blue triangle. Now, the consumer and producer surplus for the below graph are as follows;




Consumer Surplus:

“The consumer surplus at the equilibrium point is the area of the blue triangle”

From chart, it is clear that the base of the triangle=25 while height of the triangle =150-130=20.

Consumer surplus= Area of blue triangle.

Consumer surplus=(1/2)(base)(height).

Consumer surplus=(1/2)(25)(20).

Consumer surplus=250.

 

Producer Surplus:

“The producer surplus at the equilibrium point is the area of the yellowish triangle.”

From chart, it is clear that the base of the triangle=130 while height of the triangle =25.

Producer surplus= Area of yellowish triangle.

Producer surplus=(1/2)(base)(height).

Producer surplus=(1/2)(130)(25).

Producer surplus=1625.

 

CASE2:

In the second case where demand and supply curves are not straight lines as showing in the below graph titled market equilibrium. We can find consumer surplus by calculating area below the demand curve and above the equilibrium price. Similarly, producer surplus can be finding by calculating area above the supply curve and below the equilibrium price.

Lets comprehend it with the assistance of associate example.



Here in the graph you can see that supply and demand curves are not straight lines. So you can not calculate the consumer and producer surplus by the formula for area of the triangle. As we’ve performed in the first case. However we can find consumer and producer through the integrating formulas as calculated below for the above graph;

 

Consumer Surplus:

Demand Equation = Q(d) = a - b (P).

Demand Equation = D(Q) = P(d) = a -b(Q).

Where a is the intercept, b is the slope of demand curve, Q and P represent Quantity and price respectively.

From table and graph a = 70 and b= ∆P/∆Q = (P2 – P1)/(Q2 – Q1) = (70-40)/(400-0) = 0.075.

Right Arrow:                   P(d) = 70 – (0.075)(Q).

Formula of Consumer surplus

Where Pe and Qe are the equilibrium price and quantity. D(Q) is the demand equation.

Consumer surplus = 70(400) – (0.075/2)(400)2 – (400)(40).

Consumer surplus = 28000 – 6000 – 16000.

Consumer surplus = 6000.

 

Producer Surplus:.

Supply Equation = Q(s) = -a +b(P).

Supply Equation = S(Q) = P(s) = a +b(Q).

Where a is the intercept, b is the slope of supply curve, Q and P represent Quantity and price respectively.

From table and graph a = 14 and b= ∆P/∆Q = (P2 – P1)/(Q2 – Q1) = (40-15)/(400-0)  = 0.0625.

Right Arrow:                   P(s) = 14 + (0.0625)(Q).

Formula of Producer Surplus

Where Pe and Qe are the equilibrium price and quantity. S(Q) is the supply equation.




Producer Surplus = 16000 – (14(400) + (0.0625/2)(400)2) = 16000-10800 = 5400.

 

Definition of Social Surplus:

It is defined as the sum of the consumer and the producer surplus.

So, for the above example, social surplus is 11400. 


Conclusion

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