Equilibrium Conditions - Concept and Numerical Problems

Equilibrium Conditions 

A system can be said to be in equilibrium when the various important variables in it show no change, and when there are no pressures or forces working which will cause any change in the values of important variables. 

By consumer’s equilibrium, we mean that regarding the allocation of money expenditures among various goods, the consumer has reached the state where he has no tendency to re-allocate his money expenditure. 

A firm is said to be in equilibrium when it has no tendency to change its level of output, that is, when it has no tendency either to increase or to contract its level of production. 

Equilibrium in economic activities may never be realized in actual practice. But the importance of the equilibrium analysis lies in the fact that if other things remain the same, the economy would tend towards the equilibrium values. What happens is that before the final equilibrium is reached changes occur in the determining factors so that the system tends to move towards new equilibrium value corresponding to the new changed conditions. 

Market Equilibrium Condition:

Quantity demanded = Quantity supply

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NP1: Given the market equilibrium model:

Demand Function: Qd = 50 - 5P

Supply Function: Qs = - 10 + 10 P

Find the equilibrium price and quantity

Solution:

Given:

Demand Function: Qd = 50 - 5P

Supply Function: Qs = - 10 + 10 P

To Find: Equilibrium price, P* and quantity, Q*

 At Equilibrium:

$Q_d = Q_s$

$$50-5P=-10+10P$$

$$50+10=10P+5P\Rightarrow 60=15P$$

$$P^* = \frac{60}{15} = 4$$

Substitute into either $Q_d$ or $Q_s$ to find $Q^*$.
Using $Q_d = 50 - 5P$:

Q*=50 − 5(4) = 50−20 =30

∴ Equilibrium price, P*= 4 and quantity, Q*= 30

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NP2: Given the market equilibrium model:

Demand Function: Qd = 21 - 3P

Supply Function: Qs = - 4 + 8P

Find the equilibrium price and quantity

Solution:

Given:

Demand Function: Qd = 21 - 3P

Supply Function: Qs = - 4 + 8P

To Find: Equilibrium price, P* and quantity, Q*

 At Equilibrium:

$Q_d = Q_s$

$$21-3P=-4+8P$$

$$21+4=8P+3P\Rightarrow 25=11P$$

$$$$

Substitute into either $Q_d$ or $Q_s$ to find $Q^*$.
Using  Qd = 21 - 3P:

∴ Equilibrium price, P*= 25/11 and quantity, Q*= 156/11 

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NP3: Given the market equilibrium model:

Demand Function: Qd = 60- 4P

Supply Function: Qs = 10 + 6P

Find the equilibrium price and quantity

Solution:

Given:

Demand Function: Qd = 60 - 4P

Supply Function: Qs = 10 + 6P

To Find: Equilibrium price, P* and quantity, Q*

 At Equilibrium:

$Q_d = Q_s$

$$\mathrm{60-4P}=10+6P$$

$$60-10=6P+4P\Rightarrow 50=10P$$

$$P^{\ast }=5$$

Substitute into either $Q_d$ or $Q_s$ to find $Q^*$.
Using Qd = 60 - 4P

Q*=60-4(5) = 60−20=40

∴ Equilibrium price, P*= 5 and quantity, Q*= 40

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