Answer to Question #275695 in Microeconomics for David

Question

D.What is the consumer and producer surplus when the market for toasters is in equilibrium (when the quantities supplied is equal to the quantities demanded)? The inverse demand function is p = 60 - Q and the supply function is Q = 10 + p. Explain your result and draw a very precise graph of the demand and supply functions to show your results.

E. Suppose that the inverse demand function has become p = 80 - Q due to changes in the consumer income but no change in the supply function, Q = 10 + p. What is the new consumer and producer surplus when the market for toasters is in equilibrium (when the quantities supplied is equal to the quantities demanded)? Compare your result with the one you have obtained in (d) and explain the changes in consumer and producer surplus and show it on a diagram

Answer 1

Solution:

D.). Inverse demand function: P = 60 – Q

Derive the demand function: Q = 60 – P

Supply function: Q = 10 + P

At equilibrium: Qd = Qs

60 – P = 10 + P

60 – 10 = P + P

50 = 2P

P = 25

Equilibrium price = 25

Substitute in the demand function to derive equilibrium quantity:

Qd = 60 – P

Qd = 60 – 25 = 35

Equilibrium quantity = 35

 

Consumer surplus = ½ $\times$ 35 $\times$ (60 – 25) = 612.5

Producer surplus = ½ $\times$ (35 + 10) $\times$ 25 = 562.5

 

This is depicted by the below graph:

 

E.). Inverse demand function: P = 80 – Q

Derive the demand function: Q = 80 – P

Supply function: Q = 10 + P

At equilibrium: Qd = Qs

80 – P = 10 + P

80 – 10 = P + P

70 = 2P

P = 35

Equilibrium price = 35

Substitute in the demand function to derive equilibrium quantity:

Qd = 80 – P

Qd = 80 – 35 = 45

Equilibrium quantity = 45

 

Consumer surplus = ½ $\times$ 45 $\times$ (80 – 35) = 1012.5

Producer surplus = ½ $\times$ (45 + 10) $\times$ 35 = 962.5

 

This is depicted by the below graph:

 

 

 

Both the consumer surplus and producer have increased massively from the d result as a result of the demand change.