Answer to Question #256700 in Microeconomics for anu

Question

Given the following demand and supply equations for tables:

Demand: Qd = 15 - 2P (where "P" is the price per chair; Q is the quantity)

Supply: Qs = 8 + 3P

a) Do the supply and demand equations satisfy the "laws of supply and demand"? Explain [2 points]

b) Determine the equilibrium price and quantity. Show calculations. [3 points]

c) Calculate and indicate on the graph the consumer surplus and producer surplus. [6 points]

c) Assume that demand decreases by 5 (units). Determine the revised demand equation. In addition, determine the new equilibrium price and quantity. Show your work. [4 points]

Answer 1

Solution:

a.). Yes, the supply and demand equations satisfy the laws of supply and demand. That is, as the price of the commodity increases, goods demanded decreases, and the more the goods supplied increase.

 

b.). At equilibrium: Qd = Qs

15 – 2P = 8 + 3P

15 – 8 = 3P + 2P

7 = 5P

P = 1.4

Equilibrium price = 1.4

Substitute in the demand function to derive the equilibrium quantity:

Qd = 15 – 2P = 15 – (2 $\times$ 1.4) = 15 – 2.8 = 12.2

Equilibrium quantity = 12.2

 

c.). The below graph depicts the consumer and producer surplus:

 

Consumer surplus is calculated from the triangle = ½ $\times$ (12.2) $\times$ (7.5 – 1.4) = 37.21

Producer surplus is calculated from the trapezoid = ½ $\times$ (12.2 + 8) $\times$ 1.4 = 14.14

d.). New demand curve: Qd = 10 – 2P

At equilibrium: Qd = Qs

10 – 2P = 8 + 3P

10 – 8 = 3P + 2P

2 = 5P

P = 0.4

New equilibrium price = 0.4

Substitute in the demand function to derive the equilibrium quantity:

Qd = 10 – 2P = 10 – (2 $\times$0.4) = 15 – 0.8 = 14.2

New equilibrium quantity = 14.2