A5 Suppose that the demand data are 7 5 3 and the supply equ

A.5. Suppose that the demand data are: 7 5 3 and the supply equation is: P Q. a. Find the demand equation b. Calculate the equilibrium price and quantity, and consumer surplus and producer surplus. c. Suppose government imposes per unit tax of $2 on consumers. Derive the new demand curve and also calculate the new equilibrium price and quantity. Calculate the tax revenue and the deadweight loss of this tax. d.

Solution

a.

Since the demand function is linear, we know that it can be written in slope-intercept form as p = mQ + b

We have to find m(slope) and intercept from the data points given

7 = m(1) +b --> m=7-b

5= m(3) + b ---> m= (5-b)/3

Using above we equate 7-b = (5-b )/3 --> 21-3b = 3-b --> 2b= 18 ---> b= 9

Substitute the values in eqn 3=m(5) + b we get 3=5m+9 or m= -1.2

Hence the demand equation would be p = -1.2Q + 9

b.At equilibrium demand = supply

hence equating we get ; -1.2Q + 9 = Q --> 4.09 rounded off to 4 Equilibrium quantity is 4

To get equilibrium price substitute the value of 4 in demand equation we get 4.2 which is the equilibrium price