Question

A. If the inverse demand function for toasters is p = 60 - Q , what is the consumer surplus if price (p) is $30? Explain your result and show it very precisely on a diagram.

B. If the inverse demand function for toasters is p = a - b Q , what is the consumer surplus if price is a 2 ? Show it very precisely on a diagram and explain how changes in the constant term (a) and the coefficient of Q (b) cause an increase in the consumer surplus . C. If the supply function for toasters is Q = 10 + p, what is the producer surplus if price is 20? Explain your result and show it on a diagram.

Answer 1

Solution:

A.). P = 60 – Q

Given that the inverse demand function is P=60-Q:

Demand function: Q = 60 – P

P = 30

Q = 60 – 30 = 30

Consumer Surplus = ½ $\times$ 30 $\times$ (60 – 30) = 450

This is depicted by the below graph:

 

B.). i.). P = a – Bq

Q = $\frac{a}{b} - \frac{P}{b}$

P = $\frac{a}{2}$

Q = $\frac{a}{b} - \frac{(a\div 2) }{b} = \frac{a}{2b}$

Consumer surplus = ½ $\times$ ($\frac{a}{2b}$ ) $\times$ (a – $\frac{a}{2}$) = $\frac{a^{2} }{8b}$

This is depicted by the below graph:

 

ii.). Q = 10 + P

P = 20

Q = 10 + 20 = 30

Producer Surplus = ½ $\times$ (30 + 10) $\times$ 20 = 400

This is depicted by the below graph: