question archive You are hired as a consultant for a municipality, and asked to help determine how the city should price water from a surface water source for two users: Person A and Person B
You are hired as a consultant for a municipality, and asked to help determine how the city should price water from a surface water source for two users: Person A and Person B
Subject:EconomicsPrice:3.87 Bought7
You are hired as a consultant for a municipality, and asked to help determine how the city should price water from a surface water source for two users: Person A and Person B. Both users extract the water for consumptive-use. Assume that the city only needs to be concerned with current use (i.e. this surface water source is completely renewable from one period to the next). You are told that the marginal cost of supplying this water to Person A and Person B is constant at $5 per unit (i.e. MC = 5). You are able to determine that Person A’s inverse demand function for water can be represented by P = 15 –2Q, and Person B’s inverse demand function for water can be represented by P = 25 –2Q.
If the fixed supply of water is 20 units, what is the efficient allocation for person A? What is the efficient allocation for person B?
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
Answer:
We are given inverse demand functions for Person A and Person B. Also, we are given the marginal costs.
Inverse demand function
Person A
P= 15 - 2 Q
Person B
P = 25 - 2 Q
Marginal cost
$5 per unit
Also, total quantity(Q) is given as 20.
This is the case of price discrimination wherein the same product is sold at different prices having being given two inverse demand functions. Thus, efficient allocation would require the profits to be maximized. The condition for profit maximization would be as following:
Max( TR-TC)
where TR is the Total Revenue and TC is the Total Cost
TR = P x Q
TR (for person A) = (15 - 2 Q) x Q
= 15 Q - 2 Q2
TR (for person B) = [25 - 2 (20 - Q)] x (20 - Q) Because, [ We are given Q = 20]
= (25 - 40 + 2 Q ) x (20 - Q)
= (- 15 + 2 Q) x (20 - Q)
= -300 + 15 Q + 40 Q - 2 Q2
= - 300 + 55 Q - 2 Q2
TC = 5Q
To maximize:
[ 15 Q - 2 Q2 - 300 + 55 Q - 2 Q2 ] - 5(20)
differentiating w.r.t Q
15 - 4 Q + 55 - 4 Q
equating to 0
70 - 8 Q = 0
Q = 70/8
= 8.75
thus, efficient allocation for person A is 8.75 units
For person B: 20- 8.75
= 11.25 units
