Suppose fred ethel ricky and lucy have the following demand functions for a public good
Qf= 40-1/2p
Qe= 20-p
Qr= 30-1/2p
Ql= 50-p
The good can be produced at a constant cost of 5 dollars
Calculate the Lindahl Equilibrium
I know that the lindhal is the vertical summation of each price given a quantity but i have no idea how to calculate the EQ
To calculate the Lindahl Equilibrium, you need to find the total quantity demanded for the public good at a particular price. The Lindahl Equilibrium is the point where the sum of individual demand quantities equals the total quantity needed to provide the public good.
In this case, we have four individuals with their respective demand functions for the public good:
Qf = 40 - (1/2)p
Qe = 20 - p
Qr = 30 - (1/2)p
Ql = 50 - p
To find the total quantity demanded at a given price, we need to sum up the individual demand functions:
QT = Qf + Qe + Qr + Ql
Substituting the individual demand functions, we get:
QT = (40 - (1/2)p) + (20 - p) + (30 - (1/2)p) + (50 - p)
= 40 + 20 + 30 + 50 - (1/2)p - p - (1/2)p - p
= 140 - 3p
Now, we set the total quantity demanded equal to the total quantity needed to provide the public good:
QT = QN
140 - 3p = QN
Since the cost of producing the good is given as $5, we can set the total cost of providing the public good equal to the total quantity needed multiplied by the constant cost:
C = 5 * QN
Now we have two equations:
140 - 3p = QN
C = 5 * QN
Given that the constant cost is $5, we can substitute C = 5 into the second equation:
140 - 3p = 5 * QN
Now we have two equations with two unknowns (p and QN). Solving these equations simultaneously will give us the Lindahl Equilibrium.