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Homework answers / question archive / Let O be a public good consumed by consumers A, B and C whose (inverse) demands for Q are: PA= 320 - 20: PB = 240-29and Pc = 200 -0
Let O be a public good consumed by consumers A, B and C whose (inverse) demands for Q are: PA= 320 - 20: PB = 240-29and Pc = 200 -0. Suppose the cost of each unit of Q is $200. a. What is the efficient quantity of O to be consumed by these consumers? b. What are the "Lindahl prices" that would allow the efficient quantity to be consumed?
The three inverse demand function are given as,
PA = 320 - 2Q
PB = 240 - 2Q
PC = 200 - Q
Where A, B , C are the consumers and cost of each unit of Q is $200
Thus, Marginal Cost (MC) = 200
Since, PA , PB and PC are different so in order to get Total P,
P = PA + PB + PC
= 320 - 2Q + 240 - 2Q + 200 - Q
= 760 - 5Q
a. In order to get efficient quantity of Q, P = MC must be satisfied.
P = 760 - 5Q and MC = 200
Setting, P = MC
760 - 5Q = 200
5Q = 760 - 200
5Q = 560
Q* = 560 / 5
= 112
Hence, the efficient quantity of Q to be consumed by the consumers is Q* = 112
b. If Q* is set at each consumer's inverse demand then this is called Lindahl Prices.
For A,
PA = 320 - 2Q* = 320 - 2*112 = $96
For B,
PB = 240 - 2Q* = 240 - 2*112 = $16
For C,
PC = 200 - Q* = 200 - 112 = $88
