Individuals A and B are the only consumers of good X. Individual A demand for go
ID: 1207709 • Letter: I
Question
Individuals A and B are the only consumers of good X. Individual A demand for good X is given by: Q = 4 – P and individual B demand for good X is given by: Q = 8 – 2P. The supply for good X is given by MC = 3. Assume good X is a (pure) public good. Let Lindahl price for individual A equal to individual A valuation (P) of quantity Q* and Lindahl price for individual B equal to individual B valuation (P) of quantity Q*. Individual A will be charged ________ and individual B will be charged __________ for the same equilibrium quantity Q* of the public good they both consume. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands. HINTS: Sketch the Marshallian “cross” diagram of supply and demand to help you answer this question. To find the Lindahl prices, substitute Q* in each individual demand and, for each, solve for P.) Show all steps.
Explanation / Answer
Equilibrium quantity will be attained where MR = MC
TR of Individual A and B = P.Q = (4 - Q)Q + (4 - 0.5Q)Q = 4Q - Q2 + 4Q - 0.5Q2 = 8Q - 1.5Q2
MR = 8 - 3Q
MC = 3
therefore, by equating MR and MC, we get
8 - 3Q = 3
11 = 3Q
Q* = 3.67
Individual A will charge : P = 4 - Q = 4 - 3.67 = $ 0.33
Individua B will charge : 2P = 8 - 3.67
2P = 4.33
P = $ 2.165