Question

Individuals A and B are the only consumers of good X. Individual A demand for good X is given by: Q = 8 – P and individual B demand for good X is given by: Q = 6 – P. The supply for good X is given by MC = 4. Assume good X is a (pure) public good. Good X equilibrium quantity is [q]. (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. HINT: Sketch the Marshallian “cross” diagram of supply and demand to help you answer this question.)

Answer 1

Both demands are aggregated to get the market demand (Qd).

(8 – P) + (6 – P) = Qd

8 – P + 6 – P = Qd

14 – 2P = Qd

By rearranging, Qd = 14 – 2P

Supply function: Qs = MC = 4

Equilibrium condition: Qd = Qs

14 – 2P = 4

2P = 14 – 4

2P = 10

P = 5

Now by putting this value to Qd function,

Qd = 14 – 2P

Q = 14 – 2 × 5

    = 14 – 10

    = 4

Answer: The equilibrium quantity is 4 units.

Since, Qd = 14 – 2P

If (Qd = 0); 14 – 2P = 0; or P = 7; the coordinate is (0, 7)

If (P = 0); Qd = 14; the coordinate is (14, 0)