Question

1.       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) private 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

To get the equilibrium quantity [q], the total quantity demanded in the economy must be equal to the total quantity supplied.

Demand Side: In this economy, there are only two individuals, A and B. For good X, demand curve of A is Q = 4 - P, and demand curve of B is Q = 8 - 2P.

The total demand in the economy would then be (Demand of good X by A) + (Demand of good X by B).

Say the total demand for good X in the economy is [q^d]. Then,

Supply Side: In this economy, the supply of good X is given by MC = 3

MC means Marginal Cost, i.e. the cost of producing an additional unit of the good. Therefore, the given case is an example of "Perfect Competition" where competition between suppliers keeps the price per unit equals to the MC. In other words, 1 unit of good X will be supplied for $3, 2 units of good X will be supplied for $6 and so on.

Now suppose that the total quantity supplied of good X is q^s. Then,

Equilibrium: Put q^d = q^s to get q

Therefore, the equilibrium quantity of good X is 1.20 units