Question

Suppose that the market for water is perfectly competitive. Demand is described by Q = 13-P, and supply by P = 1 + (Q/2)

Answer 1

Assuming the question is asking on the equilibrium quantity and price.

The market is perfectly competitive. Thus, the equilibrium point will be determined at the point where the quantity demanded is equal to the quantity supplied.

The demand curve is:

$$Q = 13 - P$$

And the supply curve is:

$$P = 1 +\dfrac{Q}{2}$$

Solving the two equations simultaneously, we get:

$$P = 1 + \dfrac{13 - P}{2}$$

$$P = 1 + 7.5 - 0.5P$$

$$1.5P = 8.5$$

The equilibrium price of water is:

$$P^* = \dfrac{8.5}{1.5} \approx \$5.67$$

The equilibrium quantity of water is:

$$Q^* = 13 - 5.67 = 7.33$$