Question

You are interested in buying a new cell phone and consumers are willing to pay N$3 000.00.
The demand function for a cell phone is Qd = 1500 - 0.5 P
The supply function is Qs = 500 + 0.5 P
a) Calculate consumers surplus.
b) if the market price increases by 25 % and quantity sold decreases by 12 %, calculate the new consumer surplus.

Answer 1

a) Calculate consumers surplus.

The demand and supply functions are:

$$Qd = 1500 - 0.5 P\\[0.3cm] Qs = 500 + 0.5 P$$

We need to calculate the equilibrium quantity and the equilibrium price. This occurs where Qd = Qs.

$$1500 - 0.5 P = 500 + 0.5 P\\[0.3cm] P^* = \$1,000$$

Therefore, the equilibrium quantity is:

$$Q = 1500 - 0.5 (1,000)\\[0.3cm] Q^* = 1,000$$

If the consumers are willing to pay $ 3,000, then the quantity they would purchase is:

$$Q = 1500 - 0.5(3000) = 0$$

Therefore, the consumer surplus is:

$$CS = \dfrac{1}{2}(1000 - 0)(3000 - 1000)\\[0.3cm] CS = \dfrac{1}{2}\times 1000\times 2000\\[0.3cm] \color{red}{CS = \$1,000,000}$$

b) if the market price increases by 25 % and quantity sold decreases by 12 %, calculate the new consumer surplus.

The market price increases by 25% to:

$$P^{**} = 1.25\times 1,000 = \$1,250$$

And the quantity demanded decreases by 12% to:

$$Q^{**} = 0.88\times 1,000 = 880$$

The new consumer surplus is:

$$CS = \dfrac{1}{2}(880 - 0)(3000 - 1250)\\[0.3cm] CS = \dfrac{1}{2}\times 880\times 1750\\[0.3cm] \color{red}{CS = \$770,000}$$