Question

you are interested in buying a new cell phone and consumers are willing to pa y 3000.the demand function for acellphone is Qd=1500-0.5P and supply function is Qs=500+0.5P.if the market price increases by 25% and the quantity sold decreases by 12%,calculate the new consumer's surplus"

Answer 1

$$Q_D=Q_s$$

$$1500-0.5p=500+0.5p$$

$$p=1000$$

$$Q=1500-0.5\times1000=1000$$

$$p^*=1.25\times1000=1250$$

$$\varDelta p=|p^*-p|=250$$

$$Q^*=0.88\times 1000=880$$

$$\varDelta Q=|Q^*-Q|=120$$

$p|_{Q_{D}=0}=3000$

We find the consumer surplus as the area of ​​the triangle

$$\frac{1}{2} (p|_{Q_D=0}-p^*) Q^* =\frac {1}{2}(3000-1250)120=105000$$