Question

Case I: Elasticity Part I Demand and Supply are represented by the functions below: QD = 8250 – 325P QS = 850 + 175P Exercise: 1. Compute quantity and price in equilibrium 2. Determine what would happen if the price changed to 12$ 3. Plot the graph representing the first two questions. 4. Compute the elasticity of both curves assuming the price would increase from 22$ to 24$. 5. Plot the graph for question 4.

Answer 1

1.

At market equilibrium, 

   $Q _ D =Q _ S =Q^*$

 Putting values

    8250−325P=850+175P

⇒500P=7400

⇒P*=14.8

Equilibrium quantity:

Q*=8250−325(14.8)=3440

2.

If price changed to $12

In this case the quantity demanded is greater than the quantity supply. 

At P=12

$Q _D =8250−325(12) =4350$

and quantity supply

$Q _S =850+175(12)=2950$

3.

4

When price is 22

Quantity demanded 

$Q D =8250−325(22) =1100$

When P =24

Qd=8250−325(24)=450

Price elasticity of demand is calculated as

$E=\frac{\%change\space in\space demand}{ \% change\space in\space price}$

$⇒E=\frac{\frac{Q_ 2 −Q _ 1}{ Q _1} }{\frac{ P _2 −P _1}{ P _ 1}}$

$⇒E=\frac{\frac{450 −1100}{ 1100} }{\frac{ 24 −22}{ 22}}$

$⇒E=−6.5\\ ⇒| E| =6.5$

So price elasticity of demand when price increase from 22 to 24 is 6.5

Elasticity of supply:

At price P=22, 

Qs= 850+175(22)=4700

When price is P=24

Qs=850+175*24=5050

Price elasticity of supply:

$E'=\frac{\frac{5050-4700}{4700}}{\frac{24-22}{22}}$

E'=0.819

5.