Answer to Question #234295 in Microeconomics for shivani

Question

Allied Electric Co, is developing a new design for its portable electric hair dryer Test market data indicate a demand for the new hair -dryer as follows:

Q-30,000-1000P

Where Q is hair dryer sales and P its price.

1. How many hair dryers could allied sell at Rs. 22.50 each? II. What price would Allied have to charge to sell 12,000 hair dryers?

III Calculate price elasticity of demand at price of Rs. 20

Answer 1

(i)

Given

price 22.50

$Q=30,000-1000P$

Then

$Q=30000-1000(22.50)\\=30000-22500\\=7500$

(ii)

Given

Q=12000

$Q=30,000-1000P$

Then

$12000=30000-1000(P)\\P=3000012000\\P=18$

(ii)

Given

price 20

$Q=30,000-1000P$

Then

$Q=30000-1000(20)\\=30000-20000\\=10000$

price elasticity of demand$=\frac{\frac{Q_2-Q_1}{\frac{Q_2+Q_1}{2}}}{\frac{P_2-P_1}{\frac{P_2+P_1}{2}}}$

e_(p)=price elasticity

Q₁=old quantity demanded

Q₂=new quantity demanded

P₁=old price

P₂=new price

$=\frac{\frac{10000-7500}{\frac{10000+7500}{2}}}{\frac{20-22.5}{\frac{20+22.5}{2}}}$

$=\frac{\frac{2500}{8750}}{\frac{2.5}{21.25}}$

$=\frac{0.286}{-0.118}\\=-2.42$