Question

Question2: After a careful statistical analysis, the Middle East Company concludes the demand function for its product is Q = 100 - 0.8P + 0.04 1- 5P 1 and Py are the prices of where Q is the quantity demanded of its product, P is the price of its product, P rivals' products, and I is per capita disposable income in dollars). At present, P = $10, Pr = $6, Py =4 $ and I = $500. a. What is the economic meaning of this function? b. What is the price elasticity of demand for the firm's product? c. Do you think it is good advice to reduce the price to $ 6? d. What is the income elasticity of demand for the firm's product? e. What is the cross-price elasticity of demand between its product and rivals' products? —

Answer 1

The demand function of Middle East Company is as follows:

Q=100-0.8P+0.04I - 5P

Where, Q= quantity demanded

P= price of product

I= per capita disposable income

Firstly,Lets find demand of the product

As given in the question ,P= $10,I=$500

Q=100-0.8*10+0.04*500-5*$10

= 100-8+20-50

Q = 62

a) Economic meaning of the demand function can be stated as follows:

The demand function states that the quantity demanded for the product depends on the price of the product and income of the consumer. Demand is the function of price and income.If any one of two changes,demand of the product also changes.

b) Price elasticity of demand = percentage change in qauntity demanded/percentage change in price

Lets say price has been increased by 10%

New P=$11

new Q= 100-0.8*11+0.04*500-5*11

=100-8.8+20-55

=56.2

Percentage change in quantity demanded= old demand-new demand/old quantity*100

=62-56.2/62*100=9.3%

price elasticity of demand = 9.3/10=0.93

Price elasticity of demand is less than 1 ,hence elasticity is relatively inelastic,means percentage change in quantity demand is less than percentage change in price.

c)

New price =6

lets find quantity deamnded

Q=100-0.8*6+0.04*500-5*6

Q= 100-4.8+20-30=85.2

If price is reduced to 60%, quantity demanded increased only by (62-85.2/62*100) 37%,

In this context it is not a advisable to reduce price to $6

d)

Income elasticity of demand = percentage change in demand / percentage change in price

e)

cross elasticity of demand=percentage change in deamnd of firms product/percentage change in rival's product prices