Numerical Problems

Managerial Economics Numerical Problems
DEMAND AND ELASTICITY OF DEMAND
Problem 1

The following are the demand and supply equations of a pen manufacturer.
Qd = 5,00,000 – 50, 000 P Qs = -1,00,000 + 1,00,000 P
Find

At what average price, the level of demand is equal to zero.
At what average price, the level of supply is equal to zero.
 Calculate the equilibrium price and quantity. Problem 2 Yashika Limited manufactures an automatic camera that currently sells at uS$90.

Sales volume is about 2,000 cameras per month in a city. A close competitor, Minolta, has cut the price of a similar camera it makes from US$ 100 to US$80. Yashika’s economist has estimated the arc cross elasticity of demand between the two rival firms’ products at about 0. 4, given current incomes and price levels. What impact, if any, will the action by Minolta have on the total revenue generated by Yahiko, if it leaves its current price unchanged?

YASHIKA
MINOLTA

P1y = 90
P1m = 100

Q1y = 2,000
P2m = 80

Q2y = to be determined
Cross elasticity of demand = 0. 4

Problem 3
Bajaj Appliances Ltd. manufactures a line of microwave ovens costing US$500 each. Its sales have averaged about 6,000 units per month during 2001. In June 2002, Bajaj’s closest competitor LG had cut its oven’s price from US$600 to US$450. Bajaj noticed that its sales volume declined to 4,500 units per month after the price cut by its rival LG.

What is the arc cross-price elasticity of demand between the two?
Would you say that these two firms are very close competitors?
 If Bajaj knows that the arc price elasticity of demand for its ovens is –3. 0, what price it would have charged to sell the same number of units it did before its rival LG resorted to a price cut?

Problem 4
Demand for mobile phone handsets by a popular company in Bangalore city is estimated to be Qd = 2,50,000- 35P. If this relationship is approximately valid for next year also

How many mobile phones would be demanded at a price of Rs? 2,000, 4,000, and 6,000 a set?
Compute the arc price elasticity between 2,000 and 4,000; 4,000 and 6,000.
Calculate point elasticity at 2,000, 4,000 and 6,000.
If last year 25,000 units were sold, what would have been the average price?
What is the highest theoretical price for the mobile handset in Bangalore for this seller?

Problem 5
The demand function for wall clocks in a city has been estimated to be Q= 2000 +15Y-5. 5P. Where Y is income in a thousand rupees, Q is quantity in units, and P is the unit price. When P=150, y =15, find

Price elasticity of demand
Income elasticity of demand Problem 6 Two goods have a cross elasticity of +1. 2
Would describe them as substitutes or complements? Give examples for supporting the category that you chose.
If the price of one of the two rises by 5%, ceteris paribus, what happens to the Qd of the other?

Problem 7
The demand for lunches in an institute canteen was estimated to be Q= 16,415. 21-262. 743P, where Q= lunches served, P= price in rupees.

Compute the price elasticity of demand at a price of Rs. 40, Rs. 50 per lunch
What is the arc price elasticity of demand between the prices 40 and 50?

Problem 8
Pepsodent sells a toothbrush for Rs. 25. Its sales have averaged 8,000 units per month over the last year. Recently, its close competitor, Colgate, reduced the price of its product from Rs. 35 to Rs. 30 per toothbrush. As a result, Pepsodent’s sales declined by 1,500 units per month.

What is their cross elasticity? What relationship does it indicate?
If Pepsodent knows that it has a cross elasticity of –1. 5 with Colgate, how much it should now charge to restore previous sales after the price cut by Colgate? (Assume Colgate retains its price at Rs. 30 itself and does not retaliate).
What is the total monthly revenue of Pepsodent before and after the price change in (2) above?
Is the result in part (3) above necessarily desirable? What other factors would have to be taken into consideration?