Posted by Anjali Kaur on Aug 08, 2020
Learn how to solve numerical on price elasticity of demand

Numerical on Price Elasticity of Demand

After learning the law of demand, meaning, and formulas of price elasticity of demand. Now, we will understand how to solve the numerical on the price elasticity of demand. I will try to keep it simple so that it gets permanently stored in your mind’s hard drive. Haha! Let’s learn Economics in a simple way.

How to solve the numerical on the price elasticity of demand?

#Rule 1: Make a demand schedule like the one shown below. Its a must, as soon as you read a numerical, start placing the values given in the question in the demand table. Why? It avoids confusion and provides clarity on what needs to be calculated.

Demand Schedule

#Rule 2: Focus on the law of demand statement. It states that there exists an inverse relationship between price and quantity demanded, keeping other things constant. So, if the price is decreasing, then the quantity demanded will increase and if the price is increasing, then the quantity demanded will decrease. I prefer drawing an arrow near the demand schedule to avoid confusion. For example, if the price increases, then the quantity demanded will fall. As shown below:

Arrows indicate the relation

#Rule 3: Apply the Ped formula. If in the question price or quantity demanded is mentioned in percentage terms, then apply the percentage method formula of price elasticity of demand. If it’s given like in absolute numbers, then apply proportionate change method formula. Refer below formula list for your convenience:

Price Elasticity of Demand Formulas

#Rule 4: Price elasticity of demand as a final answer will be units free, that is, Ped is an absolute or pure number, and it is not written with kg, Rupees, etc. The minus sign of Ped reflects a negative relationship between price and quantity demanded.

Practice Numerical on Price Elasticity of Demand

Question 1. If the price of a commodity rises by 40% and accordingly, its demand falls by 80%. What is Ped?

Solution. Here everything is mentioned in percentage terms, so apply the percentage change method of Ped:

Price Elasticity of demand = Percentage change in quantity demanded/ percentage change in price.

Ped = 80%/ 40%

Ped = (-) 2

The minus sign of Ped reflects a negative relationship between price and quantity demanded. And Ped is a pure number, no unit is mentioned.

Question 2. If price of a commodity rises from Rs 8 to Rs 10 per unit and its demand falls by 50%. What is the price elasticity of demand?

Solution. Try making a demand schedule like this:

PriceQuantity Demanded
850% fall in demand
10

You can observe that the law of demand is still applicable, as the price increases, the quantity demanded decreases.

Apply percentage method of the price elasticity of demand and try solving this, as shown below:

Test Yourself

1. Due to a 10% fall in the price of a commodity, the demand rises from 100 units to 120 units. How much percentage will its demand fall, due to a 10% rise in its price?

Tip: apply the percentage change in quantity demanded formula

2. A consumer spends Rs 100 on a good priced at Rs 4/unit. When its price falls by 50%, the consumer continues to spend Rs 100 on that good. Calculate the Price elasticity of demand.

3. There is a 50% fall in the price of the commodity. But the quantity demanded remains to be 150 units. Find elasticity of demand.

4. A certain quantity of the commodity is purchased when its price is Rs. 10 per unit. Quantity demanded increases by 50% in response to a fall in price by Rs. 2 per unit. Find elasticity of demand.

5. At a certain price of the commodity quantity purchased is 150 units. When the price falls by 25%, the quantity purchased increases by 75 units. Find elasticity of demand.

6. Price elasticity of demand is found to be (?)2. Price falls from Rs. 10 per unit to Rs. 8 per unit. Find the percentage change in quantity demanded.

7. For a commodity, ΔP/P = -0.2, and elasticity of demand = ? 0.3. Find the percentage change in quantity demanded.

8. For a commodity, ΔP/P = -0.2, and elasticity of demand is 0.5. Find quantity demanded after a fall in price when initially it was 60 units. (66)

9. A commodity shows Ed = (-)2, Quantity demanded reduces from 300 units to 150 units. In response to an increase in price. Find the increased price when initially it was Rs. 20 per unit. ( 25 )

10. Price elasticity of demand for a good is (?)1. At a given price the consumer buys 60 units of the good. How many units will the consumer buy if the price falls by 10 percent? ( 66)

11. The price elasticity of demand of a good is (?) 4. If the price increases from Rs. 10 per unit to Rs. 12 per unit, what is the percentage change in demand? (80%)

12. At a given market price of a good, a consumer buys 100 units. When price increases by 40 percent he buys 80 units. Calculate the price elasticity of demand. (0.5)

13. A consumer buys a certain quantity of a good at a price of Rs. 10 per unit. When the price falls to Rs. 8 per unit, she buys 40 percent more quantity. Calculate the price elasticity of demand by percentage method. (2)

14. A consumer buys 80 units of a good at a price of Rs. 4 per unit. When the price falls, he buys 100 units. If the price elasticity of demand is (-) 1, find out the new price. (3)

15. A consumer buys 40 units of a commodity at a price of Rs. 5 per unit and his price elasticity of demand is (-) 1.5. Calculate the amount he will buy at the price of Rs. 4 per unit of the commodity. (52)

16. A household increases its demand for a commodity from 40 units to 50 units when its price falls by 10%. What is the price elasticity for the commodity? (2.5)

17. A consumer spends Rs. 80 on a commodity when its price is Re. 1 per unit and spends Rs. 96 when the price is Rs. 2 per unit. What is the price elasticity of demand for the commodity? (0.4)

18. Price of good rises from Rs. 4 to Rs. 5 per unit. As a result, its demand falls from 200 units to 100 units. Calculate Ep (2)

19. A consumer buys 50 units of a good at Rs. 10 per unit. At a price of Rs. 8 per unit, he buys 100 units. Find out Ep. (5)

20. A 7% fall in the price of a good leads to a 49% increase in demand for that good. Find out Ep. (7)

21. Ep of good is – 3. At a price of Rs. 8 per unit, a consumer buys 160 units of the good. How many units of the goodwill the did consumer buy when the price falls to Rs. 6 per unit? (280)

22. Ep of good is – 5. At a price of Rs. 10 per unit, the consumer buys 200 units. At what price will he buy 100 units? (11)

23. Ep of good is – 4. When the price of this good rises from Rs. 5 to Rs. 6 per unit, a consumer buys 40 units less. How many units did he buy at Rs. 5? (50)

24. Given Ep = -1, complete the following table:

 Price Demand (Rs. per unit) (Units)

4          60

–           90. Use percentage change method (2)

25. Draw a downward-sloping straight-line demand curve. Indicate the points on this demand curve, where Ep =0, Ep =1 and Ep = infinity

26. The price elasticity of demand for a good is (-) 2. 40 units of this good are bought at a price of Rs 10 per unit. How many units will be bought at a price of Rs. 11 per unit? Calculate. (32)

27. At a price of Rs 50 per unit, the quantity demanded of a commodity is 1000 units. When its price falls by 10 percent, its quantity demanded rises to 1080 units. Calculate its price elasticity of demand. Is its demand inelastic? Give reasons for your answer. (0.8 and inelastic)

28. When the price of a good falls by 10 percent, its quantity demanded rises from 40 units to 50 units. Calculate the price elasticity of demand by the percentage method. (2.5)

29. The quantity demanded of a commodity rises from 800 units to 850 units when its price falls from Rs. 20 per unit to Rs. 19 per unit. Calculate its elasticity of demand. (1.25)

30. The price elasticity of demand for a good is (-) 1. At a given price the consumer buys 60 units of the good. How many units will the consumer buy if the price falls by 10 percent? (66 units)

31. The price elasticity of demand for a good is (-) 2. The consumer buys a certain quantity of this good at a price of Rs. 8 per unit. When the price falls he buys 50 percent more quantity. What is the new Price? (6)

 32. The market for pens has three consumers – A, B, and C. If the individual demand for pens at a price of Rs 5/pen for A, B, and C is 3 pens, 7 pens, and 12 pens respectively, then what is the market demand for pens at a price of Rs 5/pen? (22)

33. A consumer buys 2,000 units of a good at a price of Rs. 10/- per unit. When the price falls he buys 2,500 units. If the price elasticity of demand is -2, what is the new price? (8.75)

34. At a price of Rs. 20/- per unit the quantity demanded of a commodity is 400 units. If the price falls by 10%, its quantity demanded rises by 90 units. Calculate its price elasticity of demand. (2.25)

35. A consumer buys 10 units of a good at a price of Rs. 4/- per unit. When the price falls by Rs 1/- per unit, he buys 20 units. Calculate the price elasticity of demand. (4)

36. A consumer spends Rs. 250/- on a good when its price is Rs. 10/- per unit. When the price rises to Rs. 11/- per unit, he spends Rs. 240/-. Calculate the price elasticity by the percentage method. (1.2)

37. As a result of a 10% fall in the price of a good, its demand rises from 200 to 240 units. Find out the price elasticity of demand. Is its demand elastic? (2 and Elastic)

38. The price elasticity of demand for a good is (-)2. 100 units of this good are bought at a price of Rs. 10/- a unit. How many units will be bought at a price of Rs 11/- per unit? (80 units)

39. The slope of a demand curve is -0.4, calculate is the elasticity of demand, if at an initial price of Rs. 5/- per unit, the initial quantity demanded was 20 units of the commodity. (0.625)

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