# Numerical on the Price Elasticity of Supply

In this post, I will be explaining the methods to solve numerical on the price elasticity of supply. I will be explaining the types of problems as well. Let’s start with the formulas that will be used in numerical on the price elasticity of supply.

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## 1. Percentage Change Method of Price Elasticity of Supply

According to this method, price elasticity of supply is the ratio between percentage change in quantity supplied and the percentage change in price

**Pes = % Change in Qss/ % Change in P**

**Percentage change in quantity supplied = Change in Q X 100/ Original Q**

**Percentage change in price = Change in P x 100/ Original P**

## 2. Proportionate Method of Price elasticity of Supply

P – Original or initial price

Q – Original or initial quantity

Note: Price elasticity of supply is always positive and it is unit free

### How to solve questions related to price elasticity of supply?

- Make a price and quantity supplied table.
- Remember there exists a direct relationship between price and quantity supplied, that is, either both will be increasing or decreasing.
- In case, the total Revenue is mentioned. Then TR = PXQss.
- The total revenue formula can be used to find either the price of the quantity supplied in the question.

Now, let’s try some of the problems.

#### Problems/ Numerical on Price Elasticity of Supply

**1. A producer offers to sell 400 units of a commodity when its price is 10 per unit, while only 200 units are offered if the price reduces to 5 per unit. Find elasticity of supply.**

Solution. Lets plot the information given in a table:

Price | Quantity Supplied |
---|---|

10 | 400 |

5 | 200 |

Since there is no mention of the method to be used. We are free to use any method I will try this question with proportionate method:

Pes

Pes = 200 x 10/ 5 x 400

Pes = (+) 1

**2. A firm earns a revenue of $50 when the market price of a good is $10. The market price increases to $15 and the firm now earns a revenue of $150. What is the price elasticity of the firm’s supply curve?**

Solution. In this question, revenue is given, so the formula of TR = PXQ will be used to solve this question. Let’s make a table first:

TR = PXQ | P | Q = TR/P |

50 | 10 | 5 |

150 | 15 | 10 |

Now apply the proportionate method to solve this question:

Pes =

Pes = 5 x 10 / 5 x 5

Pes = (+) 2

**3. The market price of good changes from $5 to $20. As a result, the quantity supplied by a firm increases by 15 units. The price elasticity of the firm’s supply curve is 0.5. Find the initial and final output levels of the firm.**

Solution. In this question, the quantity supplied by a firm increases by 15 units. It means a change in Q is given and we also have Pes = 0.5

Apply the formula:

Pes = 15 x 5/ 15 x Q

0.5 = 5/Q

Q = 5/0.5

Q = 10 units. This is initial quantity supplied.

Final quantity = Q + Change in Q

Final quantity = 10 + 15 = 25 units.

**4. At the market price of $10, a firm supplies 4 units of output. The market price increases to $30. The price elasticity of the firm’s supply is 1.25. What quantity will the firm supply at the new price?**

Solution. In this question, the initial and final price is mentioned. We also have the initial quantity supplied and Pes = 1.25.

Pes =

1.25 = Change in Q x 10/ 20 x4

1.25 = Change in Q/ 8

1.25 X 8 = Change in Q

Change in Q = 10

Final quantity supplied = Q + Change in Q

Final quantity supplied = 4 + 10 = 14

## Time to Test Yourself

Q1) When the price of good rises from Rs 10 to Rs 12 per unit, the producer supplies 10 percent more. Calculate the Price elasticity of supply.

Q2) When the price of good rises from Rs 8 to Rs 10 per unit, the producer supplies 40 units more. Pes is 2. What is the quantity supplied before the price change? Calculate.

Q3) Pes of a good is 2. A producer supplies 100 units of a good at a price of Rs 20 per unit. At what price will he supply 80 units?

Solve the above 3 problems and share your answers with me on contact@LearnWithAnjali.com I will provide the solutions after getting your responses.

Thank You!

You can read the related concepts:

- The price elasticity of supply
- The supply curve
- What is production function?
- Terms related to production concept
- Law of diminishing returns to a factor
- Total cost, Total variable cost and Total fixed cost
- The relation between TC, TVC and TFC
- Average total cost
- The demand curve

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