Question

At a price of $ 80, the quantity demanded of a given good is 200 units. If the price decreases to $ 45, the quantity demanded increases to 225 units.

1. Calculate the value of the price elasticity.

2. Explain what type of claim it is. Explain in detail what managerial action corresponds to take, raise the price, lower it or leave it the same.

3. Make the graphic representation.

4. Answer correctly if it is elastic, inelastic or unitary, there is the mathematical procedure and the formulas to be able to do it.

Answer 1

Answer:

Part 1.

At a price of $ 80, the quantity demanded of a given good is 200 units. If the price decreases to $ 45, the quantity demanded increases to 225 units.

1. Calculate the value of the price elasticity.

When price = 80, quantity demanded = 200

When price = 45, quantity demanded = 225

1. Price elasticity of demand = % change in quantity demanded/ % change in price

% change in quantity demanded = (New quantity demanded - Old quantity demanded) / Old quantity demanded*100

= (225-200)/200*100 = 25/200*100 = 12.5%

% change in price = (New Price - Old price)/Old price*100

= (45-80)/80*100 = -35/80*100 = -43.75%

Price elasticity of demand = % change in quantity demanded/ % change in price

= 12.5%/-43.75% = - 0.29 (Rounded off to two decimal)

Part 2. Explain what type of claim it is. Explain in detail what managerial action corresponds to take, raise the price, lower it or leave it the same.

If the quantity demanded has a small change in response to its price, it is termed "inelastic"; or quantity didn't stretch much from its prior point.

In the given scenario, we can see in the part 1 above that change in price is 43.75%. And due to change in price of 43.75%, respective change in quantity demanded is relatively less. Therefore, good is relatively inelastic.

Manager can use the price elasticity to fix the price. Manager should raise the price, as demand for the good is relatively inelastic, increase in price will not have that much impact on decrease in quantity demanded of the good.

Means as per the law of demand, if manager increases the price, quantity demanded will fall. But, as the good is relatively inelastic, fall in quantity demanded will be very less as compared to increase in price. Therefore, overall revenue can be increased.

Part 3. Make the graphic representation.

Part 4. Answer correctly if it is elastic, inelastic or unitary, there is the mathematical procedure and the formulas to be able to do it.

Solution : The good is inelastic.

% change in quantity demanded/ % change in price < 1 =    Inelastic

In our case, price elasticity of good = -0.29 , which is less than 1, therefore, good is inelastic.

Mathematical formula :

Price elasticity of demand = % change in quantity demanded/ % change in price

% change in quantity demanded = (New quantity demanded - Old quantity demanded) / Old quantity demanded*100

= (225-200)/200*100 = 25/200*100 = 12.5%

% change in price = (New Price - Old price)/Old price*100

= (45-80)/80*100 = -35/80*100 = -43.75%

Price elasticity of demand = % change in quantity demanded/ % change in price

= 12.5%/-43.75% = - 0.29 (Rounded off to two decimal)