You run a small business and would like to predict what will...

You run a small business and would like to predict what will happen to the quantity demanded for your product if you raise your price. While you do not know the exact demand curve for your product, you do know that in the first year you charged $$\$ 45$$ and sold 1200 units and that in the second year you charged $$\$ 30$$ and sold 1800 units. a. If you plan to raise your price by 10 percent, what would be a reasonable estimate of what will happen to quantity demanded in percentage terms? b. If you raise your price by 10 percent, will revenue increase or decrease?

You run a small business and would like to predict what will happen to the quantity demanded for your product if you raise your price. While you do not know the exact demand curve for your product, you do know that in the first year you charged $$\$ 45$$ and sold 1200 units and that in the second year you charged $$\$ 30$$ and sold 1800 units.
a. If you plan to raise your price by 10 percent, what would be a reasonable estimate of what will happen to quantity demanded in percentage terms?
b. If you raise your price by 10 percent, will revenue increase or decrease?

Key Concepts

Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price, and it indicates how sensitive consumers are to price changes. A high absolute value means consumers are very responsive to price variations, while a low value indicates less sensitivity.

Estimation of Elasticity Using Two-Point Method

When the exact demand curve is not known, elasticity can be estimated using data from two different points of price and quantity. This method involves calculating the percentage changes in both price and quantity between the two data points and then using their ratio to approximate the elasticity. This approach provides a practical way to gauge demand responsiveness in real-world situations.

Relationship Between Price Changes and Total Revenue

The effect of a price change on total revenue depends on the elasticity of demand. For elastic demand (elasticity greater than 1 in absolute value), an increase in price typically leads to a decrease in total revenue, as the reduction in quantity demanded more than offsets the higher price. Understanding this relationship is crucial for making pricing decisions in business management.

Transcript

00:01 So you run a small business and would like to predict what will happen to the quantity demanded for your product if you raise the price.

00:08 So you want to increase price and then you want to know what's going to happen to the quantity demanded when you increase the price.

00:17 So while you do not know the exact demand call for your product, you do know that in the first year, you charge $45, i'm calling it.

00:33 You charge $45 and you sold the units you sold or rather quantity you sold was 1 ,200 units and that in the second year you'll charge $30 rather and you sold 1 ,800 units.

01:03 Now, the first question is if you plan to raise your price by 10%, what? would be a reasonable estimate of what will happen to the quantity demanded in percentage terms so giving the question um we're going to substitute the values in the equation so as price elasticity of demand so price elasticity of demand um we're going to have forty five dollars divided by one thousand two hundred multiplied by six hundred divided by minus 15 and then that's um i'm sorry i didn't explain where the 600 came from um so first of all we calculate the elasticity of demand by using the formula which is the price over i'm sorry let me just start over so the formula is p over q multiplied by the change in quantity over the change in price so the initial price as you can see is 45 the quantity the quantity is 1 ,200.

02:33 So therefore, the change in the quantity would be 1 ,200, 1 ,800 minus 1 ,200.

02:40 So that's going to be 600, right? and then the change in the price would be 45 minus 30, rather 30 minus 45.

02:51 So that's minus $15 because it's the new one minus the old one, right? so the second year minus the first year.

02:58 So now knowing that, knowing those figures you can find the price elasticity of demand so that will be equals to the price is 45 the quantity is 1 ,200 and then the change is 600 as you can see divided by minus 15 so now we get that so this is going to give you minus 1 .5 and that's the price elasticity of demand so the negative sign denotes that it has the inverse relation between the price and quantity demanded so we can can say that it has an inverse relation between price and quantity demanded.

03:46 So now, as per the first question, if the firm owner plans to increase the price by 10%, then the quantity, the change in quantity demanded will be price elasticity of demand is equal to the percent change in quantity demanded divided by the percent change in price.

04:08 So here we have the price elasticity of demand as minus 1 .5.

04:13 So minus 1 .5 will be the change in quantity demanded, the percentage change in quantity demanded, divided by 10%, because the percentage change in price, as part of the question, is 10%.

04:26 So this is going to give you minus 15 % when you multiply it by 10 is equal to the percentage change in quantity demanded...

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