Suppose XYZ is a coffee shop located in one of the busy crowded universities of Pakistan.

Suppose XYZ is a coffee shop located in one of the busy crowded universities of Pakistan. This coffee shop is a popular spot for people to sit and discuss their studies and it is also famous for a quick cup of coffee on their way to class. The shop is open from 9:00 AM to 6:00 PM, Monday through Friday. The shop is currently selling 2,000 cups of coffee per day for Rs 200. The owner of the coffee shop is considering raising the price of a cup of coffee from Rs. 200 to Rs. 250. The coffee shop demand function is given below 𝑄𝑑 = 6000 − 20𝑃 Requirements:  

A. Calculate the price elasticity of demand when the price is Rs. 250.  

B. Calculate total revenue both before and after the price rise.  

C. Also explain what will be the effect of price increase on total revenue by keeping in view the results of part B? 

Solution:

A. To calculate the price elasticity of demand when the price is Rs. 250, we need to use the following formula:

Price Elasticity of Demand (Ed) = (% Change in Quantity Demanded) / (% Change in Price)

Given that the demand function is Qd = 6000 - 20P, where Qd represents the quantity demanded and P represents the price, we can calculate the change in quantity demanded and the change in price.

When the price increases from Rs. 200 to Rs. 250, the change in price is:

Change in Price = Rs. 250 - Rs. 200 = Rs. 50

To calculate the change in quantity demanded, we need to substitute the new price into the demand function:

Qd = 6000 - 20P

Qd = 6000 - 20(250)

Qd = 6000 - 5000

Qd = 1000

Change in Quantity Demanded = 1000 - 2000 = -1000

Now we can calculate the price elasticity of demand:

Ed = (% Change in Quantity Demanded) / (% Change in Price)

Ed = (-1000 / 2000) / (50 / 200)

Ed = -0.5 / 0.25

Ed = -2

Therefore, the price elasticity of demand when the price is Rs. 250 is -2.

B. To calculate the total revenue before and after the price rise, we need to multiply the quantity demanded by the price.

Before the price rise:

Quantity Demanded = 2000 cups

Price = Rs. 200

Total Revenue before = Quantity Demanded * Price

Total Revenue before = 2000 * 200

Total Revenue before = Rs. 400,000

After the price rise:

Quantity Demanded = 1000 cups (as calculated in part A)

Price = Rs. 250

Total Revenue after = Quantity Demanded * Price

Total Revenue after = 1000 * 250

Total Revenue after = Rs. 250,000

C. The effect of the price increase on total revenue can be analyzed by comparing the total revenue before and after the price rise.

Before the price rise, the total revenue was Rs. 400,000, but after the price rise, the total revenue decreased to Rs. 250,000. This indicates that the price increase led to a reduction in total revenue.

The price elasticity of demand (Ed) calculated in part A was -2, which means that the demand for coffee is relatively elastic. When the price was increased, the quantity demanded decreased by a larger percentage than the percentage increase in price, leading to a decrease in total revenue.

In this case, the price increase resulted in a decline in total revenue, suggesting that the demand for coffee at this particular coffee shop is sensitive to changes in price.