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Calculating the price elasticity of demand - A step-by-step guide

Suppose that during the past year, the price of a laptop computer fell from $2,950 to $2,450. During the same time period, consumer sales increased from 430,000 to 619,000 laptops.

1. Calculate the elasticity of demand between these two price quantity combinations by using the following steps. After each step, complete the relevant part of the table with the appropriate answers. (Note: For decreases in price or quantity, enter values in the Change column with a minus sign.)

  Original New Average Change Percentage Change
Quantity ? ? ? ?

a. 36.03%

b. 18.02%

c. 277.51%
Price $ $ $ $

a. -18.52%

b.-540%

c. -9.26%

Step 1: Fill in the appropriate values for original quantity, new quantity, original price, and new price.

Step 2: Calculate the average quantity by adding the original quantity and the new quantity, and then dividing by two. Do the same for the average price.

Step 3: Calculate the change in quantity by subtracting the original quantity from the new quantity. Do the same for the price change.

Step 4: Calculate the percentage change in quantity demanded by dividing the change in quantity by the average quantity. Do the same to calculate the percentage change in price.

Step 5: Calculate the price elasticity of demand by dividing the percentage change in quantity demanded by the percentage change in price, ignoring the negative sign.

2. Using the midpoint method, the elasticity of demand for laptops is about

a. 0.051

b. 0.97

c. 1.95

d. 3.89

 

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Romarie Khazandra Marijuan
Romarie Khazandra MarijuanLv10
28 Sep 2019

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Related questions

Suppose that during the past year, the price of a laptop computer fell from $2,950 to $2,450. During the same time period, consumer sales increased from 430,000 to 619,000 laptops. Calculate the elasticity of demand between these two price–quantity combinations by using the following steps. After each step, complete the relevant part of the table with the appropriate answers. (Note: For decreases in price or quantity, enter values in the Change column with a minus sign.) Original New Average Change Percentage Change Quantity 36.03% Price -18.52% Step 1: Fill in the appropriate values for original quantity, new quantity, original price, and new price. Step 2: Calculate the average quantity by adding the original quantity and the new quantity, and then dividing by two. Do the same for the average price. Step 3: Calculate the change in quantity by subtracting the original quantity from the new quantity. Do the same for the change in price. Step 4: Calculate the percentage change in quantity demanded by dividing the change in quantity by the average quantity. Do the same to calculate the percentage change in price. Step 5: Calculate the price elasticity of demand by dividing the percentage change in quantity demanded by the percentage change in price, ignoring the negative sign. Using the midpoint method, the elasticity of demand for laptops is about .

Use your knowledge about price-searching firms and two-part pricing to advise the company below. A company has a bar and is trying to decide on the cover charge (if any) and price for each drink. It has done a modest regression study in which it asked customers to classify themselves as light drinkers or heavy drinkers and to indicate the number of drinks they would typically consume during the evening. The estimate from the regression study is that a change in the price equal to $1 per drink causes light drinkers to change their consumption on average by 0.5 drinks per night. However, a change in the price of $1 causes heavy drinkers to change their consumption on average by 1.0 drinks per night. For both groups, a typical consumer will not consume anything once the price reaches $9 per drink. (They may instead go to another bar or not go to a bar at all.) Draw a demand curve for a typical light drinker and for a typical heavy drinker on the same diagram. Explain your diagram. Write equations for the curves in slope-intercept form.

If 300 people visit the bar on a typical evening, with 200 people being light drinkers and 100 people being heavy drinkers, draw an overall demand curve for all of the consumers combined. What is the slope and what is the intercept for this demand curve? Write an equation in slope-intercept form. If the marginal cost of making drinks (the alcohol, the bartender's labor, and the amortized cost of purchasing glasses and cleaning them repeatedly) is constant at $5 per drink, and if no cover charge is assessed, what is the best price to charge for drinks? How many drinks would be sold on a typical evening? What would your profits be? If you cut your price by $1 per drink and assess the maximum possible cover charge without causing a typical light drinker to refuse to enter the bar, would your profits improve? How high would the cover charge be? Calculate both the cover charge and your total profits. Would the new pricing increase profit?

Maybe the best price cut is not exactly $1. Write a profit equation. Profits equal to total revenue minus total cost. Total cost equals $5 times the number of drinks sold. Total revenue equals the price for drinks times the number of drinks sold, plus 300 people times the cover charge. The cover charge equals, for a light drinker, the triangle of consumer surplus above the price but below the demand curve for a light drinker. (The area of a triangle equals one half the base times the height.) You will take the derivative of the profit equation with respect to P or Q and set it equal to zero. For example, use the equation for the total demand curve and solve for Q in terms of P. Then in the profit equation substitute in an expression involving P in place of every Q that was in the original profit equation. Now you can take a derivative of profits with respect to P and set the derivative equal to zero. Eventually, you can solve for the exact best P, Q, and cover charge.

Review of the slope-intercept form: Y= a - bX; a = the intercept on the Y-axis and b = the absolute value of the slope (slope=(change in Y)/(change in X)) For a demand curve: P=a-b Q. The intercept on the vertical axis would indicate a price that is so high that the quantity demanded becomes zero. The slope is the ratio of a change in price divided by the change in quantity demanded; the extra credit problem gives you information to determine the slope for a light drinker and the slope for a heavy drinker.

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