Directions Use the table below to answer the following questions: Price Quantity

Question

Directions
Use the table below to answer the following questions:

Price Quantity Demanded Elasticity Coefficient
$5 1 —
$4 2 A
$3 3 B
$2 4 C
$1 5 D
Microeconomic Problems
1. Given the simple demand schedule information in the table above, calculate the coefficient of price elasticity of demand four times (in the cells labeled A, B, C, and D). Note that the coefficient of price elasticity of demand over the entire range of the demand schedule is 1, indicating unit elasticity. Note also that the coefficient changes between specific price and quantity demanded points, indicating that a linear downsloping demand curve has different elasticity coefficients in different parts of the curve. As the price changes from $5 to $4 and the quantity demanded changes from 1 to 2, what is the coefficient of elasticity of demand (cell A)? As the price descends from $4 to $3 and the quantity demanded jumps from 2 to 3, what is the coefficient of price elasticity of demand (cell B)? Calculate the coefficient again for the $3–$2 price range and for the $2–$1 price range (cells C and D, respectively). Use the midpoints formula for all calculations.


2. Why is the coefficient for the $5–$4 price range higher than all the other ranges? In other words, why is the upper left portion of a linear downsloping demand curve the relatively most elastic portion? Why is the lower right portion always the most inelastic? This may seem difficult to answer, but it is not—if you think about the numbers involved and you remember that elasticity measures the percentage change in quantity demanded compared to the percentage change in price.


3. Calculate the total revenues for each price-quantity demanded combination (for example, if one were sold at $5, the total revenue would be $5). What happens to total revenue as price goes down in the elastic portion of the schedule? What happens to total revenue as price goes down in the inelastic portion of the schedule?


4. Why does total revenue increase if the price of an elastic good is decreased? Why does total revenue increase if the price of an inelastic good is decreased?


5. What types of goods should government tax if the government objective is to make money? Elastic or inelastic? Why?


6. Finally—and this is a stretch question—if you were a monopolist facing a downsloping demand curve, which portion of the curve would you strive never to be in? In other words, you can choose any price and output combination you want. Which combinations would you seek to avoid? Why?

Explanation / Answer

1. From the table above, I can graph a simple linear demand curve and show that the demand equation in this case is Qd= 6-p. To calculate point price elasticity, simply use this formula, EA( point price elasticity atA)= Price/Quantiry multiply by dQd/dP, or the first derivative of the demand Qd in respect to price. In this case ,it's -1. Therefore, elasticities at each points are as follows:- EA= 4/1 * -1= -4 EB=3/2 * -1= -3/2 EC= 2/3 * -1= -2/3 ED= 1/4 * -1= -1/4 Since we are dealing with elasticities, we can drop oput the negative signs. Point A has the highest elasticity at 4....while point D has the lowest elasticity, or inelastic, at 1/4. 2. To show why the top left corner of the slope(demand curve) is more elastic than the lower left, we can take two starting points. Lets take A to B. Point A ( 4,1) and point B (3,2). Now calculate the percentage change in Quantity from A-B. therefore, take 2 minus 1 divided by 1 and that gives you 100%. Now calculate the percentage change in price from A-B. To do that, simply take 3-4/4 or -25%, a price decrease. The final step now is to take the percentagw change in Q and divide by the percentage change in P. 100%/ -25% and you get -4. Voila...same answer . Do the same thing for point C-D and you will notice that the eleasticty is getting less and less. 3).Total revenue, TR, at A= 4*1= $4 TR at B = 3 *2= $6 TR at C= 2*3= $6 TR at D= 1*4= $4 As price goes down in the elastic portion of the curve, total revenue goes up. As price goes down in the inelastic portion of the curve, total revenue goes down. 4. Total revenue will go up or increase if the price of elastic good is decreased because people will increase demand for such good as they are HIGHLY reponsive to the change in price ( lower in price). Therefore, the more quantity demanded, total revenue will increase. As for inelastic goods, total revenue DOES not neccesarily increase if the price of such good is lowered. People may not want to demand more for it. That is why we call such goods ineleastic, or they are not very reponsive to price change. We showed that as we move from point C to point D that total revenue actually fell as price was lowered from $2 to $1. 5. A tax is like a price increase. To be profiutable for the govt, they should be taking a highly inelastic good. A tax on such goods or services will not cause people to use less or buy less of such goods or service. Therefore, the tax revenue the govt. can collect will remain high. 6. The portion on the curve i would avoid is where the cost of producing a unit of this good, C, is higher than the price of it per unit, P.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.