The following is a straight-line demand curve that confronts a single firm. (a)
ID: 1146477 • Letter: T
Question
The following is a straight-line demand curve that confronts a single firm.
(a) In column 3, compute total revenue. In column 4, compute the coefficient for the price elasticity of demand at each price using the midpoints formula.
(b) Describe the character of elasticity across the prices based on the total revenue test and the elasticity coefficient.
(c) Does a straight-line demand curve have constant elasticity? (d) Of what practical significance is your answer to (c)?
PRICE Quantity Demanded Total Revenue Price Elasticity of Demand Using Midpoints Formula 6 1 5 2 4 3 3 4 2 5 1 6Explanation / Answer
The table is completed below. Revenue is the product of price and quantity. It is given by TR = P x Q. Using the mid point formula for moving along the quantity and price change, the mid point elasticities are provided below.
Ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2]
Take, for example, Q1 = 1 and Q2 = 2, P1 = 6 and P2 = 5. This gives ed = 3.67 in absolute terms.
PRICE
Quantity Demanded
Total Revenue
Price Elasticity of Demand Using Midpoints Formula
6
1
6
5
2
10
3.67
4
3
12
1.8
3
4
12
1
2
5
10
0.56
1
6
6
0.27
b) We observe that revenue increases with price fall when demand is elastic and revenue decreases with price decrease when the demand is inelastic. This verifies the revenue test where we realize that when demand is inelastic, % of price change is greater than % change in quantity so that revenue follows the price.
c) A straight-line demand curve can have different shapes, that is, it may be perfectly elastic (horizontal), perfectly inelastic (vertical) or it lies in between the two. In case of horizontal demand ir vertical demand, the elasticity remains constant but for a downward sloping one, the demand elsticity is not constant
(d) These three shapes are of major significance. When the demand is perfectly elastic (horizontal), any tax on buyer or seller is eventually paid by the sellers. Similarly, when demand is perfectly inelastic (vertical), any tax on buyer or seller is eventually paid by the buyers. The shape of the demand curve also has its effect on the amount of subsidy granted.
PRICE
Quantity Demanded
Total Revenue
Price Elasticity of Demand Using Midpoints Formula
6
1
6
5
2
10
3.67
4
3
12
1.8
3
4
12
1
2
5
10
0.56
1
6
6
0.27
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