|15||10||__ 150 __|
|10||55||__ 550 __|
|5||100||__ 500 __|
The percentage change in price, using the midpoint formula is:
( 5 - 15) / 10 = -10/10 = - 1.0 or - 100 percent.
The percentage change in quantity, using the midpoint formula is:
(100 - 10) / 55 = 90/55 = 1.636.
The coefficient of elasticity is the percentage change in quantity divided by the percentage change in price, or - 90/55 = - 1.636. Since this is greater than 1 demand is elastic over this range, as we expected from the increase in revenue.
|100||100||- 10,000 -|
|300||90||- 27,000 -|
|500||80||- 40,000 -|
Note that revenue is increasing as the price is increasing. We expect that demand will prove to be inelastic in this case.
The percentage change in price, using the midpoint formula, is:
(100 - 500)/300 = - 400/300 = - 1.33 or - 133 percent.
The percentage change in quantity, using the midpoint formula, is:
(100 - 80)/90 = 20/90 = .22 or 22 percent.
The coefficient of elasticity is the percentage change in quantity divided by
the percentage change in price:
2/9 divided by 4/3 = (2/9)*(3/4) = 1/6 or .167
Demand, as expected on the basis of the change in revenue, is very inelastic in this case.
Note in constructing the table that the slope coefficient -4 shows that the
quantity demanded goes down by 4 for every dollar the price is increased.
You do not need to use the full equation more than once; after finding that
Q = 200 - 4(10) = 160
simply adjust the quantity by 4.
Percent change in price = (11 - 9)/10 = 2/10 or 20 percent.
Percent change in quantity = (156 - 164)/160 = -8/160 or - 5 percent
Coefficient of elasticity =
(percent change in quantity)/(percent change in price) = -5/20 = - .25
Note that the revenue goes from $ 9 x 164 = $ 1476 at a price of $ 9 to
a revenue of $ 11 x 156 = $ 1716 at a price of $ 11. Since revenue goes up with price in this case, we would expect that demand is inelastic, and the computation of the coefficient of elasticity confirms this.
The percentage change in price is (41 - 39)/40 = 2/40 = 5 percent.
Note that the same two dollar price increase was a 20 percent price increase in the last problem. The difference is that in this case the average price is much higher, 40 dollars rather than 10 dollars.
The percentage change in quantity is (36 - 44)/40 = -8/40 = 20 percent.
Note that the percentage change in quantity was only 5 percent in the previous case; the average quantity is much lower in this case
The coefficient of elasticity is
(Pct. Change in Q)/(Pct. change in P) = -20/5 = 4.
The coefficient of elasticity was .25 in the previous case; it is 4.0 in this case. The higher absolute value means that
The elasticity of demand increases as the price increases if the demand curve is a straight line.
(Note: an increase in the elasticity of demand with price may not take place if the demand curve is curved; constant or declining elasticity as price increases is possible in that case.)
No, since elasticity varies as the price increases along both curves. We must specify the price at which we are making the comparison.
|PRICE||Q = 200 - 4P||Q = 100 - 1/2 P|
The coefficient of elasticity for the demand curve Q = 200 - 4 P
is the percentage quantity change of 8/80 divided by 2/30 = 240/160 = 1.5 at a price of $30.
The coefficient of elasticity at a price of $30
for the demand curve Q = 100 - 1/2 P
is 1/85 divided by a percentage price change of 2/30 = 30/170 = .1765.
Accordingly, we can say that the curve introduced in this problem is less elastic than that in the previous problem if both curves are evaluated at the price of $30.
|PRICE||Q = 200 - 4 P||Q = 100 - 1/2 P|
The elasticity of demand for Q = 200 - 2P is the quantity percentage change of (200 - 192)/196 = 8/196 = 4 percent divided by the price percentage change of 2/1 or 200 percent -- that is, the COE is .02.
The elasticity of demand for Q = 100 - 1/2 P is the percent change in quantity of 1/99.5 or about 1 percent divided by the price percentage change of 200 percent; that is, the COE is .005. Again, the curve introduced in this problem is less elastic at a common price.
Again, as in the previous case, demand is more elastic as price increases.