Answer:
(a) The total revenue at prices 6 and 7.5 are 6000 and 6227.50, since the elasticity of demand (0.8) is smaller than 1, the price elasticity of the product is inelastic. This suggests a possibility of a rise in price , since this increases TR. the strategy of 25% rise in price is justifiable. The management should work with this strategy. (B) The government can intervene in this market situation, since this is the market by which the government can have revenue tax a lot without affecting the market, such as cigarette, The demand of this product would remains the same,showing a good market for imposing a higher tax for generating higher revenue by the government
Explanation:
Solution
Given that:
The price elasticity of demand (E), the quantity consumption for an increasing price should be computed as follows:
Which is
Q1 = 1,000
Q2 =? not known
P1 = 6
P2 = P1 × (1 + 0.25) = 6 × 1.25 = 7.5
Thus,
E = -0.8; price elasticity of demand should be negative.
Therefore,
by the formula as below:
E = [(Q2 – Q1) / {(Q1 + Q2) / 2}] / [(P2 – P1) / {(P1 + P2) / 2}]
-0.8 = [(Q2 – 1,000) / {(1,000 + Q2) / 2}] / [(7.5 – 6) / {(6 + 7.5) / 2}]
so,
-0.8 = [(Q2 – 1,000) / (500 + 0.5Q2)] / [1.5 / 6.75]
-0.8 × (1.5 / 6.75) = (Q2 – 1,000) / (500 + 0.5Q2)
-0.1777 × (500 + 0.5Q2) = Q2 – 1,000
-88.85 - 0.08885Q2 = Q2 – 1,000
-0.08885Q2 – Q2 = - 1,000 + 88.85
-1.08885Q2 = - 911.15
Q2 = 911.15 / 1.08885 = 837
(A) The Total revenue (TR) at 6 price = Q1 × P1 = 1,000 × 6 = 6,000
so,
The Total revenue (TR) at 7.5 price = Q1 × P1 = 837 × 7.5 = 6,277.50
Because the elasticity of demand (0.8) is lesser than 1, the price elasticity of the product is not elastic. This suggests a possibility of a rise in price , since this increases TR.
The Sales or TR increases from 6,000 to 6,277.50 by the price increase from 6 to 7.5.
Hence, the strategy of 25% rise in price is justifiable. The management should employ this strategy.
(B) The government can intercede in this market, since this is the market by which the government can obtain tax revenue a lot without affecting the market, now cigarette is a product that a smoker smokes because of his/her habit; therefore, a change in price, will not affect the change of habit.
The Demand of this product is remains almost the same,showing a good market for forcing higher tax for earning higher revenue by the government
