If a firm supplies separable markets with price elasticities h1 = -3 and h2 = -2, it should set prices P1 and P2 so that:
a.2/3P1 = 1/2P2
b.3P1 = 2P2
c.2P1 = 3P2
d.P1 = P2
e.2P1 = 2/3P2
For your professor's, you gotta use the table , ululasy found at the back of your textbook or chapter, in the appendix, etc. I don't recommend using the table because it only works under certain uniform situations. The table's answer will also not be the exact correct answer; and the error will be bigger in bigger problems. Cheers.
2/3P1 = 1/2P2
To determine the optimal prices, we need to use the price-elasticity formula:
Elasticity (h) = (% change in quantity demanded) / (% change in price)
Given that the price elasticity of demand for market 1 (h1) is -3 and the price elasticity of demand for market 2 (h2) is -2, we can set up the following equations:
h1 = -3 = (% change in quantity demanded for market 1) / (% change in price for market 1)
h2 = -2 = (% change in quantity demanded for market 2) / (% change in price for market 2)
To make the calculation easier, we can simplify these equations:
-3 = (ΔQ1 / Q1) / (ΔP1 / P1) ----- (1)
-2 = (ΔQ2 / Q2) / (ΔP2 / P2) ----- (2)
Since the demand for price elasticity is always negative, we can discard the negative signs.
Now let's simplify the equations further using algebraic manipulation:
(ΔQ1 / Q1) / (ΔP1 / P1) = 3 ----- (1)
(ΔQ2 / Q2) / (ΔP2 / P2) = 2 ----- (2)
Cross-multiply the equations:
(ΔQ1 / Q1) = 3 * (ΔP1 / P1) ----- (3)
(ΔQ2 / Q2) = 2 * (ΔP2 / P2) ----- (4)
Re-arranging equations (3) and (4):
(ΔP1 / P1) = (ΔQ1 / Q1) / 3 ----- (5)
(ΔP2 / P2) = (ΔQ2 / Q2) / 2 ----- (6)
Now we can determine the relationship between the prices P1 and P2 by substituting the given equation options:
a. 2/3P1 = 1/2P2
b. 3P1 = 2P2
c. 2P1 = 3P2
d. P1 = P2
e. 2P1 = 2/3P2
Let's substitute equation (5) into the option a:
(2/3P1) = (ΔQ1 / Q1) / 3
Since the equation does not match, we can eliminate option a.
Let's substitute equation (5) into the option b:
3P1 = 2P2
Since the equation matches, option b could be a valid answer.
Let's substitute equation (5) into option c:
2P1 = 3P2
Since the equation does not match, we can eliminate option c.
Let's substitute equation (5) into option e:
2P1 = 2/3P2
Since the equation does not match, we can eliminate option e.
Thus, the correct answer is: b. 3P1 = 2P2.
To determine the optimal prices P1 and P2 for a firm that supplies separable markets with price elasticities h1 = -3 and h2 = -2, we need to use the concept of optimal pricing. The optimal pricing is achieved when the price elasticity of demand for each market is equal to the reciprocal of the ratio of the market's share of total revenue.
Step 1: Find the market shares of revenue for each market. In this case, the market shares can be determined by dividing the demand elasticities:
Market 1 share = (h1 / (h1 + h2))
Market 2 share = (h2 / (h1 + h2))
Given that h1 = -3 and h2 = -2, the market shares are:
Market 1 share = (-3 / (-3 + -2)) = -3 / -5 = 3/5
Market 2 share = (-2 / (-3 + -2)) = -2 / -5 = 2/5
Step 2: Use the market shares of revenue to set the prices. We need to set the prices P1 and P2 such that:
(P1 / P2) = (Market 2 share / Market 1 share)
Substituting the values we derived earlier:
(P1 / P2) = (2/5) / (3/5) = 2/3
Rearranging the equation:
2/3P1 = P2
Therefore, the correct answer is:
a. 2/3P1 = 1/2P2