The ABC Company manufactures AM/FM clock radios and sells on average 3,000 units monthly at 25$ each to retail stores.Its closest competitor produces a similar type of radio that sells for 28$.
a. If the demand for ABC's product as coefficient of-3, how many will be sell per month if the price is lowered to 22$?
b. The competitor decrease its price to 24$. If the cross-elasticity between the two radio os 0.3, what will ABC's monthly sales be?
a) Ed = (% Change in Quantity Demanded)/(% Change in Price)
-3 = (Q2 - 3000)/(22 - 25)*(22 + 25)/(Q2 + 3000)
(Q2 - 3000)/3*47/(Q2 + 3000) = 3
(Q2 - 3000)/(Q2 + 3000) = 9/47
Q2 - 3000 = 9/47*Q2 + 27000/47
38/47Q2 = 168000/47
38Q2 = 168000
Q2 = 4421 units
b) Cross-price elasticity equals:
0.3 = (28 + 24)/(3000 + Q2)*(Q2 - 3000)/(24 - 28)
52/(3000 + Q2)*(Q2 - 3000)/(-4) = 0.3
(Q2 - 3000)/(Q2 + 3000) = -0.3/13
Q2 - 3000 = -3/130Q2 - 900/13
133/130Q2 = 381000/130
133Q2 = 381000
Q2 = 2865 units.
According to a study, the price elasticity of shoes in the United States is 0.7, and the income elasticity is 0.9.
a. Would you suggest that the Brown Shoe Company cut its prices to increase its revenue?
b. What would be expected to happen to the total quantity of shoes sold in the country if incomes rise by 10 percent?
a. To calculate how many units ABC will sell per month if the price is lowered to $22, we can use the concept of price elasticity of demand. Price elasticity of demand measures the responsiveness of the quantity demanded to a change in price.
The formula for price elasticity of demand is:
Elasticity = (% Change in Quantity Demanded) / (% Change in Price)
Given that the demand for ABC's product has a coefficient of -3, this means that the demand is elastic, as the coefficient is greater than 1.
To determine the change in quantity demanded, we need to calculate the percentage change in price:
Percentage Change in Price = (New Price - Old Price) / Old Price * 100
Percentage Change in Price = (22 - 25) / 25 * 100 = -12%
Since the coefficient is -3, the percentage change in quantity demanded will be three times the percentage change in price:
Percentage Change in Quantity Demanded = -3 * (-12%) = 36%
Now, we can calculate the new quantity demanded:
New Quantity Demanded = Old Quantity Demanded + (Percentage Change in Quantity Demanded / 100) * Old Quantity Demanded
Old Quantity Demanded = 3,000 units
New Quantity Demanded = 3,000 + (36% / 100) * 3,000 = 3,000 + (0.36) * 3,000 = 3,000 + 1,080 = 4,080 units
Therefore, if the price is lowered to $22, ABC will sell approximately 4,080 units per month.
b. To calculate ABC's monthly sales when the competitor decreases its price to $24, we need to use the concept of cross-elasticity of demand. Cross-elasticity of demand measures the responsiveness of the quantity demanded of one product to a change in the price of another product.
The formula for cross-elasticity of demand is:
Cross-Elasticity = (% Change in Quantity Demanded of ABC) / (% Change in Price of Competitor)
Given that the cross-elasticity between the two radios is 0.3, this means that the demand for ABC's radio is slightly responsive to changes in the price of the competitor's radio.
To determine the change in quantity demanded of ABC, we need to calculate the percentage change in the competitor's price:
Percentage Change in Price of Competitor = (New Price - Old Price) / Old Price * 100
Percentage Change in Price of Competitor = (24 - 28) / 28 * 100 = -14.29%
Now we can calculate the change in quantity demanded of ABC:
Change in Quantity Demanded of ABC = Cross-Elasticity * (% Change in Price of Competitor)
Change in Quantity Demanded of ABC = 0.3 * (-14.29%) = -4.29%
The negative sign indicates that the quantity demanded of ABC decreases when the competitor's price decreases.
To calculate ABC's monthly sales, we subtract the change in quantity demanded from the original quantity:
New Quantity Demanded of ABC = Old Quantity Demanded - (Change in Quantity Demanded of ABC / 100) * Old Quantity Demanded
Old Quantity Demanded = 3,000 units
New Quantity Demanded of ABC = 3,000 - (4.29% / 100) * 3,000 = 3,000 - (0.0429) * 3,000 = 3,000 - 128.7 = 2,871.3 units
Therefore, if the competitor decreases its price to $24, ABC's monthly sales will be approximately 2,871 units.