MK Corp estimates that its demand function is as follows: Q = 400 - 12.5P+ 25A + 14Y + 10P* Where Q is the quantity demanded per month, P is the product’s price (in $), A is the firm’s advertising expenditure (in $’000 per month), Y is per capita disposable income (in $’000), and P * is the price of AJ Corp. a. During the next five years, per capita disposable income is expected to increase by $5,000 and AJ is expected to increase its price by $12. What effect will this have on the firm’s sales volume? b. If MK wants to change its price by enough to offset the above effects, by how much must it do so? c. Compare the profitability of maintaining sales volume by either changing price or changing advertising spending. d. If MK’s current price is $60 and it spends $10,000 per month on advertising, while per capita income is $25,000 and AJ’s price is $70, calculate the price elasticity of demand with the price change. e. What can be said about the effect of the above price change on profit? f. What can be said about the relationship between the products of MK and AJ?
Answers
a. During the next five years, per capita disposable income is expected to increase by $5,000 and AJ is expected to increase its price by $12. The increase in disposable income will have a positive effect on the demand for MK's product, as the demand function includes a positive term for Y. The increase in the price of AJ's product will also have a positive effect on the demand for MK's product, as the demand function includes a positive term for P*. Therefore, these two changes are expected to increase the firm's sales volume.
b. To offset the positive effects of the increase in disposable income and the increase in the price of AJ's product, MK must decrease its price by enough to cancel out the positive effect of these changes. Using the demand function, we can calculate the required price change as follows:
Q = 400 - 12.5P + 25A + 14(5,000) + 10(12)
Solving for P, we get:
P = (400 - 25A - 70,000)/(-12.5)
Substituting in the known values for A and P, we get:
P = (400 - 25(10,000) - 70,000)/(-12.5) = $55
Therefore, MK must decrease its price by $5 ($60 - $55) to offset the positive effect of the increase in disposable income and the increase in the price of AJ's product.
c. To compare the profitability of changing price versus changing advertising spending, we would need to know the costs associated with each option. If changing the price results in a greater increase in revenue than the cost of the price change, it would be more profitable. Similarly, if increasing advertising spending results in a greater increase in revenue than the cost of the advertising, it would be more profitable. Without knowing the specific costs and revenues associated with each option, it is not possible to determine which would be more profitable.
d. To calculate the price elasticity of demand, we need to know the percentage change in quantity demanded and the percentage change in price. Using the demand function, we can calculate the percentage change in quantity demanded as follows:
% change in Q = [(400 - 12.5P + 25A + 14Y + 10P* - 400 + 12.5P - 25A - 14Y - 10P*)/(400 - 12.5P + 25A + 14Y + 10P*)] * 100
Simplifying and rearranging the terms, we get:
% change in Q = (-25A + 14Y + 10P*)/(400 - 12.5P + 25A + 14Y + 10P*) * 100
Substituting in the known values for A, Y, P, and P*, we get:
% change in Q = (-25(10,000) + 14(25,000) + 10(70))/(400 - 12.5(60) + 25(10,000) + 14(25,000) + 10(70)) * 100 = 16.67%
To calculate the percentage change in price, we can use the following formula:
% change in P = (P2 - P1)/P1 * 100
Substituting in the known values for P1 and P2, we get:
% change in P = (55 - 60)/60 * 100 = -8.33%
Using these values, we can calculate the price elasticity of demand as follows:
Price elasticity of demand = % change in Q/% change in P = 16
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