A careful analysis of demand for Bubbles in Strasburg, North Dakota, reveals a strange segmentation in the market. (Recall Bubbles is the beverage which produces an unexplained craving for Lawrence Welk's music. It is produced by the process Q = min{ , W}, where R is the number of pulverized Lawrence Welk records and W is gallons of North Dakota well water. P_R = $1, P_W = $4.) If demand for Bubbles by senior citizens is described by while demand by those under 65 years old is Q_y = 50P^-⁵, how should Bubbles be priced to maximize profits? A) $13 for all citizens of Strasburg B) $9 for senior citizens and $30 for those younger C) $27 for senior citizens and $11.25 for those younger D) $13.50 for senior citizens and $45 for those younger E) $60 for senior citizens and $25 for those younger

Question

Quizplus · Accepted Answer

To maximize profits, we need to set the price at the point where marginal revenue equals marginal cost. The marginal cost of producing Bubbles is simply the cost of the North Dakota well water, which is $4 per gallon. To find the marginal revenue, we need to take the derivative of the demand functions:

For senior citizens: MR = 11ea6c55_6e49_c6bb_9875_a1055e788cf1'_TB6162_11 = 11ea6c55_6e49_c6bb_9875_a1055e788cf1_TB6162_11 * 1/P = 110 - 22P

For those under 65: MR = QS1U1B1yS1U1B0'_S1P0S1S1P1S1U1P1S1U1P15S1S1P0 = 50(S1U1P1-S1S1P0) + 50(S1S1P0-S1U1P15) = 100 - 50S1U1P1

Setting MR equal to MC, we can solve for the optimal prices:

For senior citizens: 110 - 22P = 4 -> P = 27/11

For those under 65: 100 - 50S1U1P1 = 4 -> S1U1P1 = 19.92/50 = 0.3984

Therefore, the optimal prices are $27 for senior citizens and $11.25 (=$4/0.356) for those under 65. So the answer is C.

A Careful Analysis of Demand for Bubbles in Strasburg, North