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{R/5, 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 Q₀ = 500P^-^3/2 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 find the price at which the marginal revenue equals marginal cost. The marginal cost of producing Bubbles is given as $5, which is independent of the quantity produced.

To find marginal revenue, we need to differentiate the demand functions with respect to quantity, and then multiply by the price:

For senior citizens: 
MR1 = (d/dQ) [500P(13/2 - P)] * P = 500(13/2 - 2P)

For those under 65: 
MR2 = (d/dQ) [50P(15 - P)] * P = 50(15 - 2P)

Setting MR1 = MC and solving for P gives: 
500(13/2 - 2P) = 5
P1 = $11.25

Setting MR2 = MC and solving for P gives: 
50(15 - 2P) = 5
P2 = $27.00

Therefore, the optimal pricing strategy is to charge senior citizens $11.25 per bottle and those under 65 years old $27.00 per bottle. Option C is the correct answer.

A Careful Analysis of Demand for Bubbles in Strasburg, North