As you know we are the only Bubble Tea vendor in West Virginia\'s coast. Right n

Question

As you know we are the only Bubble Tea vendor in West Virginia's coast. Right now we are charging a price of $4 per bubble tea to all our customers. However, we have noticed that local demand (Q1) differs from visitor demand (Q2), as seen by the given weekly demand curves:

Local: Q1 = 1,000 – 100P1

Visitor: Q2 = 500 – 100P2

In an effort to increase our profits we are thinking about lowering prices by 25% to customers that have local licence to encourage more sales to locals. So I would like you to review our current pricing strategy and let me know if a 25% discount to our locals would be profit enhancing. While you are reviewing our pricing strategy, let me now if we can improve our profits from our visitor customers by increasing their price.

In your review, keep in mind that our marginal costs per bubble tea served are $1.

Explanation / Answer

When P = 4,

For Local demand, Q1 = 1,000 - (100 x 4) = 1,000 - 400 = 600

Profit = Q1 x (P - MC) = 600 x $(4 - 1) = 600 x $3 = $1,800

For Visitor's demand, Q2 = 500 - (100 x 4) = 500 - 400 = 100

Profit = Q2 x (P - MC) = 100 x $(4 - 1) = 100 x $3 = $300

Total profit = $(1,800 + 300) = $2,100

Next, P1 decreases by 25% to $3 while P2 is unchanged at $4.

For Local demand, Q1 = 1,000 - (100 x 3) = 1,000 - 300 = 700

Profit = Q1 x (P - MC) = 700 x $(3 - 1) = 700 x $2 = $1,400

Since P2 & Q2 are same as before, Total profit = $(1,400 + 300) = $1,700

Since profit decreases, 25% discount to locals is not profit enhancing.

At the prices P1 = $3 and P2 = $4, we find the price elasticity of demand for both Local & Visitors as follows.

Elasticity = (dQ / dP) x (P / Q)

For Locals, Elasticity = (dQ1 / dP1) x (P1 / Q1) = - 100 x (3 / 700) = - 0.43

For Visitors, Elasticity = (dQ2 / dP2) x (P2 / Q2) = - 100 x (4 / 100) = - 4

Since absolute value of elasticity is higher than 1 for visitors, the Visitor demand is highly elastic. With elastic demand, an increase in price will lead to decrease in revenue and decrease in profit, ceteris paribus.

Therefore my recommendation is to keep the price unchanged as $4 since other pricing options will lower profit.

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