Questions: Amanda 110 45 Sofia 60 23 Max 300 85 Peter 220 69 Paulo 140 48 Marquis 40 19 Assume that the marginal cost to provide the vaccine is zero. Therefore, maximizing profits would be the same as maximizing revenue. Suppose Pfizer cannot price-discriminate. It has to charge everyone the same price. Pfizer would charge 190. Now suppose Pfizer can charge discriminatory prices, based on gender. Pfizer would charge women and charge men

Amanda  110  45 
Sofia  60  23 
Max  300  85 
Peter  220  69 
Paulo  140  48 
Marquis  40  19 

Assume that the marginal cost to provide the vaccine is zero. Therefore, maximizing profits would be the same as maximizing revenue.

Suppose Pfizer cannot price-discriminate. It has to charge everyone the same price. Pfizer would charge 190.

Now suppose Pfizer can charge discriminatory prices, based on gender. Pfizer would charge women  and charge men
Transcript text: Amanda & $\$ 110$ & 45 \\ Sofia & $\$ 60$ & 23 \\ Max & $\$ 300$ & 85 \\ Peter & $\$ 220$ & 69 \\ Paulo & $\$ 140$ & 48 \\ Marquis & $\$ 40$ & 19 \\ Assume that the marginal cost to provide the vaccine is zero. Therefore, maximizing profits would be the same as maximizing revenue. Suppose Pfizer cannot price-discriminate. It has to charge everyone the same price. Pfizer would charge \$ $\square$ 190 . Now suppose Pfizer can charge discriminatory prices, based on gender. Pfizer would charge women \$ $\square$ and charge men \$ $\square$
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Solution

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To solve the problem, we need to determine the optimal pricing strategy for Pfizer under two different scenarios: uniform pricing and gender-based price discrimination. The goal is to maximize revenue, given that the marginal cost is zero.

Part 1: Uniform Pricing

Pfizer cannot price-discriminate and must charge everyone the same price. To maximize revenue, Pfizer should set a price that maximizes the total amount collected from all individuals willing to pay that price or more.

  1. List the willingness to pay:

    • Amanda: \$110
    • Sofia: \$60
    • Max: \$300
    • Peter: \$220
    • Paulo: \$140
    • Marquis: \$40
  2. Sort the willingness to pay in descending order:

    • Max: \$300
    • Peter: \$220
    • Paulo: \$140
    • Amanda: \$110
    • Sofia: \$60
    • Marquis: \$40
  3. Calculate total revenue for each price point:

    • At \$300: Revenue = \$300 (1 person)
    • At \$220: Revenue = \$220 * 2 = \$440 (2 people: Max, Peter)
    • At \$140: Revenue = \$140 * 3 = \$420 (3 people: Max, Peter, Paulo)
    • At \$110: Revenue = \$110 * 4 = \$440 (4 people: Max, Peter, Paulo, Amanda)
    • At \$60: Revenue = \$60 * 5 = \$300 (5 people: Max, Peter, Paulo, Amanda, Sofia)
    • At \$40: Revenue = \$40 * 6 = \$240 (6 people: Max, Peter, Paulo, Amanda, Sofia, Marquis)
  4. Determine the price that maximizes revenue:

    • The maximum revenue is \$440, which can be achieved at either \$220 or \$110.

Since the problem suggests a price of \$190, it seems there might be a misunderstanding. However, based on the calculations, the optimal uniform price should be either \$220 or \$110 to achieve maximum revenue of \$440.

Part 2: Gender-Based Price Discrimination

Pfizer can charge different prices based on gender. We need to determine the optimal price for women and men separately.

  1. Identify willingness to pay by gender:

    • Women: Amanda (\$110), Sofia (\$60)
    • Men: Max (\$300), Peter (\$220), Paulo (\$140), Marquis (\$40)
  2. Calculate optimal price for women:

    • At \$110: Revenue = \$110 (1 person: Amanda)
    • At \$60: Revenue = \$60 * 2 = \$120 (2 people: Amanda, Sofia)

    The optimal price for women is \$60, maximizing revenue at \$120.

  3. Calculate optimal price for men:

    • At \$300: Revenue = \$300 (1 person: Max)
    • At \$220: Revenue = \$220 * 2 = \$440 (2 people: Max, Peter)
    • At \$140: Revenue = \$140 * 3 = \$420 (3 people: Max, Peter, Paulo)
    • At \$40: Revenue = \$40 * 4 = \$160 (4 people: Max, Peter, Paulo, Marquis)

    The optimal price for men is \$220, maximizing revenue at \$440.

Summary:

  • Part 1: The optimal uniform price should be either \$220 or \$110, achieving maximum revenue of \$440.
  • Part 2: Pfizer should charge women \$60 and men \$220 to maximize revenue with gender-based price discrimination.
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