Question

1. Two types of customers make up the market for Armoyas. There are 80 type A customers, each of whom is willing to pay up to $10 for an Armoya. There are 40 type B customers, each willing to pay up to $8 for an Armoya. No customer wishes to buy more than a single Armoya. The monopolist cannot differentiate between the types of customer. The average and marginal cost of production is constant at $6/Armoya.
   
2. 1. What is the selling price of the good, and how much profit does the monopolist make?
      
   2. The monopolist is offered the opportunity to advertise Armoyas at a cost of $80. The advertisement is predicted to attract another 100 type B customers. Will the advertisement be placed? What is the selling price of the good, and how much profit does the monopolist make?
      
   3. Suppose the advertisement attracts no new customers, but raises the price all existing customers are willing to pay by $1. Will the advertisement be placed? What is the selling price of the good, and how much profit does the monopolist make?

Answer 1

a.

Selling price = $8

Profit = $240

The monopolist should capture the lowest willingness-to-pay for charging price. Compare to $10, the lowest willingness-to-pay is $8. Therefore, the price is $8. At this price, the product could be sold to both types of customers.

This price would give the highest profit.

Profit = Total revenue – Total costs

Profit at $10 price = 80 × $10 – 80 × $6 = 800 – 480 = $320 (profit, if customers are differentiated)

Profit at $8 price = (80 + 40 =) 120 × $8 – 120 × $6 = 960 – 720 = $240 (profit, if customers are not differentiated)

b.

Yes; there should be an advertisement, since it gives higher profit than $240.

Selling price is still $8, since the lowest willingness-to-pay should be captured because of non-differentiating between customers.

Profit at $8 price = (80 + 40 + 100 =) 220 × $8 – 220 × $6 + $80 = 1,760 – 1,400 = $360 (higher than earlier $240).

c.

The scenario:

Willingness to pay by A type = 10 + 1 = $11

Willingness to pay by B type = 8 + 1 = $9

Advertisement cost is still $80

New profit at $9 price = (80 + 40 =) 120 × $9 – 120 × $6 + 80 = 1,080 – 800 = $280

Since the new profit ($280) increases from the earlier profit ($240), the advertisement should be placed.

Since there is no differentiation between customers, the lowest willingness to pay should be the price because of keeping both types of customers. Selling price is $9.

Profit (as calculated above) is $280.