Question

In: Economics

You have the option to produce different versions of a product or service: high quality, or...

You have the option to produce different versions of a product or service: high quality, or
low quality. The marginal cost to produce the low quality version is $3 and the marginal
cost to produce the high quality version is $15. There are two types of consumers Type
A and Type C with 100 consumers of each type. Each consumer will buy at most one
version of the product. These consumers have the following willingness to pay:

Low Quality High Quality
Customer Type A $14 $28
Customer Type C $18 $52

1. Suppose you were to offer only the low quality version. Find the optimal price and profit. Show/Explain why these are the optimal prices/profits.

2. Suppose you were to only offer the high quality version. Find the optimal price and profit. Show/Explain why these are the optimal prices/profits.

3. Suppose you offer high and low quality versions. Find the optimal prices and profit.

Solutions

Expert Solution

1. The marginal cost of the low-quality product is $3 and the willingness to pay by Customer Type A and C for the low-quality product are $14 and $18 respectively. Now, assuming that the firm mentioned in the question is a monopoly and it can engage in price discriminatory practice based on the various willingness to pay by different types of customers, it will maximize its total or overall profit by selling that level of output at which the marginal cost of production equals the price charged by the firm, or the willingness to pay for the product by each customer type.

Therefore, in this case, the price charged by the firm to both the customer type A and B will be $3 for each low-quality product as at that price for per product, the marginal cost of the firm and the per product price charged are equal or identical and eventually, the firm's overall profit from selling low-quality products to both types of customers is maximized for each type of customer.

Now, the maximum willingness to pay for the low-quality product is $14, and if the firm charges $3 for each low-quality product, the customer type A will buy a total of==4.66 or rounding off to 4 low-quality products.

Similarly, the maximum willingness to pay for the low-quality product by customer type B is $18, and considering that the firm charges $3 for each product to maximize its profit, the customer type B will purchase a total of==6 low-quality products.

Now, the overall or total market surplus extracted by the firm from selling low-quality products to customer type A==$28 and the total surplus extracted by the firm from selling the same to the customer type B==$54.

Note, that while selling the low-quality products to both customer types A and B, the firm essentially extracts the entire consumer surplus from both customer types by charging the product price equal to its marginal cost of production with respect to a much higher willingness to pay for the low-quality product by each customer types. Therefore, it extracts the entire consumer surplus in the market as part of its total or overall profit from both customer types A and B.

2. Now, the willingness to pay for the high-quality product by customer type-A is $28 and the willingness to pay for the high-quality products by customer type-B is $52. The marginal cost of producing a high-quality product is $15. Therefore, in this case, the firm will charge a price of $15 per product which is equal or identical to its marginal cost of production in this case.

Hence, at this price level, customer type A will buy==1.86 or rounding off to 1 high-quality product and customer type B will purchase==3.46 or 3 high-quality products.

The overall or total producer surplus extracted by the firm by selling a high-quality product to a customer type-A==$14 and the total producer surplus obtained by the firm by selling a high-quality product to customer type-B==$78.

Again, the firm basically extracts the entire consumer surplus in the market for high-quality products by selling the number of products that would diminish the maximum willingness to pay by each customer type to purchase high-quality products. It maximizes its overall or total profit level by selling the number of products to the respective customer types at which the price of the per product is equal to the marginal cost of producing each of those products and extracting the overall consumer surplus from the market by exploiting the maximum willingness to pay by these consumers or buyers based on their types.

3. Considering the constant marginal cost of production of producing both the low and high-quality products given in the question, the firm will practically stick to its profit-maximizing price level at $3 for each low-quality and $15 for each of the high-quality product., which reflects first-degree price discrimination based on the maximum willingness to pay for each type of products by the respective customer types.

As calculated in parts 1 and 2, the total producer surplus from selling a low-quality product to a customer type-A and B are $28 and $54 respectively. Therefore, the total producer or market surplus obtained by the firm from selling a low-quality product in the market==$82 and the total market or producer surplus extracted by the firm from selling a high-quality product to a customer type A and B are $14 and $78 respectively. Hence, the overall market or producer surplus obtained by the firm from selling a high-quality product in the market including both types of customers==$92.

Now, considering all the 100 customers belonging to type-A and B and both low and high-quality products, the overall producer surplus obtained by the firm would be==$17,400


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