you are the manager of a firm that produces two products X and Y at zero cost. there are three types of consumers(1000 of each type) with the following valuations of the two products.
consumer type Product X($) ProductY($)
1 90 60
2 70 140
3 40 160
What are your profits if you charge $150 for a bundle containing one unit of product X and one unit of product Y?
since there is zero cost, what you charge is all profit, right?
To calculate your profits, you need to determine the total revenue and the total cost. In this case, since the firm produces the products at zero cost, the total cost is zero. Therefore, your profit will be equal to the total revenue.
To determine the total revenue, we need to calculate the number of consumers who are willing to purchase the bundle and multiply it by the price of the bundle.
Let's analyze the valuation of each consumer for the bundle:
- Consumer type 1 has a valuation of $90 for product X and $60 for product Y. Since the bundle contains both products, their valuation for the bundle would be the sum of the valuations, which is $150.
- Consumer type 2 has a valuation of $70 for product X and $140 for product Y. The bundle's valuation for this consumer would also be the sum of the valuations, which is $210.
- Consumer type 3 has a valuation of $40 for product X and $160 for product Y. The valuation for the bundle for this consumer would be $200.
Now let's calculate the number of consumers who are willing to purchase the bundle:
- For the first consumer type, we can see that they are willing to pay $150 for the bundle. Since there are 1000 consumers of this type, the number of consumers who are willing to purchase the bundle is 1000.
- Similarly, for consumer type 2, all 1000 consumers are willing to purchase the bundle.
- For consumer type 3, only 1000 consumers are willing to pay for the bundle.
Therefore, the total number of consumers willing to purchase the bundle is 3000 (1000 + 1000 + 1000).
Now, we can calculate the total revenue by multiplying the price of the bundle ($150) by the number of consumers:
Total Revenue = Price of Bundle * Number of Consumers
= $150 * 3000
= $450,000
Hence, your profit will be $450,000 since the total revenue is equal to your profit in this case.