You have recently founded a factory that produces RAM chips for computers. One year ago you bought the land for $2M and then used $4M of your own money to build the factory and buy the necessary equipment. The factory you've built can produce up to 1M chips per year.

You know that you could sell the land and factory for $8M currently, and you also think that it will gain 8% in value over the next year. The current interest rate you are receiving on your saving and borrowing is 10% per year. (For this question, suppose we are just planning at a one-year horizon.)

Producing chips incurs various operating costs such as energy, labor, and materials. You estimate this at $3 per chip, regardless of how many you produce in a year. In addition, producing RAM chips cause you to incur a fixed cost of $500,000 per year for items such as security, legal, HR, and utilities.

(a) Write down your cost function C(q), where q is the number of chips you produce during the year.

(b) What is the minimum price at which you would find it profitable to operate your factory at all during the upcoming year?

(c) Suppose that the type of RAM chips you produce is a commodity and thus is sold in a highly competitive market. The current market price is $4.42 per chip. How many chips should you produce to maximize your profits? What will your annual profits be? (Remember, we're always talking about economic profits.)

(d) Now, suppose that (unlike in the previous part) the type of RAM chip you produce is very specialized so that the market you are selling into is not a competitive market. You have done some market research and learned that if you price at $6.00 per chip the total demand you face will be 1M chips, while if you price at $7.00 per chip the total demand you face will be 750,000 chips. (And you are willing to assume that demand between these two points is linear.) How many chips should you produce and what price can you sell them at to maximize your profits? What will your annual profits be?

2/3 2. You have recently founded a factory that produces RAM chips for computers. One year ago you bought the land for $2M and then used $4M of your own money to build the factory and buy the necessary equipment. The factory you've built can produce up to IM chips per year. You know that you could sell the land and factory for $8M currently, and you also think that it will gain 8% in value over the next year. The current interest rate you are receiving on your saving and borrowing is 10% per year. (For this question, suppose we are just planning at a one-year horizon.) Producing chips incurs various operating costs such as energy, labor, and materials. You estimate this at $3 per chip, regardless of how many you produce in a year. In addition, producing RAM chips causes you to incur a xed cost of $500,000 per year for items such as security, legal, HR, and utilities. (3) (b) (C) ((0 Write down your cost function C(q), where q is the number of chips you produce during the year. What is the minimum price at which you would nd it protable to operate your factory at all during the upcoming year? Suppose that the type of RAM chips you produce are a commodity and thus are sold in a highly competitive market. The current market price is $4.42 per chip. How many chips should you produce to maximize your prots? What will your annual prots be? (Remember, we're always talking about economic prots.) Now, suppose that (unlike in the previous part) the type of RAM chip you produce is very specialized, so that the market you are selling into is not a competitive market. You have done some market research and learned that if you price at $6.00 per chip the total demand you face will be 1M chips, while if you price at $7.00 per chip the total demand you face will be 750,000 chips. (And you are willing to assume that demand between these to points is linear.) How many chips should you produce and what price can you sell them at to maximize your prots? What will your annual prots be