3.1. DRAM factory. You own and operate a facility located in Taiwan that manufac- tures 64-megabit dynamic random-access memory chips (DRAMs) for personal comput- ers (PCs). One year ago you acquired the land for this facility for $2 million, and used $3 million of your own money to finance the plant and equipment needed for DRAM manufacturing. Your facility has a maximum capacity of 10 million chips per year. Your cost of funds is 10% per year for either borrowing and investing. You could sell the land, plant, and equipment today for $8 million; you estimate that the land, plant, and equip- ment will gain 6% in value over the coming year. (Use a one-year planning horizon for this problem.) In addition to the cost of land, plant, and equipment, you incur various operating expenses associated with DRAM production, such as energy, labor, raw materials, and packaging. Experience shows that these costs are $4 per chip, regardless of the number of chips produced during the year. In addition, producing DRAMs will cause you to incur fixed costs of $500k per year for items such as security, legal, and utilities. (a) What is your cost function, C(q), where q is the number of chips produced during the year? Assume now that you can sell as many chips as you make at the going market price per chip of p. (b) What is the minimum price, p, at which you would find it profitable to pro- duce DRAMs during the coming year? (Cabral, 20170224)
3.1. DRAM factory. You own and operate a facility located in Taiwan that manufac- tures 64-megabit dynamic random-access memory chips (DRAMs) for personal comput- ers (PCs). One year ago you acquired the land for this facility for $2 million, and used $3 million of your own money to finance the plant and equipment needed for DRAM manufacturing. Your facility has a maximum capacity of 10 million chips per year. Your cost of funds is 10% per year for either borrowing and investing. You could sell the land, plant, and equipment today for $8 million; you estimate that the land, plant, and equip- ment will gain 6% in value over the coming year. (Use a one-year planning horizon for this problem.)
In addition to the cost of land, plant, and equipment, you incur various operating expenses associated with DRAM production, such as energy, labor, raw materials, and packaging. Experience shows that these costs are $4 per chip, regardless of the number of chips produced during the year. In addition, producing DRAMs will cause you to incur fixed costs of $500k per year for items such as security, legal, and utilities.
(a) What is your cost function, C(q), where q is the number of chips produced during the year?
Assume now that you can sell as many chips as you make at the going market price per chip of p.
(b) What is the minimum price, p, at which you would find it profitable to pro- duce DRAMs during the coming year? (Cabral, 20170224)
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