Answers to Chapter 3 Exercises
Answers to Chapter 3 Exercises
3.1. DRAM factory. You own and operate a facility located in Taiwan that manufactures
64-megabit dynamic random-access memory chips (DRAMs) for personal computers (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 equipment 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?
Answer: The $5 million you originally spent for the land, plant, and equipment is a sunk expenditure and thus not an economic cost. However, there is a “user cost of capital” associated with the land, plant and equipment, based on its current market value of $8 million and your cost of funds and the rate of depreciation or appreciation of the asset over the planning horizon. Your (opportunity) cost of investing $8 million for one year is $800k, but these assets will appreciate by $480k over the year, giving a (net) user cost of capital of
$320k. (The depreciation rate is 6%.) This is a fixed cost of making DRAM’s, to which we must add the other fixed costs of $500k to get a combined fixed cost of $820k for the year.
The
3.1. DRAM factory. You own and operate a facility located in Taiwan that manufactures
64-megabit dynamic random-access memory chips (DRAMs) for personal computers (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 equipment 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?
Answer: The $5 million you originally spent for the land, plant, and equipment is a sunk expenditure and thus not an economic cost. However, there is a “user cost of capital” associated with the land, plant and equipment, based on its current market value of $8 million and your cost of funds and the rate of depreciation or appreciation of the asset over the planning horizon. Your (opportunity) cost of investing $8 million for one year is $800k, but these assets will appreciate by $480k over the year, giving a (net) user cost of capital of
$320k. (The depreciation rate is 6%.) This is a fixed cost of making DRAM’s, to which we must add the other fixed costs of $500k to get a combined fixed cost of $820k for the year.
The