You own and operate a facility located in Taiwan that manufa

You own and operate a facility located in Taiwan that manufactures 64-gigabit dynamic random-access memory chips (DRAMS) for personal computers (PCS). One year ago you acquired the land for this facility for $3 million, and used $5 million of your own money to nance 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 8% per year for either borrowing or investing. You could sell the land, plant, and equipment today for $7 million; you estimate that the land, plant, and equipment will gain 8% 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 $6 per chip, regardless of the number of chips produced during the year. In addition, producing DRAMS will cause you to incur fixed costs of $750,000 per year for items such as security, legal, and utilities. Assume now that you can sell as many chips as you make at the going market price per chip of p. What is the minimum price, p, at which you would find it protable to produce DRAMS during the coming year?

$6.000

$6.025

$6.075

$6.750

Solution

Your (opportunity) cost of investing $7 million for one year is $560,000 ----------> 7,000,000*0.08

but these assets will appreciate by $560,000 over the year, --------------> 7,000,000*0.08

giving a (net) user cost of capital of $0.00 (The depreciation rate is 6%.) This is a fixed cost of making DRAM\'s, to which we must add the other fixed costs of $750,000 to get a combined fixed cost of $750,000 for the year

The variable costs are a constant $6 per chip

cost function is

C(Q)= 750,000 + 6Q

The average cost function is AC (Q) = 750,000/Q + 4, again up to ten million chips per year. This declines with Q, so the minimum AC is achieved at full capacity utilization. At ten million chips per year, the fixed costs come to $0.075 per chip,

so average costs are $6.075 per chip. (6+0.075) This is your minimum average cost, and thus the minimum price at which is makes sense to stay open for the year