Question

You are a producer of potatoes. You have to decide whether to sell your crop now or store it and sell later. You have just harvested your crop and the current market price is $30 per cwt. You have enough storage capacity for your entire crop and your storage cost per cwt. is defined by:

SC$ = 0.25 + .1T²

where T = 1,..N the number of months in storage, T = 1...11. You can only keep your potatoes in storage until the new crop is harvested.

The sales price for potatoes changes through time according to a premium over the price at harvest time in the following table. You will note that this premium starts to decline at some point, because of the deterioration in the quality of stored potatoes.

Time	Market Price Premium ($)	Market Price ($)	Storage cost ($)	Net Sales price ($)
Harvest Month (0)	0	30	0	30
Month 1	1
Month 2	2
Month 3	3
Month 4	4
Month 5	5
Month 6	6
Month 7	7
Month 8	7
Month 9	5
Month 10	3
Month 11	1

1. Calculate the market price and the storage cost in each month and put these in the table. Calculate the net sales price for each month.

2. Which is the most profitable month for selling the stored potatoes? Explain.

3. Which is the last month in which you make a positive return from storing potatoes? Explain.

4. If you were offered a contract by a supermarket to deliver a fixed quantity of potatoes per month at a price of $35 per cwt., when does it become unprofitable to supply potatoes under the contract? Explain.

Answer 1

1)

Storage Cost Function:

The storage cost function is SCS = 0.25+ O.1T²

Using equation (1), storage cost is calculated in the Table -1, Market price is calculated by adding the Market Price Mark-up with Current Market Price.

2)

During the Month 5, selling the potato is highly profitable by

$32.25

3)

During the month 8, gives positive return of $035 Ion storage.

4)

During the month 9, 10, and 11, selling price is below $35, which is higher than the market price. Thus, commitment of during month 9, 10 and 11 gives positive cash flow.