Consider a manufacturer that needs to find supply sources for electricity. The m

Question

Consider a manufacturer that needs to find supply sources for electricity. The manufacturer produces and sells products to end customers at a unit price $22. The production of the products consumes electricity intensively. To simplify the example, we assume that a unit of electricity is required to produce a unit of finished good. Excluding the cost of electricity, the production incurs a variable cost of $1, which includes raw material, machine depreciation and maintenance, manpower, etc., The manufacturer knows that demand for the product (equivalently, for electricity) follows the probabilistic forecast in the table below. Two power companies are available for supply:

Demand Probability
8,000 10%
10,000 11%
12,000 29%
14,000 22%
16,000 18%
18,000 10%

A. Company 1 offers a fixed commitment contract with the following conditions: power is bought in advance at a price $10 per unit.

B. Company 2 offers a so-called option contract, namely, the manufacturer can pay a reservation price of $6 per unit in advance and then later she can pay $6 per unit for each unit delivered. In other words, the advance payment is just to buy an option.

Consider the following two sub-cases: 1) The manufacturer cannot buy more than her earlier advance purchase amount later on. 2) Company 2 is willing to sell to the manufacturer at the spot market later on at a price $14 per unit.

Answer the following questions. We assume all companies try to maximize their average (or expected) profit. Further assume the unit cost of the power production is $4. (1) If the manufacturer purchases from Company 1, what’s her optimal purchasing amount? (2) If the manufacturer purchases from Company 2, what’s her optimal purchasing amount? (3) If you own Company 1, how would you set your price? (4) If you own Company 2, in both cases 1) and 2), how would you set your reservation prices, respectively? Suppose the delivery price remains unchanged. (5) If you’re a Company 2, do you think you can have another contract offer that will make yourself and the manufacturer both better off?

Explanation / Answer

1. If the Manufacturer purchases from company 1 then , Optimal Purchase should be 12000 Units as Probablity is higher of consumption costing the amount equivalent to 1,20,000 USD.

2. If the Manufacturer Purchases from the company 2 then , Optimal purchase should be 12,000 Units only as reservation price involved in this which is equivalent to 72000 USD only and later on if purchase will be less as per demand some money can be saved. But if Company goes for higher demand then spot buying will cost higher money @ $14/ Unit.

3. If I own company 1 I will set the Price for Demand Vs supply as Demand goes higher i will increase per unit price to get maxium profit out of that sell.

4. If I own Company 2 in both cases 1 and 2 then in case 1 i will charge a nominal $4 / Unit booking advance which will be not be refundable money. In this way if company doesnt take the committed unit some money can be recovered..

In case 2 Instead of spot buying of $14/ unit, i iwll allow the manufacturer to buy as much quantity they want instead of restricting the buying unit to maximize the profits.

5. If I would be company 2, i can make another better offer by offering $8 upto 3000 units, then $10 for 3000 to 5000 units and $ 12 for 5000 to 10000 Units and above 10000 Units it will be charged @ $14 .

So buying of units will come without cap and also there will not be any contract boundation to adhere and it will appear to be a win win situation for Company and manufacturer.

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