The newly formed Bangladesh Automobile Corporation plans to produce and export an expensive sports car and has asked your consulting firm for advice on the size of plant to construct. Because of the union contract and technical features of automobile production, labour must be paid the equivalent of $12,000 per person per annum, and each incremental change in plant size involves $900,000 in annual expenses for depreciation, interest, and other fixed costs. The maximum the firm will have available for expenditure on capital and labour is $9 million per annum. BAC has supplied the following details of its production function, meticulously derived by its chief engineer. (The data in the body of the table represent automobiles produced, in units.) Labour can be varied virtually continuously; the table shows units of fifty persons for convenience. All other variable expenses are constant at $2,500 per vehicle produced.

Capital (units of $900,000)	Labour (units of 50 persons)
1	2	3	4	5	6
3	40	90	140	170	180	185
4	60	120	180	220	230	236
5	100	170	230	250	260	268
6	170	200	240	270	280	289

BAC's market research indicates that the new vehicle should be sold at around $50,000 per unit and that the expected demand situation is as follows:

Units Demanded (annually) 100 150 200 250

Probability 0.200.50 0.200.10

1. Calculate the short-run average costs for each of these plants.
2. Plot the short run ATC curves as per your calculations in part (a).
3. Comment on the economies and diseconomies of plant size (if any) which are evident in your graph.
4. Disregarding the probabilities, which plant do you suggest that BAC build if the demand is expected to be (i) 150, (ii) 200, or (iii) 250, and why?
5. Now regarding the probabilities, which plant do you suggest that the company build, and why?