BUSINESS ECONOMETRICS (ECO601) Assignment No. 1 (Spring 2019) DUE DATE: 23 RD MAY, 2019

The Case:
In Business, the change in the total cost which has been observed due to production of one more unit of a product/output is called marginal cost. In most of the manufacturing endeavors, initially, the marginal cost falls as the volume of output rises because of economies of scale. In the beginning, costs are lower for the reason that there are some discounts on bulk purchases of raw materials, efficient use of machinery and specialized labors are engaged in performing the tasks. However, a point comes in the production process where the marginal cost will begin to rise again as a result of diseconomies of scale. At this stage, the cost may rise because of multiple factors like to hire more management, buy more equipment, to tap out a local source of raw materials or to spend more money to obtain the sources.
Now consider the following marginal cost function (MC) where Q is the level of output:
Where a, b and c are coefficients. If
,
and
then the marginal cost function will be as following:
Requirements:
1. Calculate cost minimizing output level and minimized cost by using the optimization process. Also, confirm that cost is minimized which is produced at the output level.
2. What will be the conditions (signs) of coefficients b and c in order to get the required shape of the marginal cost (MC) curve?
3. If the required condition of coefficients for the MC curve is violated then what will be the shape of the curve?

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