9. a. This equation represents a quadratic cost curve. Total fuel cost (Y) is the dependent variable and quantity produced (X) is the independent variable. Since the cost function includes a positive squared term, marginal costs are increasing. The average variable cost curve is also increasing, while the total cost curve (which includes a fixed element, 16.68) probably exhibits a u-shape. The total cost curve rises at an increasing rate. Since the observations were taken for one plant over a period of time, time-series regression analysis was used.
b. This is a time-series analysis of the steel industry. The total cost equation shown is a straight line. The marginal and average variable cost curves are horizontal, i.e. costs are constant. If $182.1 million is assumed to be fixed cost, then the average total cost curve will be declining. A twelve-year period is probably too long a period over which to assume that plant sizes and technology remained unchanged.
10. a. FALSE Decision-makers should always use the replacement or current cost of raw materials because it is considered to be relevant to the decision.
b. TRUE The mathematical relationship between the marginal and average assures that this will always be the case.
c. TRUE Declining average cost indicates economies of scale and increasing average cost indicates diseconomies of scale.
d. FALSE Marginal cost is also considered in the long run cost structure. See Table 7.3 and Figure 7.5 in text.
e. FALSE The rational firm will try to operate most efficiently by making sure that its unit costs are exactly as indicated by its cost structure (i.e. as seen by observing any of the points on its average cost curve).