Chapter 8 Cost Curves
Solutions to Review Questions
1. The long-run total cost curve plots the minimized total cost for each level of output holding input prices fixed. In other words, for a given set of input prices, the long-run total cost curve represents the total cost associated with the solution to the long-run cost minimization problem for each level of output. When the price of one input increases, the isocost line for a particular level of total cost will rotate in toward the origin. Assuming the isocost line was tangent to the isoquant for the firm’s selected level of output, when the isocost line rotates it will no longer touch the original isoquant. In order for an isocost line to reach a tangency with the original isoquant, the firm would need to move to an isocost line associated with a higher level of cost, i.e. an isocost line further to the northeast. If the price of a single input goes up leaving all other input prices the same and the level of output constant, total cost will rise but by a smaller percentage than the increase in the input price. This occurs because the firm will substitute away from the now relatively more expensive labor to the now relatively less expensive other inputs. So, if the price of labor rises by 20% holding all other input prices constant, total cost will rise by less than 20%. If the prices of all inputs go up by the same percentage, total cost will rise by exactly that same percentage. So, if input prices rise by 20%, total cost will also rise by 20%. 4. An increase in the price of labor would result in a long-run total cost curve that lies above the initial long-run total cost curve at every quantity except Q = 0 . Since AC = TC / Q , increasing total cost will raise average cost at every quantity except Q = 0 . Therefore, the long-run average cost curve will shift up.
When MC > AC , average cost is increasing, and when MC < AC , average cost is decreasing. So, if the average cost curve is increasing it must lie below the marginal cost curve. If the marginal cost curve is increasing, it may lie above or below the average cost curve. The only determining factor here is whether or not marginal cost lies above or below average cost. If it lies above, average cost will be increasing and
Copyright © 2008 John Wiley & Sons, Inc.
Chapter 8 - 1
Besanko & Braeutigam – Microeconomics, 3rd edition
if it lies below, average cost will be decreasing. Knowing that marginal cost is increasing or decreasing tells us nothing about average cost. 6. TC MC AC
Q When average cost is falling, marginal cost will lie below average cost, and when average cost is increasing, marginal cost will lie above average cost. Over the flat-bottomed portion where average cost is neither increasing nor decreasing, marginal cost and average cost will be equal. 7. The output elasticity of total cost, when simplified can be written as
ε TC ,Q =
Since AC = TC / Q , and since TC and Q must always be positive, AC will always be positive. Marginal cost, MC, represents the change in total cost associated with an increase in output. When output increases, total cost must always rise for a given set of input prices, implying that MC is also always positive. Therefore, the output elasticity of total cost must always be positive. 8. Because fixed cost does not change, marginal costs reflect the change in variable costs. Thus, as with the relationship between any average and marginal, if average variable cost is decreasing, marginal cost must be below average variable cost, and if average variable cost is increasing, marginal cost must lie above average variable cost. This implies marginal cost will intersect average variable cost at the minimum of average variable cost. If the average variable cost curve is flat, average variable cost is neither increasing nor...