Technology Choice and Average Cost Analysis
A company is evaluating two different production technologies, Tech Alpha and Tech Beta, to manufacture a new product. On a graph with total cost on the vertical axis and quantity on the horizontal axis, the total cost curves for both technologies are plotted.
- The curve for Tech Alpha starts at a high point on the vertical axis but rises slowly as quantity increases.
- The curve for Tech Beta starts near the origin but rises more steeply as quantity increases.
The two cost curves intersect at an output level of 1,000 units.
The company anticipates its long-run production target will be significantly greater than 1,000 units per month. Based on the graphical interpretation of average cost, which technology should the company choose to achieve a lower average cost at these high production volumes? Justify your decision by explaining how the slope of a line from the origin to a point on each total cost curve would differ at high output levels.
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The Average Cost Curve
Consider a graph where the vertical axis represents a firm's total cost and the horizontal axis represents the quantity of output produced. The total cost curve starts at a positive value on the vertical axis and increases with output. Three points are marked on this curve: Point A is at a low output level. Point B is at a medium output level, where a straight line drawn from the origin is just tangent to the total cost curve. Point C is at a high output level, to the right of Point B. At which of these points is the average cost of production minimized?
Evaluating a Production Decision
Explaining the Graphical Representation of Average Cost
Imagine a graph where a firm's total cost is plotted on the vertical axis and the quantity of output is on the horizontal axis. A point on this graph, Point X, corresponds to producing 50 units at a total cost of $500. Another point, Point Y, corresponds to producing 100 units at a total cost of $800. By considering the slopes of straight lines drawn from the origin (0,0) to these points, what can you conclude about the average cost (AC) of production at these two output levels?
Consider a production scenario where the total cost of producing any quantity of a good is directly proportional to the quantity produced, and there are no costs incurred if production is zero. On a standard graph with total cost on the vertical axis and quantity on the horizontal axis, this implies that the average cost of production decreases as more units are produced.
Consider a production scenario where the total cost of producing any quantity of a good is directly proportional to the quantity produced, and there are no costs incurred if production is zero. On a standard graph with total cost on the vertical axis and quantity on the horizontal axis, this implies that the average cost of production is constant for any positive level of output.
Analyzing Average Cost Behavior from a Total Cost Function Description
Consider a graph where a firm's total cost is on the vertical axis and quantity of output is on the horizontal axis. A typical total cost curve is drawn, starting from a positive value on the vertical axis and increasing with output. Three points are identified on this curve, corresponding to different output levels:
- Point A: An early point on the curve where a straight line drawn from the origin to this point is steep.
- Point B: The specific point where a straight line drawn from the origin is tangent to the total cost curve. This line has the shallowest slope of any possible line from the origin to the curve.
- Point C: A point on the curve at a higher output level than Point B, where a straight line from the origin to this point is steeper than the line to Point B.
Given that the slope of a line from the origin to any point on the total cost curve represents the average cost at that output level, match each point to the correct description of average cost.
Technology Choice and Average Cost Analysis
Consider a firm whose production costs are represented on a graph with total cost on the vertical axis and quantity of output on the horizontal axis. If the point corresponding to producing 10 units of output is (10, $200) and the point for producing 30 units is (30, $450), then the average cost of production is lower when producing 30 units than when producing 10 units.