Microeconomics Homework

Chapter 11: Output and Costs

· In the short run, a firm needs to increase the quantity of labor employed in order to increase its production.

· In the long run, a firm can increase the quantity of any or all of the factors of production it employs to increase its production.

· Firms must pay for the factors they use, so when a firm changes its production, its costs change.

I. Decision Time Frames

· A firm owner’s decisions can be categorized as short run decisions and long run decisions.

· The short run is a time frame in which the quantities of some factors of production are fixed. The fixed factors include the firm’s management organization structure, level of technology, buildings and large equipment. These factors are called the firm’s plant.

· The long run is a time frame in which the quantities of all factors of production can be varied. Long-run decisions are not easily reversed so usually a firm must live with the plant size that it has created for some time. The past cost of buying a plant that has no resale value is called a sunk cost.

Try to understand that the difference between the long run and short run is not related to calendar time. Compare the street vendor, who is a firm owner operating out of a food truck, to the giant automaker firm, Honda. How long it would take for the food vendor to double the size of his or her plant (truck, oven, etc.) versus Honda to double its plant size (factory buildings covering multiple blocks, computerized assembly lines and robotics, etc.). The length of time covered by the long run differs among firms.

II. Short-Run Technology Constraint

To increase its output in the short run, a firm must increase the quantity of labor employed. There are three relationships between the quantity of labor and the firm’s output.

Product Schedules

· Total product is the maximum output that a given quantity of labor can produce. The marginal product of labor is the increase in total product that results from a one-unit increase in the quantity of labor employed with all other inputs remaining the same. The average product of labor is equal to the total product of labor divided by the quantity of labor. The table to the right has examples of these product schedules.

Product Curves

· The total product curve illustrates the total product schedule. The slope of the total product curve equals the marginal product of labor at that quantity of labor.

· The marginal product curve shows the additional output generated by each additional unit of labor. The marginal product of labor curve (MP) has an upside-down U shape. Increasing marginal returns occurs when the marginal product of an additional worker is greater than the marginal product of the previous worker. At low levels of employment, increasing marginal returns is likely because hiring an additional worker allows large gains from specialization. Eventually these gains become small or nonexistent and diminishing marginal returns set in. Diminishing marginal returns occur when the marginal product of an additional worker is less than the marginal product of the previous worker. The law of diminishing returns states that as a firm uses more of a variable factor of production, with a given quantity of the fixed factor of production, the marginal product of the variable factor eventually diminishes.

· The average product curve shows the average product that is generated by labor at each level of labor. As the figure shows, the average product of labor curve (AP) has an upside-down U shape.

· As the figure shows, the marginal product curve and the average product curve are related: when the marginal product of labor exceeds the average product of labor, the average product of labor increases; when the marginal product of labor is less than the average product of labor, the average product of labor decreases; and the marginal product of labor equals the average product of labor when the average product of labor is at its maximum.

The marginal pulls (but cannot not push) the average. Don’t fall into the trap of thinking that if the marginal measure rises (falls) with the level of an activity, then the average measure must also rise (fall). This is a sloppy statement of the relationship between marginal and average measures. Use the tried-and-true grade point average (GPA) example used in the text. If a student’s GPA is a 3.5 and his or her next marginal class grade is a C (2.0), followed by a B (3.0), this increasing marginal grade will not be pushing the GPA up at all. Conceptually, you should understand that the marginal value can’t “push” the average measure higher when it is, itself, lower than the average measure. The marginal measure must be higher (lower) than the average value if the average value is to rise (fall) with the level of activity, thereby “pulling” the average up (down).

Understanding marginal returns: Picture a typical fast food restaurant. This is a “plant” and equipment with which you familiar as a customer if not also as a worker. Fixed inputs include the building and the equipment. Imagine one worker trying to cook the food, take the orders and run the drive through. Add a second worker and specialization can begin to occur, so the MP initially rises. But keep adding workers and marginal product will inevitably fall. Diminishing returns is not the same as negative returns; total product is still rising, but at a decreasing rate.

III. Short-Run Cost

Labor	Output	Fixed cost (dollars)	Variable cost (dollars)	Total cost (dollars)	Average fixed cost (dollars)	Average variable cost (dollars)	Average total cost (dollars)	Marginal cost (dollars)
0	0	50	0	50
								10.00
1	10	50	100	150	5.00	10.00	15.00
								5.00
2	30	50	200	250	1.66	6.67	8.33
								16.67
3	36	50	300	350	1.39	8.33	9.72

The table above continues the previous product schedule table and shows different costs.

Total Cost

· Total cost (TC) is the cost of all the factors of production a firm uses. Total fixed cost (TFC) is the cost of the firm’s fixed factors. Total variable cost (TVC) is the cost of the firm’s variable factors. Total cost is the sum of total fixed cost plus total variable cost so TC = TFC + TVC.

Marginal Cost and Average Cost

· Marginal cost (MC) is the increase in total cost that results from a one-unit increase in output. The MC curve is U-shaped.

· Average fixed cost (AFC) is total fixed cost per unit of output. The value of AFC falls as output increases.

· Average variable cost (AVC) is total variable costs per unit of output. At low levels of output, AVC falls as output increases but at higher levels of output, AVC rises as output increases.

· Average total cost (ATC) is the total cost per unit of output. ATC = AFC + AVC. At low levels of output, ATC falls as output increases but at higher levels of output, ATC rises as output increases.

· The figure illustrates typical MC, AFC, AVC, and ATC curves. As the figure shows, the MC curve, the AVC curve, and the ATC curve are all U-shaped. There are other additional important points about this figure:

· The vertical distance between the AVC curve and the ATC curve is the AFC. Because the AFC decreases as output increases, these curves become vertically closer to each other as output increases.

· The MC curve intersects the AVC curve and ATC curve at their minimums.

· The shape of the cost curves is related to the shape of the productivity curves.

· The shape of the AVC curve is determined by the shape of the AP curve. Over the range of output for which the AP curve is rising, the AVC curve is falling and over the range of output for which the AP curve is falling, the AVC curve is rising.

· The shape of the MC curve is determined by the shape of the MP curve. Over the range of output for which the MP curve is rising, the MC curve is falling and over the range of output for which the MP curve is falling, the MC curve is rising.

Making Decisions Using the Relationships Between Productivity and Cost. Try to understand the intuition behind the relationship between productivity measures and cost measures. For example:

If a firm manager knows that average productivity of labor has been falling with the last additional quantity of labor hired, then the manager knows that the average variable cost (AVC) of production has necessarily been rising as the output from that additional labor has increased.

If the manager knows that AVC is rising as output increases, then the manager also knows that the marginal cost (MC) of the additional output has been higher than the AVC (which has been pulling AVC up).

If the manager has sold the previous units of output at a small profit, the manager might be faced with a time-sensitive contractual opportunity that arises within the same short run time period. The manager might be asked to sell a little more output at the same market price as the previous sales. The manager can quickly infer that the profitability of this potential new contract will not be as high because the marginal cost of producing the extra output will be higher than the last units of output produced. The manager can infer this result through productivity-cost relationships rather than knowing marginal costs directly.

Firm managers must frequently make quick decisions with little information. If managers have knowledge of a useful relationship between input measures (which are relatively easy to get) and production cost measures (which are more difficult to get—especially marginal cost figures) they can use their understanding of this link to make inferences about how production costs might behave when the firm’s output must change to accommodate market changes.

· The cost curves shift with changes in technology or changes in prices of factors of production.

· An increase in technology that allows more output to be produced from the same resources shifts the cost curves downward. If the technology requires more capital, a fixed input, then the average total cost curve shifts upward at low levels of output and downward at higher levels of output.

· A fall in the price of the fixed factor shifts the AFC and ATC curves downward but leaves the AVC and MC curves unchanged. A fall in the price of a variable factor shifts the AVC, ATC, and MC curves downward but leaves the AFC curve unchanged.

IV. Long-Run Cost

In the long run, a firm can vary the level of all resources so both labor and capital are variable factors. As a result, in the long run all costs are variable costs.

The Production Function

· The production function determines the behavior of long run costs.

· A firm’s production function typically exhibits diminishing returns to capital as well as diminishing returns to labor. The marginal product of capital is the change in total product divided by the change in capital when the quantity of labor is held constant. Holding constant the quantity of employment, after some level of output the firm will have diminishing returns to capital—the marginal product of capital decreases as more capital is used.

Short-Run Cost and Long-Run Cost

· In the long run, a firm can use different plant sizes. Each plant size has a different short-run ATC curve. Each short-run ATC curve is U-shaped and the larger the plant size, the greater is the output at which the average total cost is a minimum.

· The figure illustrates three average total cost curves for three plant sizes. ATC1 pertains to the smallest plant size and ATC3 to the largest.

The Long-Run Average Cost Curve

· The long-run average cost curve, LRAC, is the relationship between the lowest attainable average total cost and output when both the plant size and labor are varied. This curve is derived from the short-run average total cost curves. It shows the lowest average total cost to produce a given level of output. In the figure, the LRAC curve is the darkened parts of the three short-run ATC curves.

Economies and Diseconomies of Scale

· Economies of scale are features of a firm’s technology that lead to falling long-run average cost as output increases. With given factor prices, economies of scale occur if the percentage increase in output exceeds the percentage increase in all factors of production. The long-run average cost curve slopes downward in this range of output. The main source of economies of scale is greater specialization of both labor and capital.

· Constant returns to scale are features of a firm’s technology that lead to constant long-run average cost as output increases. With given factor prices, economies of scale occur if the percentage increase in output equals the percentage increase in all factors of production. The long run average cost curve is horizontal in this range of output.

· Diseconomies of scale are features of a firm’s technology that lead to rising long-run average cost as output increases. With given factor prices, economies of scale occur if the percentage increase in output is less than the percentage increase in all factors of production. The long run average cost curve slopes upward in this range of output.

· The minimum efficient scale is the smallest quantity of output at which the long-run average cost curve reaches its lowest level.

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