MICRO week 10
a. when a firm's long-run average costs increase with output. b. Firms have difficulty coordinating production
*What are diseconomies of scale?* a. Diseconomies of scale is *What is the main reason that firms eventually encounter diseconomies of scale as they keep increasing the size of their store or factory?*
a horizontal line
To model the input decisions for a production system, we plot labor on the horizontal axis and capital on the vertical axis. In the short run, labor is a variable input and capital is fixed. The short-run expansion path for this production system is
a. No since MPL/w does not equal MPC / c b. Yes, they need to increase L which would cause MPL to decrease and MPc to increase
Suppose that a paving company produces paved parking spaces (q) using a fixed quantity of land (T) and variable quantities of cement (C) and labor (L). The firm is currently paving 1,000 parking spaces. The firm's cost of cement is $4,200.00 per acre covered (c) and its cost of labor is $35.00/hour (w). For the quantities of C and L that the firm has chosen, MPC=70 and MPL=7. a. Is this firm minimizing its cost of producing parking spaces? b. Does the firm need to alter its choices of C and L to decrease cost?
The Marginal Rate of Technical Substitution
The analogous concept in production theory to the marginal rate of substitution is called the marginal rate of technical substitution, or MRTS. It is the rate at which one input can be exchanged for another without altering output. Geometrically, the MRTS at a point is the absolute value of the slope of the isoquant at that point. For example, if L is on the horizontal axis, *MRTS=|ΔK / ΔL|* Diminishing MRTS for most production processes.
Average Product
The average product of a variable input is defined as the total product divided by the quantity of that input. The average product of labor, denoted AP_L, it is given by *AP_L=Q/L* When the variable input is labor, the average product is also called labor productivity. Geometrically, the average product is the slope of the line joining the origin to the corresponding point on the total product curve. [5.2 slide 23 graphs] Three such lines, R_1, R_2, and R_3, are drawn to the total product curve shown in the top panel in the figure. The average product at L=2 is the slope of R_1, which is 14/2=7. Note that R_2 intersects the total product curve in two places—first, directly above L=4, and then directly above L=8. Accordingly, the average products for these two values of L will be the same—namely, the slope of R_2, which is 43/4=86/8=10.75. R_3 intersects the total product curve at only one point, directly above L=6. The average product for L=6 is thus the slope of R_3, 72/6=12. Also, since R_3 is the steepest ray we can get, the AP_L curve peaks at L=6.
Marginal Product
The change in the total product that occurs in response to a unit change in the variable input (all other inputs held fixed). Formally, if ΔL denotes a small change in labor, and ΔQ denotes the resulting change in output, then the marginal product of L, denoted MP_L, is defined as *MP_L=ΔQ/ΔL* Geometrically, the marginal product at any point is simply the slope of the total product curve at that point, as shown in the top panel of next figure. A business manager trying to decide whether to hire or fire another worker has an obvious interest in knowing what the marginal product of labor is.
Inputs, or Factors of Production
Land, labor, capital, and entrepreneurship.
Law of Diminishing Returns
The law of diminishing returns is a short-run phenomenon. Formally, it may be stated as follows: as *equal amounts of a variable input* are sequentially added while *all other inputs are held fixed,* the resulting increments to output will eventually diminish. Why can't all the world's people be fed from the amount of grain grown in a single flowerpot? The law of diminishing returns perfectly explains why can't all the world's people be fed from the amount of grain grown in a single flowerpot: No matter how much labor, fertilizer, water, seed, capital equipment, and other inputs were used, only a limited amount of grain could be grown in a single flower-pot. With the land input fixed at such a low level, increases in other inputs would quickly cease to have any effect on total output. It is worth mentioned once more that the law of diminishing returns is a short-run phenomenon, that is, you need to fix all other inputs when increasing the variable inputs in consideration. If you overlooked the requirement of fixing all other inputs, you will make a mistake by applying the law of diminishing returns.
a U shape, initially falling when the marginal product of labor is rising and then eventually rising when the marginal product of labor is falling.
The marginal cost of production shows the change in a firm's total cost from producing one more unit of a good or service. What is the shape of the marginal cost curve? Graphically, the marginal cost curve is
Short Run
The period of time during which at least one of the inputs used in a production process cannot be varied. In the short run, assume labor input is variable but the capital input is fixed, say, at the value K=K_0=1. Then F(K,L)=2K_0 L=2L
An Analogy
The relationship between the marginal and average product curves is analogous to the relationship between the grade of an additional student and the class average grade. If the class average is 85 points, and the grade of the additional student is 90 (or anything greater than 85), then the class average will increase. If the class average is 85 points, and the grade of the additional student is 80 (or anything below 85), then the class average will decrease.
The Relationship between the Marginal and Average Product Curves
The relationship between the marginal product curve and the average product curve: When the marginal product curve lies above the average product curve, the average product curve must be rising; and when the marginal product curve lies below the average product curve, the average product curve must be falling. The two curves intersect at the maximum value of the average product curve Because of the way the marginal and average products are defined, systematic relationships exist between them. In words, their relationship can be summarized as follows: (read the slides) [5.2 slide 25 graphs] (L=6, intersection) The steepest of the three rays, R_3, is tangent to the total product curve at L=6. Its slope, 72/6=12, is the average product of labor at L=6. The marginal product of labor at L=6 is defined as the slope of the total product curve at L=6, which happens to be exactly the slope of R_3, since R_3 is tangent to the total product curve. Thus AP_(L=6)=MP_(L=6), as shown in the bottom panel by the fact that the AP_L curve intersects the MP_L curve for L=6. (L<6, MPL>APL) For values of L less than 6, note in the top panel that the slope of the total product curve is larger than the slope of the ray to the corresponding point. Thus, for L<6, MP_L>AP_L, as reflected in the bottom panel. (L>6, MPL<APL) Note also in the top panel that for values of L greater than 6, the slope of the total product curve is smaller than the slope of the ray to the corresponding point. This means that for L>6, we have MP_L>AP_L, as shown in the bottom panel. (transit) Using their geometric meaning, we have proved that (i) The two curves intersect at the maximum value of the average product curve and (ii) When the marginal product curve lies above the average product curve, the average product curve must be rising; and when the marginal product curve lies below the average product curve, the average product curve must be falling. (intuition) A moment's reflection on the definitions of the two curves akes the intuitive basis for this relationship clear. If the contribution to output of an additional unit of the variable input exceeds the average contribution of the variable inputs used thus far, the average contribution must rise.
Production Function
The relationship by which inputs are combined to produce output. (Intro) Many people think of production as a highly structured, often mechanical process whereby raw materials are transformed into finished goods. And without doubt, a great deal of production—like Tesla manufacturing a Model 3 sedan, or Apple designing and assembling an iPhone —is this sort. In Economics, however, we emphasize that production is a much more general concept, and it can include many activities that are not ordinarily thought of as production. (Production examples) For example, for a stand-up comedian, the simple act of telling a joke constitutes production. Similarly, the postal worker who delivers my tax return to the IRS is engaged in production, the young lady who gives me a haircut every few weeks is engaged in production, and a 7-year old kid selling drinks behind his/her lemonade stand is also engaged in production. Even I myself is engaged in production by giving a lecture on economics. (goods and services) From these examples, you can see that production is not only about physical goods, it could also be about services, and the process does not have to sophisticated to be called production. (Concepts) Formally, production can be described as a process that transforms inputs (factors of production) into outputs. Here inputs, or factors of production, could be land, labor capital, entrepreneurship, and so on, and outputs could be cards, smartphones, haircuts, lectures and so forth. In economics, at least in the classical theory of firms in microeconomics, we are not interested in the details of the production process, like how a smartphone is assembled step by step on an assembly line from hundreds of parts. Rather, we treat the production process as a black box as shown on the slide. All that we are interested in is the relationship by which inputs are combined to produce output. So, by hiring 10 people and renting 2 pieces of assembly equipment, how many smartphones I can make in one day, that input and output quantity relationship is what we are interested in here. And this relationship is called a production function. (technology) As you can imagine, this production function, this black box of the production process, depends on the existing state of technology which has been improving steadily over time.
Isoquants
"Iso" comes from the Greek word for "same" Similarity of an isoquant map to an indifference map: movements towards northeast means increasing levels of output. Difference: outputs are cardinal, whereas utilities are ordinal.
a. increase; remain unchanged; increase b. remain unchanged; increase; increase
*Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. How does this tax affect the firm's fixed, marginal, and average costs?* a. With a lump-sum tax, the fixed cost of production will ________ the marginal cost of production will ______ _________ and the average cost of production will ________. *Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how does this tax affect the firm's fixed, marginal, and average costs?* b. With a proportional tax, the fixed cost of production will ______ _________ the marginal cost of production will ________ and the average cost of production will ________.
Total Product Curve
A curve relates the total amount of output to the quantity of the variable input.
a. TC = 5,000 + 900q b. ATC = (5000 + 900q) / q c. very large because the average total cost of production falls with output.
A firm has a fixed production cost of $5,000 and a constant marginal cost of production of $900 per unit produced. a. What is the firm's total cost function? b. The firm's average total cost (ATC) of production is c. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.
Regardless of whether MC is decreasing, AVC could be increasing or decreasing depending on whether MC is greater than or less than AVC.
Assume that the marginal cost (MC) of production is decreasing. Can you determine whether the average variable cost (AVC) is increasing or decreasing? Explain.
there are at least as many possibilities for substitution between factors of production in the long run as in the short run.
At every output level, a firm's short-run average cost (SAC) equals or exceeds its long-run average cost (LAC) because
average variable cost equals marginal cost.
At the point where average variable cost reaches its minimum value
Production
Can be described as a process that transforms inputs into outputs.
Production Function
Consider a production process that employs two inputs, capital (K) and labor (L), to produce meals (Q) *Q=F(K,L)* where F is a mathematical function that summarizes the production process. For example, F(K,L)=2KL, where K is measured in equipment-hours per week, L is measured in person-hours per week, and output is measured in meals per week. (That is, both inputs and outputs are flows.) The function from of F can be used to reflect the technology of production. For example, the coefficient 2 in F(K,L)=2KL can be used to reflect a certain level of technology of production. If it increases to 3, the technology of production advances.
Concept Check
Consider a short-run production process for which AP_(L=10)=7 and MP_(L=10)=12. If we increase the labor input by a sufficiently small amount, will AP_L increases or decreases at L=10 for this process? APL increases
Production in the Short Run
Consider again Q=F(K,L)=2KL, where K is measured in equipment-hours per week, L is measured in person-hours per week, and output is measured in meals per week. Suppose in the short run, the labor input is variable but the capital input is fixed, say, at the value K=K_0=1. Then the short-run production function is Q=F(K_0,L)=2L We can plot this production function in a two-dimensional diagram, as in (a). Generally, for F(K_0,L)=2K_0 L, the graph is a straight line through the origin whose slope is ΔQ/ΔL=2K_0 for any fixed K_0.
total costs to increase by more than double when output doubles.
If input prices are constant in the long run, a firm with decreasing returns to scale can expect
Disagree: the student confused diminishing returns, which refers to the behavior of costs in the short run, with diseconomies of scale.
In 2019, an article in the Wall Street Journal noted that the federal government's Office of the Comptroller of the Currency had said about Wells Fargo bank, "We continue to be disappointed with...its inability to execute effective corporate governance and a successful risk management program." According to the article, a senior member of Congress "suggested the bank should be downsized because it was too large to manage." Source: Rachel Louise Ensign and Andrew Ackerman, "Regulator Slams Wells Fargo after CEO Testifies to Congress," Wall Street Journal, March 12, 2019. After reading this article, a student remarks: "It seems that Wells Fargo is suffering from diminishing returns." Briefly explain whether you agree with this remark.
will not be a straight line if the ratio of inputs used changes with output.
Is the firm's expansion path always a straight line? A firm's expansion path
Two Extreme cases for Input Subsitution
The shape of the isoquant tells us how a firm is "willing" wo substitute one input for another. The extreme cases of inputs are *perfect substitutes* and *perfect complements.* Just as the shape of the indifference curve tells us how the consumer is willing to substitute one good for another, In production theory, the shape of the isoquant tells us how a firm is willing wo substitute one input for another A production function with perfect complementary input is also called a fixed-proportions production function or Leonitief production function.
will lose money if it remains in business.
What is likely to happen in the long run to firms that do not reach minimum efficient scale? A firm that does not reach its minimum efficient scale
the level of output at which the long−run average cost of production no longer decreases with output.
What is minimum efficient scale? Minimum efficient scale is
Perfect Substitutes
[5.3 Slide 17] Car wash: workers vs automatic wash systems. MRTS is some constant.
the isoquant line is tangent to the isocost line.
When the cost minimizing combination of inputs is being used and there is no corner solution,
the long-run average cost curve
Which of the following terms refers to the lowest cost at which a firm is able to produce a given level of output in the long run, when no inputs are fixed?
The draftsman since the lowest point on each SAC curve will have a horizontal tangent line which only occurs at the lowest point on the LAC.
Whose argument is stronger regarding the SAC curves and the LAC curve?
Equals the ratio of input prices, and this ratio is fixed
Why are isocost lines straight lines? Isocost lines are straight because the slope of such line
a. not minimizing the cost of production because MPK/r < MPL/w b. The firm could decrease the cost of production holding output constant by using more labor and less capital
A firm produces output with capital and labor. Suppose currently the marginal product of labor is 29 and the marginal product of capital is 5. Each unit of labor costs $6 and each unit of capital costs $2. Is the firm minimizing the cost of production? Explain. Let MPK be the marginal product of capital, MPL be the marginal product of labor, r be the price of capital, w be the cost of labor, and MRTS be the marginal rate of technical substitution. a. The firm is b. If not, how could the firm decrease the cost of production holding output constant?
use more labor and less capital
A firm uses 80 hours of labor and 6 units of capital to produce 10,000 gadgets per day. Labor's marginal product is 4 gadgets per hour and the marginal product of capital is 20 gadgets per unit. Each unit of labor costs $8 per hour and each unit of capital costs $50 per unit. If the firm wants to continue producing 10,000 gadgets per day at the lowest possible cost, it should
a. that aren't producing at minimum efficient scale will have higher costs than their competitors. b. fewer firms in the industry and the remaining firms will likely be larger.
An article in the Wall Street Journal described the Chinese automobile industry as "a hodgepodge of companies," most of which produce fewer than 100,000 cars per year. Ford Chief Executive Alan Mulally commented on the situation by saying, "If you don't have scale, you just won't be able to be competitive." Source: Colum Murphy, "Chinese Car Makers Struggle to Lure Buyers," Wall Street Journal, April 19, 2014. a. Mulally meant that Chinese firms b. We can predict that, as the Chinese automobile industry develops over the next 10 years, there should be
The Importance of Marginal Product Concept
Decisions about running an enterprise most naturally arise in the form of decisions about *marginal changes.* - Should we hire another engineer or accountant? Should we install another copier? Should we lease another delivery truck? To answer such questions intelligently, we must compare the benefit of the change in question with its cost. The marginal product concept plays a pivotal role in the calculation of the benefits when we alter the level of a productive input.
decreases
Economies of scale happen when the firm's long run average total cost ________ as output increases.
slope of the isocost lines will change, and the firm will substitute toward the relatively cheaper input, pivoting the expansion path toward the axis of the relatively cheaper input.
How does a change in the price of one input change the firm's long-run expansion path? If the price of an input changes, then the
MRTS as Ratio of Marginal Products
Imagine adding some labor (ΔL) and reducing the amount of capital just sufficient to keep output constant (ΔK; note that it is negative). - The gain in output is MP_L ΔL. (MP_L: the marginal product of labor.) - The reduction is MP_K ΔK. (MP_K: the marginal product of capital.) The reduction in output from having less K is exactly offset by the gain in output from having more L *MP_K ΔK+MP_L ΔL=0* Rearranging terms: *|ΔK/ΔL|=(MP_L)/(MP_K )* which says the MRTS is the ratio of the marginal product of labor to the marginal production of capital.
there will eventually be diminishing marginal products for the firm's variable inputs.
In the short run when some inputs are fixed, marginal cost must eventually rise as a firm's output increases because
Long Run
The period of time required to alter the amounts of all inputs used in a production process. In the long run, both K and L are variable, so F(K,L)=2KL
Perfect Complements
Typing: typists and typewriters MRTS not defined
Short Run vs. Long Run
In practice, there are many production processes in which the quantities of at least some inputs cannot be altered quickly, making it useful to distinguish between: - *Long Run:* the period of time required to alter the amounts of all inputs used in a production process. - *Short Run:* the period of time during which at least one of the inputs used in a production process cannot be varied. This gives rise to the distinction between: - *Variable Input:* an input that can be varied in the short run - *Fixed Input:* an input that cannot vary in the short run In the long run, all inputs are variable inputs, by definition. *Transit:* The production function tells us how output will vary if some or all of the inputs are varied. In practice, there are many production processes in which the quantities of at least some inputs cannot be altered quickly. (Example) The FM radio broadcast of classical music is one such process. To carry it out, complex electronic equipment is needed, and also a music library and a large transmission tower. Records and compact discs can be purchased in a matter of hours. But it may take weeks to acquire the needed equipment to launch a new station, and months or even years to purchase a suitable location and construct a new transmission tower. (transit) This difference in the times needed to adjust the amount of various inputs makes it useful to distinguish between the short run and the long run in production. (Concepts) Formally, the long run is defined as the period of time required to alter the amounts of all inputs used in a production process, whereas the short run is defined as the period of time during which at least one of the inputs used in a production process cannot be varied. This divide between the short run and the long run also gives rise to the distinction between two types of inputs, namely the variable input and the fixed input. By definition, a variable input is an input that can be varied in the short run to change the output level. A fixed input on the other hand is defined as an input that cannot vary in the short run. Note that in the long run, all inputs are variable inputs by definition. (Example) In the classical music broadcast example, compact discs are variable inputs in the short run, but the broadcast tower is a fixed input. If sufficient time passes, however, even the broadcast tower becomes a variable input. (Specific length) Note that short run or long run is not associated with a specific period of time. In the FM radio example, the long run is months or years. In some production activities, like those of a street-corner hot dog stand, the long run may be just a few days.
Since firms can reach minimum efficient scale at a relatively low output rate, there will continue to be a large number of firms drilling for oil in the United States
In recent years, the United States has experienced large increases in oil production. The increases in oil production are due in large part to a new technology, hydraulic fracturing ("fracking"). Fracking involves injecting a mixture of water, sand, and chemicals into rock formations at high pressure to release oil and natural gas. A news story indicates that economies of scale in fracking may be considerably smaller than in conventional oil drilling. Source: Russell Gold and Theo Francis, "The New Winners and Losers in America's Shale Boom," Wall Street Journal, April 20, 2014. If this view is correct, what would the likely consequences be for the number of firms drilling for oil in the United States?
Too Many Dimensions
In the long run, all factors of production are by definition variable. This creates a problem for graphical representation: - For Q=F(K,L) with both K and L variable, we need a three-dimensional diagram to deprescribe the production function. - When there are more than two variable inputs, we require even more dimensions. Solution: *isoquants.* The idea is similar to using indifference curves to describe utility functions of two goods.
Common Properties of Short-Run Production Functions
Passes through the origin Output initially grows at an increasing rate. - The benefits of division of tasks and specialization of labor Beyond some point, output grows at a diminishing rate with increases in the variable input — *the law of diminishing returns.* Eventually, the limitation of fixed capital emerges, and employees starts to get in each other's way. The property that output initially grows at an increasing rate may stem from the benefits of division of tasks and specialization of labor. With one employee, all tasks must be done by the same person, while with two or more employees, tasks may be divided and employees may better perform their dedicated tasks. (Example) To understand the benefits of division of tasks and specialization of labor, imagine you manages a kitchen in a restaurant. When you have only one chef working in the kitchen, he needs to do everything by himself, and when he switches from preparing vegetables to cooking them, he needs to move around, he may also need to change his equipment, all of which takes times. Also, he may not be good at every step. When you add one more chef to the kitchen, then each can specialization in one task. You will save the transition time, and each chef can specialize in his own task to further improve his skills in that task. Overall, having one more chef more than doubles the productivity, and you will see the output increases at an increasing rate. The final property noted about the short-run production function —that beyond some point, output grows at a diminishing rate with increases in the variable input—is known as the law of diminishing returns. And although it too is not a universal property of short-run production functions, it is extremely common. (Example) This law of diminishing returns can also be understood with the help of the restaurant kitchen example. After all, the size of the kitchen and the number of stoves are fixed at least in the short run. If you keep hiring more chefs to work for you, at some point, the benefits from division of labor and specialization will be exhausted, and they may started to get in each other's because of the limited space and equipment. The result is that output will start to increase at a slower and slower rate.
Isoquants
Such curves are called *isoquants,*and are defined as the set of all input combinations that yield a given level of output. Consider Q=F(K,L)=2KL. Suppose we want to describe all possible combinations of K and L that give rise to a particular level of output—say, Q=16. Solving Q=2KL=16 for K in terms of L yields *K=8/L* The (L, K) pairs that satisfy the above equation are shown by the curve labeled Q=16 in next figure. The curves labeled Q=32 and Q=64 are similarly obtained.
Production Function in the Short Run vs. The Long Run
Recall: Q=F(K,L)=2KL In the long run, both K and L are variable, so *F(K,L)=2KL* In the short run, assume labor input is variable but the capital input is fixed, say, at the value K=K_0=1. Then *F(K,L)=2K_0 L=2L* (transit) What about the production equation Q=F(K,L) we mentioned? How does this differentiation between the short run and the long run affect it? Consider again the production process described by 2KL. In the long run, both K and L are variable, the period of time is long enough to change both of them, so, the long-run production function is just 2KL itself. In the short run, things are different. Suppose we are concerned with production in the short run—here, a period of time in which the labor input is variable but the capital input is fixed, say, at the value K=K_0=1. With capital held constant, output becomes, in effect, a function of only the variable input, labor: F(K,L)=2K_0 L=2L. The short-run production function Q=2L corresponds to the first row of the previous table. (Implication) What's the implication? Well, obviously, the short-run production function is easier to analyze because it is a function of only one variable. Graphically, it means we can plot the production function in a two-dimensional diagram. For the long-run production function, things are a little more complicated and we need to use some other tools to represent the production function graphically in a two-dimensional diagram.
A More Practical Short-Run Production Function
[5.2 Slide 10] As you saw in the last Concept Check, the graphs of short-run production functions will not always be straight lines. The short-run production function shown in the current Figure has several properties that are commonly found in production functions observed in practice. First, it passes through the origin, which is to say that we get no output if we use no variable input. Second, initially the addition of variable inputs augments output at an increasing rate: moving from 1 to 2 units of labor yields 10 extra units of output, while moving from 2 to 3 units of labor gives 13 additional units. Finally, the function has the property that beyond some point (L > 4 in the diagram), additional units of the variable input give rise to smaller and smaller increments in output. Thus, the move from 5 to 6 units of labor yields 14 extra units of output, while the move from 6 to 7 units of labor yields only 9. For some production functions, the level of output may actually decline with additional units of the variable input beyond some point, as happens here for L > 8. With a limited amount of capital to work with, additional workers may eventually begin to get in one another's way The curvilinear shape shown here is common to many short-run production functions. Output initially grows at an increasing rate as labor increases. Beyond L > 4, output grows at a diminishing rate with increases in labor.
Inevitable Starvation for Human Race?
[5.2 Slide 14] Employing the logic based on fixed agricultural land and the law of diminishing returns, the British economist Thomas Malthus argued in 1798 that population growth will drive average food consumption down to the starvation level. Reality so far: food production per capita grew more than twenty-fold in the last 200 years. Is the law of diminishing returns wrong? In fact, even famous scholars can overlook the importance of this requirement for diminishing returns to labor. For example, in 1798, the British economist Thomas Malthus, employing the same logic of in the example of growing grain in a flowerpot, argued that the law of diminishing returns would imply eventual misery for the human race. His logic is that agricultural land is fixed and, beyond some point, the application of additional labor will yield ever smaller increases in food production. The inevitable result is that population growth will drive average food consumption down to the starvation level. Is Malthus correct? We do not know for sure what will happen in a thousand years from now, but we do know that at least in the past 200 years, food production per capita has grown more than twenty-fold. In the last 70 years alone, food production per capita grew more than 50%. What's happening here? Is the law of diminishing returns wrong? Apparently, the law of diminishing returns is still valid. What changed in the last 200 years is the state of agricultural technology. With the same amount of land, we are able to produce much more. Since we are not fixing the state of technology, it is possible for the returns to labor to increase at an increasing rate as output increases.
Technological Improvements in Production
[5.2 Slide 15] Technological improvements in production are represented graphically by an upward shift in the production function. The law of diminishing returns applies to each of these curves, and yet the growth in food production has kept pace with the increase in labor input during the period shown. To see the effect of technological improvements on returns to labor, we can look at this graph shown on the slide. Here technological improvements in production are represented graphically by an upward shift in the production function. The law of diminishing returns applies to each of these curves, and yet the growth in food production has kept pace with the increase in labor input during the period shown. Thomas Malthus failed to anticipate the capacity of productivity growth to keep pace with population growth. Of course, his basic insight—that a planet with fixed resources can support only so many people—remains valid. But he apparently overlooked or underestimated the power of technological advancement.
Short Run to MPL graph
[5.2 Slide 19 graphs] MPL reaches maximum at inflection point (Top panel: How to compute MPL from TP) For example, the marginal product of labor when L=2 is MP_(L=2)=12. Likewise, MP_(L=4)=16 and MP_(L=7)=6 for the total product curve shown in the figure. Note, finally, that MP_L is negative for values of L greater than 8. (Inflection, concave and convex) inflection point on the total product curve, the point where its curvature switches from convex (increasing at an increasing rate) to concave (increasing at a decreasing rate). (Bottom panel) The marginal product curve itself is plotted in the bottom panel in the figure. Note that it rises at first, reaches a maximum at L=4, and then declines, finally becoming negative for values of L greater than 8. Note also that the maximum point on the marginal product curve corresponds to the inflection point on the total product curve.
Isoquant Map
[5.3 slide 7 graph] "Iso" comes from the Greek word for "same," The isoquant map describes the properties of a production process in much the same way as an indifference map describes a consumer's preferences. (The similarity) On an indifference map, movements to the northeast correspond to increasing levels of satisfaction. Similar movements on an isoquant map correspond to in-creasing levels of output. A point on an indifference curve is preferred to any point that lies below that indifference curve, and less preferred than any point that lies above it. Likewise, any input bundle on an isoquant yields more output than any input bundle that lies below that isoquant, and less output than any input bundle that lies above it. Thus, bundle C in the figure yields more output than bundle A, but less output than bundle D. (The difference) The only substantial difference between an isoquant map and an indifference map lies in the the significance of the labels attached to the two types of curves. From our discussion on utility, remember we said that utilities are ordinal, that is, the actual numbers assigned to each indifference curve were used to indicate only the relative rankings of the bundles on different indifference curves. This is to say that, with indifference curves, we are free to relabel the indifference curves in any way that preserves the original ranking of bundles. By contrast, the number assigned to an isoquant corresponds to the actual level of output we get from an input bundle along that isoquant. So, with isoquant maps, the labels are determined uniquely by the production function, and we are not allowed to scale them up or down.
