PRODUCTION AND COSTS: PRODUCTION FUNCTION AP Economics Mr. Bordelon.

PRODUCTION AND COSTS:PRODUCTION FUNCTION

AP Economics

Mr. Bordelon

Production Function

Production Function—Concepts

• Production function. Relationship between the quantity of inputs a firm uses and the quantity of output it produces.• Function. Relationship between a set of inputs and a

set of outputs so that each input is related to exactly one output.

• Fixed input. Input whose quantity is fixed for a period of time and cannot be changed.

• Variable input. Input whose quantity the firm can change at any time.

Joslyn Farms

• Kyle and Ryan have a farm sitting on 10 acres.• No more land is available.• They can neither increase or decrease the size of the farm.

• This is…?

• Kyle and Ryan can decide how many workers to hire.• This is…?

Production Function—Concepts• Whether or not the quantity of an input is fixed depends

on the time.• Short run. Time period in which at least one input is

fixed.• Example. Time period is too short for a firm to alter its plant size capital

is fixed.

• Long run. Time period in which all inputs can be changed.• Example. Time period is long enough for a firm to alter all inputs including

capital.

• There are no fixed inputs in the long run.

• Katie, DO NOT obsess over how much time is in either short run or long run. Pinky swear it.


• Marginal product. Marginal product of an input is the additional quantity of output produced by using one more unit of that input.• Example. Marginal product of labor. Additional quantity of output from using one more unit of labor.


• Total Product. (TP or Q) Total output produced by the firm.

• Total product curve. Shows how the quantity of output depends on the quantity of variable input, for a given quantity of the fixed input.• A graph of the firm’s TP when it uses different levels of a variable input with a given level of fixed inputs is the firm’s production function.

Joslyn Farms’ Production Function andTotal Product Curve


• The Joslyns know that the amount of wheat they produce depends on the number of workers they hire.• Wheat: output• Labor: variable

input• Land: fixed input

• TPC shows that the quantity of output depends on quantity of variable input, given quantity of fixed input.

• Why is the TPC sloped upward?


• TPC slopes upward because more bushels of wheat are produced as more workers are employed.

• TPC slope is not constant! Notice that it flattens more as you increase the number of workers.

• Why? HINT: look at table.


• The marginal product of labor declines as more and more workers are employed.

• The slope is the MPL!• OMG IDK MY BFF

Jill?

• MPL declines as more workers are higher. Each worker adds less to output than the previous worker.

Joslyn Farms’ Marginal Product of Labor Curve


• MPL curve shows how MPL depends on number of workers employed.

• Notice that the MPL coordinates don’t line up with the quantity of labor. Why?


• MPL falls as number of workers increases. We call this diminishing returns to labor.

• Diminishing returns to an output. Exists when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that input.

• Because of diminishing returns to labor, MPL curve is negatively sloped.

Production Function—Diminishing Returns

• Why are there diminishing returns?• Variable output: Joslyns can hire more laborers.• Fixed output: Joslyns only have 10 acres.• So what happens to the amount the laborers can

produce every time the Joslyns hire a new worker?


• Why are there diminishing returns?• Variable output: Joslyns can hire more laborers.• Fixed output: Joslyns only have 10 acres.• As the number of workers increase, the number of

bushels of wheat increases overall.• But what about the production of each individual

worker?


• Why are there diminishing returns?• Variable output: Joslyns can hire more laborers.• Fixed output: Joslyns only have 10 acres.• As the number of workers increase, the number of

bushels of wheat increases overall.• Because each individual worker is working with a

smaller and smaller plot of land for each one the Joslyns hire, the additional worker cannot produce as much as the previous worker.

• Result. MPL falls.


• Key point: Each successive unit of an input will raise production by less than the last if the quantity of all other inputs is held fixed.• In other words, ceteris paribus, baby.

• But what if we did allow the other inputs to change?

Joslyn Farms: TPC, MPLC and Fixed Input


• Let’s assume that the Joslyns bought an additional 10 acres.

• In the case of the TPC, at every point except 0, TP20 is above TP10. Why?


• Let’s assume that the Joslyns bought an additional 10 acres.

• In the case of the TPC, at every point except 0, TP20 is above TP10.

• Since there’s now 20 acres instead of 10, any given number of workers will produce more.


• For the MPL curves, both slope downward because the amount of land is fixed. Remember:

• MPL20 is above MPL10 at every point. Why?


• For the MPL curves, both slope downward because the amount of land is fixed. Remember:

• MPL20 is above MPL10 at every point. MP of same worker is higher when he has more of the fixed input to work with.


• Result. Position of TPC depends on quantities of other inputs. If you change quantities of other inputs, both TPC and MPC of remaining input will shift.

Katie and Dagny’s Lemonade Stand

• Katie and Dagny are running their lemonade stand and in order to increase output there are some variables they can easily change.• Variable inputs. Labor, lemons, sugar, water, cups,

ice.

• However, there are some inputs that can’t be increased.• Fixed inputs. Lemonade stand.

• The lemonade stand is capital. Capital is usually a fixed input.


• If the capital is currently fixed, how much time must pass before they can expand?• Short run. Time period that is too brief for a firm to

alter its plant capacity. In this case, the lemonade stand is fixed in the short run.

• Long run. Time period long enough for a firm to change the quantities of all resources used. Here, that would include the lemonade stand.

Katie and Dagny’s Lemonade StandUnits of Labor Total Product

(# of cups/hour)

0 0

1 8

2 18

3 26

4 32

5 36

6 38

7 36

Let’s focus on hiring. The table shows total production of lemonade at each quantity of labor hired. This is plotted out on the TPC on the right.


The TPC increases rapidly as the first couple of workers are hired. This is due to specialization as workers perform the tasks best suited to their talents.

However, workers 3 through 6, TP continues to increase, but at a slower rate. Opportunities to specialize have been exhausted, and remember, the lemonade stand is fixed.

Once the 7th worker is hired, the lemonade stand is too crowded, and actually gets in the way of the production process. Total output falls.

Katie and Dagny’s Lemonade StandUnits of Labor

Total Product

(# of cups/hour

)

Marginal Product of

Labor

0 0

1 8 8

2 18 10

3 26 8

4 32 6

5 36 4

6 38 2

7 36 -2

Now look at it as a matter of MPL.


MP declines as more labor is hired to a fixed amount of capital (the lemonade stand).

Dimishing marginal product of labor (any input). As you add more labor to a fixed quantity of capital, the next worker contributes less and less to the total than the workers who came before. Diminishing marginal product of any input is a defining characteristic of product functions in the short run.


Note: The workers are not becoming more and more stupid. We assume that they are equal in terms of capability. Diminishing marginal product is the result of having less space or tools to work with.


• In the long run, Katie and Dagny expand the size of their lemonade stand.

• Even if output doubles, MP still declines. Even though the lemonade stand is larger, once additional workers are added, diminishing returns still occur.

Units of Labor

TP(# of

cups/hour)

MPL

0 0

1 16 16

2 36 20

3 52 16

4 64 12

5 72 8

6 76 4

7 72 -4

PRODUCTION AND COSTS: PRODUCTION FUNCTION AP Economics Mr. Bordelon.

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