Productionslide 1 PRODUCTION PRODUCTION FUNCTION: The term economists use to describe the technology of production, i.e., the relationship between inputs and the output of a good or service.

Productionslide 2 There is a production function for every good that shows the maximum output you can get from any quantities of inputs. The production function is the description of the current best technology for making a good. Production functions apply to firms. E.g., MSU has a production function for producing alfalfa. GM has a production function for producing Chevy’s.

Productionslide 3 The next slide shows a production function when there are two variable inputs, L and K.

Productionslide 4

Productionslide 5 ISOQUANT Definition: All combinations of inputs that yield the same output. The isoquants for the production funtion in the last slide can be seen by viewing the function "from above".

Productionslide 6

Productionslide 7 Notice that isoquants seem to have many of the same properties as indifference curves.

Productionslide 8 TOTAL PRODUCT CURVE The total product curve shows output as a function of a single variable input, holding all other inputs constant.

Productionslide 9

Productionslide 10 The production function for tax returns in a small accounting firm can be written like this: Q(returns) = f(office space, accountants, computers, furniture, supervisors, office supplies, etc.) The dependent variable is quantity of output (number of returns filed in this case). The independent variables are quantities of inputs.

Productionslide 11 Here’s a table of values for tax return production as a function of a single variable input, LABOR: Labor Total Product

Productionslide 12 Total product curve for tax returns as a function of the amount of labor Plot the remaining points Q LABOR

Productionslide 13 Total product curve for tax returns as a function of the amount of labor Q LABOR TP When labor is 5, output is 56 When labor is 5, output is 56

Productionslide 14 Average product: Output per unit of input, or (output / input). AP L = Q/L Average product is a measure of input productivity.

Productionslide 15 If we know the total product curve for tax preparation services, we can compute the average product: 15 / 2 56 / 5 TOTALAVERAGE LABORPRODUCT

Productionslide 16 If we know the total product curve for tax preparation services, we can compute the average product: 15 / 2 56 / 5

Productionslide 17 The average product curve shows the average product of an input as a function of the amount of input used. The independent variable is the amount of the input (labor). The dependent variable is the average product (of labor).

Productionslide 18 Graph the points showing AP, and connect them here. Label the axes correctly. AP LABOR AP L The average product of 7 units of labor is

Productionslide 19 Here’s the final result of graphing the AP curve. AP LABOR AP L The average product of 7 units of labor is 9.43.

Productionslide 20 Marginal product of an input: The change in output per unit change in input. Marginal product is the slope of the total product curve:  Q/  L Marginal product is a measure of input productivity.

Labor Total Product Marginal Product (48-36)/ (4-3) (48-36)/ (4-3)

Labor Total Product Marginal Product (48-36)/ (4-3) (48-36)/ (4-3)

Productionslide 23 The marginal product curve shows the marginal product as a function of the quantity of labor used. The independent variable is the amount of the input (labor). The dependent variable is the marginal product of labor.

Productionslide 24 Plot the remaining points showing MP here, and connect the them. Label the axes correctly

Productionslide Here’s the final result of graphing the MP curve. MP L LABOR MP The marginal product of the 6th unit of labor is 6.

Productionslide 26 Here’s a way to see the relationship between total product curve and the marginal product curve. Total Product CurveMarginal Product Curve L Q MP L TPTP  Q=6  L=1  Q /  L The marginal product of the 6th unit of L is

Productionslide 27 There is an important relationship between average product and marginal product of an input: 1) When AP is rising, MP is greater than AP, 2) When AP is falling, MP is less than AP. 3) When AP is constant (neither rising nor falling), MP equals AP.

Productionslide 28 So the average and marginal products must look like this: L MP, AP AP MP

Productionslide 29 Law of Diminishing Returns As the amount of an input increases, all other inputs being held constant, the marginal product of the input will eventually decline.

Productionslide 30 L MP, AP AP MP Diminishing returns begin here with the 4th unit of labor. Diminishing returns begin here with the 4th unit of labor

Productionslide 31 The general shapes of the average and marginal product curves can be deduced from the total product curve.

Productionslide 32 Total Product Curve Marginal Product Curve Q TP L MP L When the slope of the TP curve is increasing, MP is rising. When the slope of the TP curve is decreasing, MP is falling

Productionslide 33 The shape of the average product curve also can be found by looking at the total product curve.

Productionslide 34 Q L AP L TP THE SLOPE OF A LINE FROM THE ORIGIN TO A POINT ON THE TP CURVE MEASURES AVERAGE PRODUCT. To find AP draw lines from the origin to points on the TP curve at different levels of L. The slope of this line is 12 (36/3) So this distance is

Productionslide 35 Q L AP L TP THE SLOPE OF A LINE FROM THE ORIGIN TO A POINT ON THE TP CURVE MEASURES AVERAGE PRODUCT. To find AP draw lines from the origin to points on the TP curve at different levels of L. The slope of this line is 9.43 (66/7) So this distance is

Productionslide 36 So to find the matching set of AP and MP curves for any TP curve proceed as follows: 1) Find the general shape of the MP curve by seeing what happens to the slope of the TP curve as input increases. 2) Find the general shape of the AP curve by seeing what happens to the slopes of lines from the origin as input increases. 3) Remember the correct relationships between the curves, and sketch the curves to follow the required relationships.

Productionslide 37 Q input TP A few practice problems: Find the corresponding MP and AP curves for each TP curve:

Productionslide 38 Q input TP A few practice problems: Find the corresponding MP and AP curves for each TP curve: AP=MP input Q/I

Productionslide 39 Q input TP

Productionslide 40 Q input TP input Q/I MP AP

Productionslide 41 Q input TP

Productionslide 42 Q input TP input Q/I AP MP

Productionslide 43 Q input TP EXTRA CREDIT !!!

Productionslide 44 Q input TP EXTRA CREDIT !!! Q/I input AP MP