Production. Any activity that creates present or future economic value (utility). The transformation of inputs into outputs

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1 Production Any activity that creates present or future economic value (utility). The transformation of inputs into outputs Inputs can include categories such as: labour, capital, energy, land, entrepreneurship etc...

2 Production Function Q = F(.) The form of the production function F(.) depends on the technology available. It can be thought of as the blueprint for production. Technology: All knowledge that creates economic value Eg: Dual Input Production Function Q = F(K,L)=2KL Labour (person-hours/wk) Capital (equipment-hours/wk

3 Fixed and Variable Inputs The minimum time it takes to change an input varies with the type of input. For this reason we differentiate: Long Run: The shortest period of time required to alter the amounts of all inputs used in a production process. Short Run: The longest period of time during which at least one of the inputs cannot be altered Note that this definition has nothing to do with months, years etc... for some industries (semiconductors) the short run may be years, while for others (hot dog vending) the long run may be hours.

4 Production in the Short Run Say we hold one of the inputs constant, in this case capital.

5 Total Product Curve Most production processes can be described by the following function. Diminishing Returns: If other inputs are fixed, the increase in output from an increase in the variable input must eventually decline

6 Marginal Product The Total Product curve relates the total amount of production to the variable input. The Marginal Product curve relates the change in total production due to a unit change in the variable input (ie: it is the slope of the TP curve). MP L = Q L = δq δl Are there any levels of L a producer would not choose?

7 Average Product The average product is the total output divided by the quantity of the variable input, the line joining the origin to the corresponding point on the total product curve. In a sense, it reflects productivity. AP L = L Q

8 MP, AP Relationships When the marignal 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.

9 Example Using MP, AP Say you are the owner of 4 fishing boats, and you must decide how to divide your fleet between two locations. If you currently have 2 boats at the west end and 2 boats at the east end, will you change this ratio? General Rule for Indivisible Resources: Allocate each unit of resources to the production activity where the MP is the highest. When goods are divisible, this rule becomes: Allocate each unit of resources to the production activity until the MPs are equal

10 Production in the Long Run All inputs are now variable Q(K,L)=2KL Isoquant: The set of all technically efficient input combinations that yield a given level of output. Note: The labels of the isoquants are now output quantities. They can not be arbitrarily relabeled as can be done with indifference maps.

11 The Long Run Production Function Q = F(K,L) Isoquant: The locus through all combinations of K and L which yield the same amount of output

12 Marginal Rate of Technical Substitution The rate at which one input can be exchanged for another at the same level of output. MRT S = slope of isoquant = MP L MP K

13 Elasticity of Substitution Measures the degree of substitution of a production function. If it is close to zero, there is little opportunity to substitute. If it is large, then significant substitution. σ = % K L % MRT S

14 Perfect Substitutes and Perfect Complements Q=F(K,L)=aL+bK Q=F(K,L)=min(aL,bK) MRTS is constant There is no MRTS Note: σ = Note: σ =0

15 Cobb-Douglas Production Function Q = AK a L b where A, a, b > 0 and b =1 a Note: σ =1

16 Only applies to the Long Run Returns to Scale αq = F (λk, λl) What happens to output when all inputs are increased in proportion? Does production take place more efficiently in small scale or large scale? The answer will dictate whether an industry is served by many small firms or a few large ones. Increasing Returns to Scale: A proportional increase in every input yields a more than proportional increase in output Constant Returns to Scale: A proportional increase in every input yields an equal increase in output Decreasing Returns to Scale: A proportional increase in every input yields a less than proportional increase in output

17 Returns to Scale A production function may have different returns to scale over its domain or it may have the same returns to scale over its domain. Eg: Cobb-Douglas

18 Technological Change Technological improvements are represented graphically by a shifting of the production function Note that even though both production functions exhibit diminishing returns, the growth in output outpaces the growth in labour, and productivity per worker rises. Can be thought of as: 1) Produce same Q with less inputs 2) Produce more Q with same inputs 3) Something in between

19 Neutral Technological Change Technological change can be classified by its impact on MRTS at a given K/L ratio MRT S pre = MRT S post

20 Labour Saving Technological Change Now marginal product of capital rises faster than that of labour, which in effect causes firms to use more capital in their choices than labour. MRT S pre > MRT S post

21 Capital Saving Technological Change Now marginal product of capital rises faster than that of labour, which in effect causes firms to use more capital in their choices than labour. MRT S pre < MRT S post