Production Summary

Production/Profit-Maximization Review & Extension Concave Short Run (1 input) production Long Run Production (Isoquant Map)

Profit Using Output Price and Input Price Effects of Changes in Output Price Effects of Changes in Input Price

Technologies Process where inputs are converted to an output

(labour, computer, electricity, software) Several technologies will produce same product

o Which is best?

Input Bundles xi = amount used of input i (level of input i) input bundle: vector of input levels (x1,x2…xn)

(x1,x2,x3) = (6,0,9*3)

Production Functions y = output level production function: max amount of output possible for an input bundle

y = f(x1,…,xn)

Technology Sets production plan: input bundle and an output level (x1…xn, y )

o is feasible if output produced is no greater than max possible given prod function

y < f(x1,…xn) technology set: collection of all feasible production plans

T = {(x1… xn,y) | y < f(x1…xn) and x1 > 0 … xn > 0}

Technologies with Multiple Inputs 2 input case: input levels = x1, x2; output level = y suppose:

o max output level possible from input bundle (x1,x2) = (1,8) = 4o max output level possible from (x1,x2) = (8,8) = 8o y output unit isoquant = set of all input bundles that yield at most the same output level y

(isoq wth 2 variable inputs bottom right) complete collection of isoquants = isoquant map

o equiv to production function (each contains same relationship

Isoquants with 2 variable inputs graphed by adding an output level axis displaying each isoquant at height of isoquants output

level

2-Dimensional Representation of 3-D relationship isoquant map = topological map: point of equal altitude are connected isoquant map: connect all input bundle that can produce a specified quantity of output 3-D rep of production

o inputs x1,x2o output (vertical) yo take 3-d rep and “bird-eye-view”

Short-Run, 1 input fixed: Diminishing Marginal Product Long run:

o In/decreasing/constant returns to scaleo All inputs varied

Isoquants of Cobb-Douglas production function o Long run: constant returns to scale

20 units capital, 20 labour = twice output produced using 10 capital, 10 labouro shirt run: diminishing marginal product of labour

Returns-to-Scale marginal product: rate-of-change of output as 1 input levels increased, holding all other inputs fixed marginal product diminished b/c the other input levels are fixed increased inputs units have less and less of other

inputs with which to work

Graph: isoquants (level curves) for outputs 10,20,30,40 all isoquants are scaled versions of the units isoquant (distances between( if we hold constant the quantity of capital need to employ increasing

amount of labour to move to next higher isoquant diminishing marginal product of labour

- as capital use increases, amount of labour needed to increase output by 100 units is falling

o with higher capital input marginal product of labour is HIGHER

Returns-to-scale when all input levels are increased proportionately input productivities don’t fall

o returns to scale can be constant/increased

Long-Run and the Short-Runs long run: unrestricted in its choice of all input levels short run: restricted in some way in its choice of at least one input level

o many possibilities what do SR restrictions imply for a firms technology?

o Suppose restriction = fixing level of input 2o Input 2 = fixed inputo Input 1 = variable

SR:o With some rate of input fixed (x2), diminishing marginal product implies EACH SR production function will be

concave (increasing at decreasing rate)o Isoquant map several possible rates of x2

Look at from side of 3-d Each level of x2 implies a different SR production function