WEEK 4 producer theory Flashcards
Technology
describes the constraints that turn inputs into outputs
6 assumptions about technology
- No Free Lunch- nothing is free- if you have no inputs you have no output
- Non reversibility- cant run production process in reverse- cant make pigs from sausages (may be able but typical case)
- Free disposability- can produce a certain output with a particular combinations of inputs then we can always produce a little less with that combination of inputs
- Additivity- if we can produce an output level x using a combination of inputs and another output level y using another combination of inputs then we can produce output level x + y. E.g certain no. of workers and wood it will get 10 tables. e.g x and y make an output combined
- Divisibility- if er can produce output level z using a combination of inputs then can produce 0.5z by using some combination of inputs. We can produce a fraction of whatever amount of goods you are producing
Convexity- if output level z can be produced by a particular combination of inputs and z can also be produced by using a different combination of inputs then can also produce z by using a mixture of the two combinations of inputs. Ex. 10 tables using 10 wood and 2 worker also produce 10 tables using 10 workers and 2 wood. We can use and average of these two e.g. 6 workers 6 wood to get 10 tables.
production function
maximum output attainable using a certain amount of inputs
output= function(Labout,Captial)
q=f(L,K)
marginal product
extra output from 1 unit increase in the input (holding others constant)
calculation of marginal product
Derivative of the production function with respect to L (Dq/DL)
an increasing marginal product means for example each worker increases output larger than the last worker
types of marginal product and what they mean and how its found
an increasing marginal product means for example each worker increases output larger than the last worker
constant- each worker same output as last
decreasing- each worker doesnt increase output as large as the previous worker
find using second derivative of marginal product of Labout
isoquant
combinations of inputs to produce an amount of output.
MRTS
MRTS marginal rate of technical substitution- is the rate at which you can substitute 1 input for the other and keep output constant.
how to find MRTS
Slope of an isoquant is equal to the marginal rate of technical substitution
Marginal product of labour divided by the marginal product of capital
Which is equal to Dq/DL divided by Dq/DK
Returns to scale and types
What happens to output when we multiply all inputs by the same factor.
Increasing RTS- when you double inputs you get more than double outputs. Constant RTS- double inputs equal double outputs
Decreasing RTS- double inputs less than double outputs (may increase but not by double)
Cobb-douglas technology
Output is function of labour and capital, and both are to the power of some positive number.
Leontief tech
Amount of output is equal to whatever is the minium of either labour or capital.
MPL OF cobb douglas
Marginal product of labour, if you differentiate with respect to L, is positive because k alpha and L is positive. So higher an additional worker output rises
Rate of change MPL
what is alpha minus 1, depends on alpha if aplha is less than 1 than decreasing MPL, Alpha equals 1 constant MPL and if alpha is bigger than 1 increasing MPL
returns to scale of cobb douglas
Short Run
At least 1 factor of production is fixed usually land or capital
Long run
all Factors of production are variable
cost minimization
producing q units at lowest cost.
What happens when there is a change in the price of inputs?
Suppose price of labour increases
What would happen to the optimal choice to produce q units
Iso cost curve gets steeper- any point on iso cost gives a certain amount if w increases and not going to spend any more than 100 so able to by less so iso cost curve swings inwards. Less L with higher w
Cost function
Minimum cost of producing q units
Find cost function
write Lagrangian wL=rK+lambda(q*-f(L,K)
first order conditions
eliminate Lambda
Solve factor demand L(w,r,q’) and K’(w,r,q) into C=wL+rK to get cost function
fixed cost
a cost that doesn’t depend on the amount of output produced. Pay regardless of output in SR amount paid for capital is fixed cost.
variable
a cost that depends on the amount of output produced. 1 more additional worker needed for each unit of output therefore labour costs are variable.
total costs
The sum of fixed costs and variable costs.
Short run cost concepts
Short run total costs (SRTC)- the cost function with capital fixed
Short run average cost (SRAC)- SRTC divided by output. How much does it cost on average to produce q units
Short run marginal cost (SRMC)- The change in SRTC when an extra unit is produced
Facts about SR concepts
Initially MC declining as we have fixed cost as we produce more and more the fixed cost is only relevant for the first unit, so MC is only increase in variable cost.
SRMC increases due to diminishing marginal product of labour, too many cooks in the kitchen.
SRAC- declines at first as most of the total cost is from fixed cost as increase q small slope of variable costs being added. Short run fixed cost dilution, total cost of 100 as you increase quantity it’ll get smaller eventually increasing due to diminishing marginal product of labour.
SRAC AND SRMC intersect at the minimum of the average cost.
long run concepts
Ability to choose all factors of production
e.g Capital chosen optimally
LRTC- the cost-function where all factors of production are variable.
LRAC- LTRC divided by quantity
LRMC- The change in LRTC when an extra unit is produced
how do long ans short run costs relatate
To find long run total cost for example what to choose from 1, 5 or 10 units of capital. For different level of output
0-A choose 1 unit as the black line is less than the green and blue
A-B as output increases, optimal to have 5 unit of capital as the blue line is lower than the black
Above B choose 10 as optimal cost.
Long run cost function, lowest line on all short run total costs.
what cost function is bigger
SHORT RUN COST FUNCTION>LONG RUN COST FUNCTION
As in long run we sub away from expensive inputs.
Firms cost minimisation problem
Firms cost minimisation problem- choose the amount of labour to minimise their costs where the amount of capital is a fixed parameter subject to the production function.
