WEEK 4 producer theory

Question 1

Technology

Answer 1

describes the constraints that turn inputs into outputs

Question 2

6 assumptions about technology

Answer 2

1. No Free Lunch- nothing is free- if you have no inputs you have no output
   2. Non reversibility- cant run production process in reverse- cant make pigs from sausages (may be able but typical case)
   3. 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
   4. 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
   5. 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.

Question 3

production function

Answer 3

maximum output attainable using a certain amount of inputs

output= function(Labout,Captial)

q=f(L,K)

Question 4

marginal product

Answer 4

extra output from 1 unit increase in the input (holding others constant)

Question 5

calculation of marginal product

Answer 5

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

Question 6

types of marginal product and what they mean and how its found

Answer 6

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

Question 7

isoquant

Answer 7

combinations of inputs to produce an amount of output.

Question 8

MRTS

Answer 8

MRTS marginal rate of technical substitution- is the rate at which you can substitute 1 input for the other and keep output constant.

Question 9

how to find MRTS

Answer 9

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

Question 10

Returns to scale and types

Answer 10

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)

Question 11

Cobb-douglas technology

Answer 11

Output is function of labour and capital, and both are to the power of some positive number.

Question 12

Leontief tech

Answer 12

Amount of output is equal to whatever is the minium of either labour or capital.

Question 13

MPL OF cobb douglas

Answer 13

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

Question 14

Rate of change MPL

Answer 14

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

Question 15

returns to scale of cobb douglas

Question 16

Short Run

Answer 16

At least 1 factor of production is fixed usually land or capital

Question 17

Long run

Answer 17

all Factors of production are variable

Question 18

cost minimization

Answer 18

producing q units at lowest cost.

Question 19

What happens when there is a change in the price of inputs?

Answer 19

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

Question 20

Cost function

Answer 20

Minimum cost of producing q units

Question 21

Find cost function

Answer 21

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

Question 22

fixed cost

Answer 22

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.

Question 23

variable

Answer 23

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.

Question 24

total costs

Answer 24

The sum of fixed costs and variable costs.

Question 25

Short run cost concepts

Answer 25

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

Question 26

Facts about SR concepts

Answer 26

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.

Question 27

long run concepts

Answer 27

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

Question 28

how do long ans short run costs relatate

Answer 28

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.

Question 29

what cost function is bigger

Answer 29

SHORT RUN COST FUNCTION>LONG RUN COST FUNCTION

As in long run we sub away from expensive inputs.

Question 30

Firms cost minimisation problem

Answer 30

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.