Week 2 - Production + Cost Functions Flashcards
What are the steps of describing a firm’s behaviour?
1) Examine short and long run production processes
2) Analyse relationship between inputs and outputs - production function
3) Examine output cost relationship in short and long run
What is a firm?
An organisation that employs factors of production to produce goods and services
General Equation for Production Function
Y = Q = A * F(K, L) where:
Q = Quantity/Output, K = Capital, L = Labour, A = Technology Level
(Place a bar on top for fixed values)
What is the goal of a firm?
To maximise profit, recalling the constrained maximisation problem
What is the Short Run?
Time frame where at least one of the factors of production is fixed (A and K are likely to be fixed and L is viable)
What is the Long Run?
The time frame in which all input factors are variable
Difference between a short and long run
How long it takes for a firm’s inputs to become available
How is Total Production of Labour depicted?
By a graph
Impact of small amount of labour for the short run?
output increases very fast = increasing returns, because more of increased specialisations
Impact of medium-high amounts of labour for short run?
Output increases but slower, because of law of diminishing returns. Fixed capital technology, at some point addition of labour means each worker has less fixed capital to work with
Impact of very large amounts of labour for short run
Output decreases because of the law of diminishing returns
Equation for Average Product of Labour
APL = Q/L
- Average output each worker can produce
Equation for Marginal Product of Labour
MPL = Change in Q/Change in L = Derivative of Q w/ respect to L
- The production function slope (0 gives maximum output)
Trends of TPL for short run
1) MPL cuts through APL at maximum
2) When MPL > APL, average is increasing with L
3) When MPL < APL, average starts falling too with L
What is the Law of Diminishing Returns?
As successive units of a variable source are added to a fixed resource, beyond some MP attributable to each additional unit of the variable resource will decline
What is the LDR in the context of the TPL
There comes a point if we employ more labour, we probably can product more output, but output is going to increase at a decreasing rate
What are we interested in for the long run?
How output quantity changes when there is a proportional change in the factors of production
What are returns to scale for the long run?
Quantity of output changes when there is a proportional change in the quantity of all inputs
Difference between returns to scale and LDR
Returns to scale is a LR phenomenon (inputs are variable) and LDR is a short run phenomenon (capital = fixed)
What are constant returns to scale
Increase output by same proportional change (Double inputs = Double outputs)
What are increasing returns to scale?
Output increases by more than proportional input change (double inputs = triple outputs)
What are decreasing returns to scale?
If outputs increase by less than proportional input increase (triple inputs = double outputs)
What does a firm’s cost function relate?
Total cost of population and output
What type of relationship is there between production function and cost function?
One-to-one
Firms aim to maximise profits where profit = ___
Economic Profit
How do economic profits differ from accounting profits?
Accounting Profits = Revenue - Explicit Costs
Economic Profits (pi)= Revenue - Total Opportunity Costs
Economic Profits (pi) =
Total Revenue - Total Cost
TR = Amount a firm received for output sale
TC = Amount paid for production inputs + forgone opportunities (not including sunk)
What is zero economic profit
When revenues just cover opportunity cost, i.e. Revenue = OC
What is a cost function?
A function that links the quantity of output with its associated production cost, i.e. TC = f(q)
Equation for TC in short run
TC = Total Fixed Costs + Total Variable Costs
What are TFC
Total costs that do not vary with output changes
What are TVC
Total costs that change with output level
Effects of the TVC and TC Curve (Short Run)
1) Low output level = TVC and TC increase at decreasing rate because of production function and low output level
2) High output level = TVC and TC increase at increasing rate because more labour increases production
Equation for Average Fixed Costs
AFC = TFC/Q
Equation for Average Variable Costs
AVC = TVC/Q
Equation for Average Total Costs
ATC = TC/Q or AFC + AVC
Marginal Cost (for TVC and TC Short Run Curve)
MC:
= Change in TC / Change in Q
= dTC / dQ
= dTVC / dQ
Relationships between AFC, AVC, and MC:
1) AFC declines as Q increases (Q is denominator)
2) AVC declines, reaches min, then increases - U shape (LDR, VC increase)
3) MC declines sharply, reaches min, then increases- U shape (MPL rises then falls + LDR)
Why does the MC cut both AVC and ATC @ minimums?
1) When MC > ATC, ATC increases
2) When MC < ATC, ATC decreases
3) When MC = ATC, ATC is at its minimum
Why should LR costs < SR costs (for a given level of output)
A firm producing a positive output has flexibility to adjust its inputs allowing:
- To choose the most efficient production method
- The cheapest combination of all inputs
What does the LRAC show?
Lowest per-unit cost at any output that can be produced after the firm has had the time to make all appropriate adjustments in its plant size
How can we draw the LRAC
A combination of all the minimum points of the SRAC curves
