Production Theory Flashcards
What type of Units are Inputs + Outputs measured in?
Flow Units
- e.g. Labour p/w + Machine hours p/w = Output p/w
What is a Production Function?
Measures MAX. possible Output a firm can obtain from a Given amount of Inputs
What is Prod. Func. with Fixed Proportion Inputs?
y = ƒ(x1,x2) = min{x1,x2}
e.g. 1 man + 1 shovel = Holes
What is Prod. Func. with Perfect Sub. Inputs?
y = ƒ(x1,x2) = x1 + x2
e.g. Use Black OR Blue pens to ‘Produce’ solution
What is Cobb-Douglas Prod. Func.
y = ƒ(x1,x2) = A((x1)^a)((x2)^b)
- ‘A’ measures Scale of Prod.- Output if each Input Increased by 1 unit
- ‘a + b’ - measure how Output responds to changes in inputs
What are 2 main Assumptions we make about Technology?
Monotonic + Convex
What does it mean if Technology is Monotonic?
More of any Input generates at least as much Output as Original Amount- can’t produce less
What does it mean if Technology is Convex?
If 2 ways produce y units of Output- (x1,x2) + (z1,z2)
– Their Weighted Average- produce at least y units of Output
Define MP of Input i
Measures how much more Output we get per Additional Unit of Input i - holding all other Input levels fixed
MPi = ∂y / ∂xi
What is Law of Diminishing MP
MPi Diminishes as level of Input i Increases
==> ∂MPi / ∂xi < 0 - MP has Negative Slope
Define R.t.S
Describes how Output level changes as ALL Input levels change in Direct Proportion
What are Constant R.t.S?
Output Increases by Same Proportion as Inputs
– ƒ(kx1…kxn) = kƒ(x1…xn)
What are Decreasing R.t.S?
Output Increases by Smaller Proportion than Inputs
– ƒ(kx1…kxn) < kƒ(x1…xn) - Multiplying each Input gives higher Output than Multiplying Initial Inputs by same factor
What are Increasing R.t.S?
Output Increases by Larger Proportion than Inputs
– ƒ(kx1…kxn) > kƒ(x1…xn) - Multiplying each Input gives lower Output than Multiplying Initial Inputs by same factor
For Cobb-Douglas Prod. Func.- under what conditions would there be Constant, Decreasing + Increasing R.t.S?
Power of k = Sum of Powers of each Input
Constant R.t.S - Power of k = 1
Decreasing R.t.S - Power of k < 1
Increasing R.t.S - Power of k > 1
Define Isoquant
Different Combinations of Input levels that Produce the SAME Output Level
- IC for Production- Inputs = Goods
- Output = Utility
What is the Slope of an Isoquant?
Rate at which Input 2 must be given up as Input 1 is Increased where the Output level does NOT Change
What is the Slope of Isoquant called?
Technical Rate of Sub. - TRS
How is TRS calculated?
Differentiate Production Function-
- dy = ∂y/∂x1 (dx1) + ∂y/∂x2 (dx2) = 0 - keep same Output level
=> dx2/dx1 = – (∂y/∂x1) / (∂y/∂x2) = – MP1/MP2
TRS = ∆x1 / ∆x2 = – MP1/MP2
Define LR
Firm is Unrestricted in its choice of All Input Levels
- All FoPs can vary
Define SR
Firm is Restricted in its choice of at least 1 Input Level
What is Cost Minimiser?
Produces any given Output level y ≥ 0 - at Smallest possible Total Cost
– c(y) = firms smallest possible TC for Producing y
=> TC function for firm
What is TC with given Input prices?
w = (w1, w2,..., wn) - Input Prices TC = c(w1, w2,..., wn, y)
What is smallest possible TC for y Output?
c(w1, w2, y) = w1 x1(w1, w2, y) + w2 x2(w1, w2, y)
How is AC calc.?
AC = TC / y = c(w1, w2,…, wn, y) / y
How do Constant R.t.S determine how AC changes w/ Output level?
y –> 2y requires Doubling (2x) ALL Input Levels
TC Doubles –> AC Unchanged
How do Decreasing R.t.S determine how AC changes w/ Output level?
y –> 2y requires More than Doubling (>2x) ALL Input Levels
TC More than Doubles –> AC Increases
How do Increasing R.t.S determine how AC changes w/ Output level?
y –> 2y requires Less than Doubling (<2x) ALL Input Levels
TC Less than Doubles –> AC Decreases
