Production Theory

Question 1

What type of Units are Inputs + Outputs measured in?

Answer 1

Flow Units

- e.g. Labour p/w + Machine hours p/w = Output p/w

Question 2

What is a Production Function?

Answer 2

Measures MAX. possible Output a firm can obtain from a Given amount of Inputs

Question 3

What is Prod. Func. with Fixed Proportion Inputs?

Answer 3

y = ƒ(x1,x2) = min{x1,x2}

e.g. 1 man + 1 shovel = Holes

Question 4

What is Prod. Func. with Perfect Sub. Inputs?

Answer 4

y = ƒ(x1,x2) = x1 + x2

e.g. Use Black OR Blue pens to ‘Produce’ solution

Question 5

What is Cobb-Douglas Prod. Func.

Answer 5

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

Question 6

What are 2 main Assumptions we make about Technology?

Answer 6

Monotonic + Convex

Question 7

What does it mean if Technology is Monotonic?

Answer 7

More of any Input generates at least as much Output as Original Amount- can’t produce less

Question 8

What does it mean if Technology is Convex?

Answer 8

If 2 ways produce y units of Output- (x1,x2) + (z1,z2)

– Their Weighted Average- produce at least y units of Output

Question 9

Define MP of Input i

Answer 9

Measures how much more Output we get per Additional Unit of Input i - holding all other Input levels fixed
MPi = ∂y / ∂xi

Question 10

What is Law of Diminishing MP

Answer 10

MPi Diminishes as level of Input i Increases

==> ∂MPi / ∂xi < 0 - MP has Negative Slope

Question 11

Define R.t.S

Answer 11

Describes how Output level changes as ALL Input levels change in Direct Proportion

Question 12

What are Constant R.t.S?

Answer 12

Output Increases by Same Proportion as Inputs

– ƒ(kx1…kxn) = kƒ(x1…xn)

Question 13

What are Decreasing R.t.S?

Answer 13

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

Question 14

What are Increasing R.t.S?

Answer 14

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

Question 15

For Cobb-Douglas Prod. Func.- under what conditions would there be Constant, Decreasing + Increasing R.t.S?

Answer 15

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

Question 16

Define Isoquant

Answer 16

Different Combinations of Input levels that Produce the SAME Output Level

• • IC for Production- Inputs = Goods
• Output = Utility

Question 17

What is the Slope of an Isoquant?

Answer 17

Rate at which Input 2 must be given up as Input 1 is Increased where the Output level does NOT Change

Question 18

What is the Slope of Isoquant called?

Answer 18

Technical Rate of Sub. - TRS

Question 19

How is TRS calculated?

Answer 19

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

Question 20

Define LR

Answer 20

Firm is Unrestricted in its choice of All Input Levels

- All FoPs can vary

Question 21

Define SR

Answer 21

Firm is Restricted in its choice of at least 1 Input Level

Question 22

What is Cost Minimiser?

Answer 22

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

Question 23

What is TC with given Input prices?

Answer 23

w = (w1, w2,..., wn) - Input Prices
TC = c(w1, w2,..., wn, y)

Question 24

What is smallest possible TC for y Output?

Answer 24

c(w1, w2, y) = w1 x1(w1, w2, y) + w2 x2(w1, w2, y)

Question 25

How is AC calc.?

Answer 25

AC = TC / y = c(w1, w2,…, wn, y) / y

Question 26

How do Constant R.t.S determine how AC changes w/ Output level?

Answer 26

y –> 2y requires Doubling (2x) ALL Input Levels

TC Doubles –> AC Unchanged

Question 27

How do Decreasing R.t.S determine how AC changes w/ Output level?

Answer 27

y –> 2y requires More than Doubling (>2x) ALL Input Levels

TC More than Doubles –> AC Increases

Question 28

How do Increasing R.t.S determine how AC changes w/ Output level?

Answer 28

y –> 2y requires Less than Doubling (<2x) ALL Input Levels

TC Less than Doubles –> AC Decreases