The Production Process and Costs

Question 1

What is the linear supply function?

Answer 1

Qs = β0 + βxPx + βrPr + βwW + βHPH

Question 2

What is the algebraic form of a linear production function?

Answer 2

Q = F(K,L) = aK + bL

Question 3

What is the algebraic form of a leontiff production function?

Answer 3

Q = F(K,L) = min{aK,bL}

Question 4

What is the algebraic form of a Cobb Douglas production function?

Answer 4

Q = F(K,L) + K^aL^b

Question 5

What is MPK, MPL, APK and APL of a linear production function?

Answer 5

• MPK = a and MPL = b

- APK = (aK+bL)/K and APL = (aK+bL)/L

Question 6

How does the Leontief production function predict output?

Answer 6

if Q = F(K,L) = min{4K,8L}, when K = 2 and L = 3, output is 8

Question 7

What is the slope of the K=sL line that defines Leontief production functions?

Answer 7

s = b/a

Question 8

What is the cost minimising input mix for a Leotniff production function?

Answer 8

• The cost minimising input mix for a certain output (isoquant) is necessarily the corner
  
  • i.e. The cost-minimising level of perfectly complementary inputs does not depend on w or r

Question 9

What is meant by constraint in regards to a Leontief production function?

Answer 9

Output at a particular input mix is said to be constained by capital or labour depending on which factor is not on the corner, and thus the MP of that factor is 0 along the line (not corner)

Question 10

What is MPK, MPL, APK and APL of a Cobb Douglass production function?

Answer 10

• MPK = aK^a-1L^b and MPL = bK^aL^b-1

- APK = (K^aL^b)/K and APL = (K^aL^b)/L

Question 11

Where do managers hire to?

Answer 11

• Labour until the VMPL = wage

- Capital until the VMPK = r

Question 12

VMPL/K =

Answer 12

Value magical product: MPK/MPL * P(output price)

Question 13

What are isoquants?

Answer 13

capture the tradeoff between combinations of inputs that yield the same output in the LR, where all inputs are variable

Question 14

What is the slope of an isoquant (in particular for a linear function)?

Answer 14

• Marginal rate of technical substitution
  
  • The rate at which a producer can substitute between two inputs and maintain the sam e level of output
  • Absolute value of the slope of the isoquant: MRTSkl = MPL/MPK
    • i.e. for linear function, = b/a

Question 15

What is an isocost and what are the equation forms?

Answer 15

• Combination of inputs that yield cost the same cost
• wL + rK = C
• i.e. K = (C/r) - (w/r)L

Question 16

What is true of isocost shifts?

Answer 16

For given prices, isocosts farther from the origin are associated with higher costs

Question 17

What is the effect of an extraneous effect on relative isocost prices?

Answer 17

• A factor which for example lowers the cost of using capital would reduce the relative price of capital to about, increasing w/r, thereby making the isocost line steeper
• This means that cost-min input mix will now involve more K and less L
• While L input will fall, MPL will rise, making domestic workers more affordable

Question 18

Where does cost minimisation occur when comparing an isocost and isoquant?

Answer 18

• MRTS (=MPL/MPK) = w/r

- MPL/w = MPK/r

Question 19

What occurs during optimal input substitution in a isocost, isoquant model?

Answer 19

When an isocost pivots due to a r or w change, the tangent point of this angle of the new isocost with the OLD isoquant is the new cost min point

Question 20

What are short run total costs?

Answer 20

TC(Q) = FC + VC(Q)

Question 21

What is marginal cost?

Answer 21

• MC = ∆C/∆Q

- derivative of cost function

Question 22

What is true of the relation between AVC, ATC and MC?

Answer 22

MC crosses both AVC and ATC at min point

Question 23

What is the long run average cost curve?

Answer 23

A curve that defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production

Question 24

How is the profit max level of L determined?

Answer 24

VMPL = w

Question 25

How is the profit max level of K determined?

Answer 25

VMPK = r

Question 26

What is the essential distinction in output decision?

Answer 26

SR (i.e. VMPL/K = w/r) vs LR (i.e MPL/w = MPK/r)

Question 27

What is VMPL/K?

Answer 27

The value of the output produced by the last unit of an input

Question 28

What are economies of scale?

Answer 28

Portion of the long run average cost curve where long-run average costs decline as output increases

Question 29

What are economies of scope?

Answer 29

• Exist when the total cost of producing Q1 and Q2 together in less than the total cost of producing each of the type of output separately
• C(Q1,0) + C(0,Q2) > C(Q1,Q2)

Question 30

What is the working for economies of scope?

Answer 30

• Just expand full cost functions and compare
  
  • NB: when working out C(Q1,0) or C(0,Q2) individually and summing, the first element i.e. aQ1Q2 in C(Q1, Q2) = f – aQ1Q2 + bQ12 +cQ22, will disappear as it will be multiplied by zero for both C(Q1,0) and C(0,Q2)

Question 31

What is cost complementary and how can the cost function help to determine it?

Answer 31

• Exist when the marginal cost of producing one type of output decreases when the output of another good is increased
• (∆MC1(Q1,Q2))/∆Q2
• Just determine the MC for each product and look at the signs in front of the other product’s Q
• i.e if determining MC for Q1, remove Q1 from combined element (aQ1Q2), product rule the lone Q1 (bQ1) and remove the remaining Q2 (cQ2)

Question 32

How is SR cost min accomplished?

Answer 32

VPML = w

Question 33

How is LR cost min accomplished?

Answer 33

MPL/w = MPK/r

Question 34

What are the steps to determining how much of the variable input is used in the SR?

Answer 34

1. Write SR production function
2. Determine MPL
3. Equate VMPL = w

Question 35

What are the steps to determining how the input mix will change from the SR to the LR?

Answer 35

1. Determine MPL/MPK using current input mix
2. Compare MPL/w to MPK/v
3. Increase q of more productive input