The Production Process and Costs Flashcards
What is the linear supply function?
Qs = β0 + βxPx + βrPr + βwW + βHPH
What is the algebraic form of a linear production function?
Q = F(K,L) = aK + bL
What is the algebraic form of a leontiff production function?
Q = F(K,L) = min{aK,bL}
What is the algebraic form of a Cobb Douglas production function?
Q = F(K,L) + K^aL^b
What is MPK, MPL, APK and APL of a linear production function?
- MPK = a and MPL = b
- APK = (aK+bL)/K and APL = (aK+bL)/L
How does the Leontief production function predict output?
if Q = F(K,L) = min{4K,8L}, when K = 2 and L = 3, output is 8
What is the slope of the K=sL line that defines Leontief production functions?
s = b/a
What is the cost minimising input mix for a Leotniff production function?
- 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
What is meant by constraint in regards to a Leontief production function?
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)
What is MPK, MPL, APK and APL of a Cobb Douglass production function?
- MPK = aK^a-1L^b and MPL = bK^aL^b-1
- APK = (K^aL^b)/K and APL = (K^aL^b)/L
Where do managers hire to?
- Labour until the VMPL = wage
- Capital until the VMPK = r
VMPL/K =
Value magical product: MPK/MPL * P(output price)
What are isoquants?
capture the tradeoff between combinations of inputs that yield the same output in the LR, where all inputs are variable
What is the slope of an isoquant (in particular for a linear function)?
- 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
What is an isocost and what are the equation forms?
- Combination of inputs that yield cost the same cost
- wL + rK = C
- i.e. K = (C/r) - (w/r)L
What is true of isocost shifts?
For given prices, isocosts farther from the origin are associated with higher costs
What is the effect of an extraneous effect on relative isocost prices?
- 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
Where does cost minimisation occur when comparing an isocost and isoquant?
- MRTS (=MPL/MPK) = w/r
- MPL/w = MPK/r
What occurs during optimal input substitution in a isocost, isoquant model?
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
What are short run total costs?
TC(Q) = FC + VC(Q)
What is marginal cost?
- MC = ∆C/∆Q
- derivative of cost function
What is true of the relation between AVC, ATC and MC?
MC crosses both AVC and ATC at min point
What is the long run average cost curve?
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
How is the profit max level of L determined?
VMPL = w
How is the profit max level of K determined?
VMPK = r
What is the essential distinction in output decision?
SR (i.e. VMPL/K = w/r) vs LR (i.e MPL/w = MPK/r)
What is VMPL/K?
The value of the output produced by the last unit of an input
What are economies of scale?
Portion of the long run average cost curve where long-run average costs decline as output increases
What are economies of scope?
- 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)
What is the working for economies of scope?
- 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)
What is cost complementary and how can the cost function help to determine it?
- 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)
How is SR cost min accomplished?
VPML = w
How is LR cost min accomplished?
MPL/w = MPK/r
What are the steps to determining how much of the variable input is used in the SR?
- Write SR production function
- Determine MPL
- Equate VMPL = w
What are the steps to determining how the input mix will change from the SR to the LR?
- Determine MPL/MPK using current input mix
- Compare MPL/w to MPK/v
- Increase q of more productive input
