07 Flashcards
(33 cards)
Topics of the 7th slide: technology
How do we describe innovations and technological progress? An introductory example: Costs and revenues in AI What are cost functions? Example: Technological progress & Dell Computers An alternative producer problem (cost minimization) What are opportunity costs, and why/when is it worthwhile to consider them? Example: Why it was profitable to demolish a profitable hotel in Hong Kong.
-Concepts you should know and understand: Cost minimization
Marginal costs, average costs, average variable costs
Producer surplus Opportunity costs
-Methods you should be able to apply: Graphical analysis of the cost minimization problem and computing solutions. Calculating the producer’s supply given cost functions.
-What you should be able to explain yourself:
The economic interpretation of changes in producer surplus.
When and why opportunity costs are important.
-What else we discussed: Example: Hong Kong Hilton. Example: Dell Computers. Example: Forbes 400.
cost minimisation perspective
The goal is to achieve a given production quantity y at the lowest
possible cost. The company therefore selects the optimal input quantities x1* and x2* that are necessary to produce a given output quantity y.
The cost function c(y ) indicates
the minimum cost required to produce a given output level y
How do we find cost function c(y )?
determine the cheapest input combination:
min w1x1 + w2x2
x1, x2
subject to the constraint that the production function is satisfied:
f (x1, x2) = y.
The solutions to this optimization problem, x1* (w1,w2,y) and x2* (w1,w2,y) then determine the cost function:
c(w1, w2, y ) = w1x1* + w2x2*
How do we solve the cost minimization problem? That is, how do we solve:
min w1x1 + w2x2
x1, x2
such that the production function is satisfied: f (x1, x2) = y ?
We seek the cheapest input bundle on the isoquant f (x1, x2) = y.
Differentiate the costs of input bundles, draw isocost
lines x2 = c / w2 - w1 / w2 . x1
Isoquant “equal quantity”
A curve representing combinations of two inputs (x₁ and x₂) that produce the same output level y.
Isocost Line
A line showing all input combinations with the same total cost
x2= c/w2 - w1/w2 . x1
Cost Function
c(y ,w1, w2) = w1 . x1* + w2 . x2*
where (x1* , x2*) is the cost-minimising bundle for output y
What condition defines the cost-minimizing input bundle?
The TRS equals the input price ratio:
MP1/MP2 = w1/w2
What is the cost function c(y ,w1, w2)?
It’s the minimal cost of producing output y with input prices w1 and w2.
Total Cost Function
c (y) = VC(y) + F
This formula tells us the total cost c(y) of producing output y is the sum of variable costs for that quantity and the fixed costs.
What are fixed costs and variable costs?
Fixed Costs (F): Costs paid even if output is 0. Example: rent.
Variable Costs (VC): Change with output level y.
Marginal costs (MC)
indicate how much total costs increase when an additional unit of output is produced. They correspond to the derivative of the cost function with respect to output:
MC(y) = d c(y) / d (y)
Average costs (AC)
represent the cost per produced unit.
Mathematically, they correspond to the ratio of total costs to output:
AC (y) = c(y) / y
Average variable costs (AVC)
represent how much the variable costs
per produced unit amount to.
They are equal to the ratio of variable
costs to output:
AVC(y) = VC(y) / y
What is the formula for marginal cost MC?
MC (y) = dc(y) / dy
At what point does the average cost curve reach its minimum?
When marginal cost equals average cost
MC (y) = AC (y)
How can you prove that MC=AC at minimum average cost?
By minimizing AC(y)=C(y)/y, taking the derivative and setting it to zero:
AC’ (y) = C′(y)⋅y−C(y) / y^2 =0 ⇒ MC=AC
Opportunity Cost
are forgone revenues (or forgone utility) that arise when existing opportunities for the use of resources are not taken
advantage of.
Fırsat maliyeti, bir şeyi seçtiğinizde vazgeçtiğiniz en değerli alternatifin değeridir.
Producer’s Problem (Alternative Formulation):
Profit maximization in terms of output:
max ( p.y - c(y) )
y
First-order condition (internal optimum):
p = MC (y)
What is the profit-maximizing condition for positive output?
p = MC (y)
The firm produces where price equals marginal cost.
Shutdown Rule (Short Run):
Firm should produce if:
p ≥ AVC(y)
Bir firma, fiyat (p), ortalama değişken maliyeti (AVC) karşılıyorsa veya aşıyorsa üretim yapmalıdır. Yani:
“p ≥ AVC(y)” → “Satış fiyatı, birim başına değişken maliyetten düşük değilse” firma kısa vadede üretmeye devam eder.
Sebep: Bu durumda firma, ürettiği her birim için değişken maliyetlerini (işçilik, hammadde vb.) karşılar ve sabit maliyetlere kısmen katkı yapar. Üretmemek daha büyük zarar getirir.
Örnek:
AVC = 10 TL, p = 12 TL ise (12 ≥ 10) → Üret! (Birim başına 2 TL katkı sağlar).
p = 8 TL ise (8 < 10) → Üretme! (Her birimde 2 TL zarar).
Not: Bu kural, kısa vadede geçerlidir. Uzun vadede firma p ≥ ATC (ortalama toplam maliyet) koşulunu arar.
