1- Intro Flashcards
How does the Production function change across Labour f(L; K=K*)?
-Output (Q) first increases convexly
-Diminishing returns set in until a transitory point
-Output reduces as factories become suffocating
How can you get the variable cost curve from the production function?
Flip production function and multiply by wage:
VC(Q) = wL = wf⁻¹(Q; K=K*)
How do you get Marginal cost MC(Q) from the variable cost function?
First derivative (slope) of variable cost:
VC(Q)’ = MC(Q)
How do you get Average variable cost AVC(Q) from the variable cost function?
Slope of intercepting line from origin i.e. Variable cost divided by quantity: VC(Q)/Q
Why do marginal and average variable costs start at the same point?
At Q=0, there will be a cost of producing 1 unit, once this sole unit is produced its cost will be the average
Why does marginal cost always intersect average variable cost at the minimum?
If Marginal cost is below the average, AVC must decrease with a unit produced, if MC is higher AVC must increase with a unit produced
How do you find the marginal revenue MR(Q) from a profit function π?
Differentiate wrt Q using chain rule
What is Market Power?
The ability to profitably charge a price above perfectly competitive levels
What is Market demand Q(p)?
Demand whole market faces
What is Residual demand q(p)?
Demand individual firm faces i.e. Market demand minus supply of other firms q = Q - S⁰
How do you derive best response functions?
- Setup profit function πᵢ = (P(Q) - cᵢ)qᵢ
- Differentiate wrt p or q
- Equate to 0 and solve for p or q
How do you derive Nash Equilibrium functions for each firm (qᵢ*)
Substitute best responses into each other and solve such that neither has any choice variables
How can you tell if goods are strategic complements or substitutes from best response functions?
If quantity is increasing in the other firms quantity they are strategic complements and vice versa
What is the difference between Cournot and Bertrand games?
In Cournot firms compete on quantity, Bertrand firms compete on price
What is a Nash equilibrium?
Given a rival’s action, a player cannot improve payoff by deviating from equilibrium
How do you derive Nash Equilibrium market price (P*)?
Substitute firm equilibrium levels into market price function
How do you derive Nash Equilibrium market quantity (Q*)?
Add the firm equilibrium levels
What is product substitutability?
How consumers perceive 2 products
What is strategic substitutability?
How firms react to each others’ actions
What is the differential of (Σqᵢ)qᵢ ?
2qᵢ + Σⱼ≠ᵢqⱼ
How do you find the symmetric Nash equilibrium from a best response function?
Impose symmetry on best response function and solve for q(/p)
How do you find Nash equilibrium when each firm has a different marginal cost?
-Write symmetric FOC in terms of qi and Q only
-Multiply constants by n and sum choice variables to n
-Solve for Q and P
How can you tell whether 2 products are substitutes or complements from the inverse demand function?
If price is increasing in the quantity demanded for the other good they are complements and vice versa
How can you tell whether 2 products are substitutes or complements from the demand function?
If quantity demanded is increasing in the price charged by the other firm they are substitutes and vice versa
