1- Intro

Question 1

How does the Production function change across Labour f(L; K=K*)?

Answer 1

-Output (Q) first increases convexly
-Diminishing returns set in until a transitory point
-Output reduces as factories become suffocating

Question 2

How can you get the variable cost curve from the production function?

Answer 2

Flip production function and multiply by wage:
VC(Q) = wL = wf⁻¹(Q; K=K*)

Question 3

How do you get Marginal cost MC(Q) from the variable cost function?

Answer 3

First derivative (slope) of variable cost:
VC(Q)’ = MC(Q)

Question 4

How do you get Average variable cost AVC(Q) from the variable cost function?

Answer 4

Slope of intercepting line from origin i.e. Variable cost divided by quantity: VC(Q)/Q

Question 5

Why do marginal and average variable costs start at the same point?

Answer 5

At Q=0, there will be a cost of producing 1 unit, once this sole unit is produced its cost will be the average

Question 6

Why does marginal cost always intersect average variable cost at the minimum?

Answer 6

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

Question 7

How do you find the marginal revenue MR(Q) from a profit function π?

Answer 7

Differentiate wrt Q using chain rule

Question 8

What is Market Power?

Answer 8

The ability to profitably charge a price above perfectly competitive levels

Question 9

What is Market demand Q(p)?

Answer 9

Demand whole market faces

Question 10

What is Residual demand q(p)?

Answer 10

Demand individual firm faces i.e. Market demand minus supply of other firms q = Q - S⁰

Question 11

How do you derive best response functions?

Answer 11

1. Setup profit function πᵢ = (P(Q) - cᵢ)qᵢ
2. Differentiate wrt p or q
3. Equate to 0 and solve for p or q

Question 12

How do you derive Nash Equilibrium functions for each firm (qᵢ*)

Answer 12

Substitute best responses into each other and solve such that neither has any choice variables

Question 13

How can you tell if goods are strategic complements or substitutes from best response functions?

Answer 13

If quantity is increasing in the other firms quantity they are strategic complements and vice versa

Question 14

What is the difference between Cournot and Bertrand games?

Answer 14

In Cournot firms compete on quantity, Bertrand firms compete on price

Question 15

What is a Nash equilibrium?

Answer 15

Given a rival’s action, a player cannot improve payoff by deviating from equilibrium

Question 16

How do you derive Nash Equilibrium market price (P*)?

Answer 16

Substitute firm equilibrium levels into market price function

Question 17

How do you derive Nash Equilibrium market quantity (Q*)?

Answer 17

Add the firm equilibrium levels

Question 18

What is product substitutability?

Answer 18

How consumers perceive 2 products

Question 19

What is strategic substitutability?

Answer 19

How firms react to each others’ actions

Question 20

What is the differential of (Σqᵢ)qᵢ ?

Answer 20

2qᵢ + Σⱼ≠ᵢqⱼ

Question 21

How do you find the symmetric Nash equilibrium from a best response function?

Answer 21

Impose symmetry on best response function and solve for q(/p)

Question 22

How do you find Nash equilibrium when each firm has a different marginal cost?

Answer 22

-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

Question 23

How can you tell whether 2 products are substitutes or complements from the inverse demand function?

Answer 23

If price is increasing in the quantity demanded for the other good they are complements and vice versa

Question 24

How can you tell whether 2 products are substitutes or complements from the demand function?

Answer 24

If quantity demanded is increasing in the price charged by the other firm they are substitutes and vice versa