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hWhat is positive economics?
objective and fact-based where the statements are precise, descriptive, and clearly measurable. These statements can be measured against tangible evidence or historical instances.
What is normative economics
subjective and value-based, originating from personal perspectives or opinions dependent on notions of welfare
Is this a normative question ‘Are people better off if they know their habit formation tendencies’
Yes as what is better off? It is subjective
How do economists approach the Kitty Genovese Problem and how do they model this
They care about just one person calling the police:
* Each person helps with probability p
* Probability no one helps is (1-p)^n
Thus, probability that at least one person helps is
1-(1-p)^n
What is the set-up of the Kitty Genovese Game
public goods problem
What assumptions do we make about the players in the Kitty Genovese Model
- Rationality- each neighbour has a belief about the behaviour of other neighbours and best responds to that
- Beliefs are correct
what does the P(calling) being between 0<p<1 imply
Neighbour is indifferent between calling or not calling such that their expected payoff is the same whether they call or not, giiving them no incentive to deviate.
Payoff from calling = Payoff from not calling
Find the implied solution from the neighbour being indifferent between calling or not calling
What does this solution imply
As n increases, the probability that someone calls the police decreases
Draw the game theory matrix for the Kitty Genovese Game and identify the nash equilibriums
2 nash equilibriums in top right and bottom left. Explain why.
B and D
Moral Decay - Normative
Should- Normative
Define consumption bundle
The bundle of goods consumed
What consumption bundle will a rational agent always consume
the bundle that optimises her preferences given her income and the prices of the goods that are avaliable
What is the budget line
P(x1)X1 + P(x2) X2 = Y
what is always the y,x intercept and gradient of the budget line
y intercept: x1/Y
x intercept: x2/Y
gradient: -P(x2)/P(x1)
Where is the optimal consumption bundle on a graph + the optimal consumption rule
gradient of indifference curve = gradient of budget line
(exchange rate in market = exchange rate in preferences)
Define a company
a social organisation that buys or hires productive inputs, coordiantes them in production to produce goods and services, and then sells the output
Our assumptions about firms
- Decision making carried out by one agent (avoids principal-agent problem)
- Firm objective is profit maximisation
- Profit = Revenue - Oppostunity Costs
How is a firm restrictied in the short run compared to the long run
Short run, at least one input factor is fixed.
What is the production function
q=q(l,k) - the higher number of unit ouputs given l units of labour and k units of capital
q=output/unit time
l = people-days labour/unit
k= (machine days)/unit time
Marginal Product of Labour
By how much does output increase if we employ one more unit of labour
NOTICE CURLY D, because partial derivative of q(l,k) w.r.t L
Marginal Product of Capital
By how much does output increase if we employ one more unit of capital
What are the 2 general types of production functions
- Fixed Coefficients Production function (Pedagogical)
- Variable coefficients
Fixed coefficient production functions
Labour and Capital must always be used in fixed proportions e.g. 2 brewer hours and 1 brewing system to produce 1 pint per hour.
Variable Coefficient Production Functions
Marginal product of each factor increases then decreases but always remains positive
With variable coefficient production, what does the marginal product of a factor depend on
Provide the usual assumption and graph of the variable coefficients production function.
Depends on the quantitites used of all factors. L and K become cooperant factors
Usual Assumption:
If k increases holding L constant then MPL rises
If L increases holding K constant then MPK rises
What are the different returns to scale and what are the implications for the plant size.
figure out decreasing returns implications
Assumptions about returns to scale
Production functions displays firstly increasing and then decreasing returns to scale over a range of output
–> implies there is an efficient level of production
Assumptions of a rational consumer
- Completeness
- Transitivity
- Continuity
- Non-Satiation
- Convexity
What is completeness
Ability of a consumer to choose between options or be indifferent
What is transitivity
if x>y and y>z, then x>y
What is continuity
a technical assumption
what are the main 3 assumptions that allow us to use a utility function to represent preferences
Completeness, Transitivity, continuity
What is non satiation
What is the key implication of non-satiation
- Indifference curve slope downwards and the preferred set is above the indifference curve
What is convexity and the key implication
Convexity means a preference for averages
What is the implication of non-convex preferences
A preference for extremes rather than averages
What are the main styles of preferences
- Cobb Douglas
- Quasi-Linear
- Perfect substitutes
- Perfect Complements
- Non-Convex
What is the Cobb Douglas Function and what does it look like
u(x1,x2) = (x1)^a* (x2)^B
where a>0 and B>0
What is the Quasi Linear Function and what does it look like
u(x1,x2) = x1 + v(x2)
or
u(x1,x2) = v(x1) + x2
where v(0)=0, v’(.)>0 and v’’(.)<0
What is the Perfect Subtitutes Function and what does it look like
u(x1,x2) = ax1 + Bx2
where a>0 and B>0
What is the Perfect Complements Function and what does it look like
u(x1,x2) = min(ax1,Bx2) where a>0 and B>0
What is the Non-convex Function and what does it look like
u(x1,x2) = a(x1)^2+B(x2)^2
where a>0 and B>0
Uncompensated demand function maximised subject to…
x1(p1,p2,m) and x2(p1,p2,m) subject to:
- Budget constraint
- Non Negativity constraints x1>0, x2>0
Also called Marshallian Demand
What are the steps to find uncompensated demand
- Find MRS and Price Ratio
- Check non-satiation and convexity satisfied, explain implications
- Find MRS=Price Ratio
What is a general rule for cobbs douglas funcitons with the form
u(x1,x2) = (x1) ^ a * x2 ^ 1-a
P1X1(p1,p2,m) = am
p2x2(p1,p2,m)= (1-a)m
How is the demand curve derived from indifference curves
Demand is derived when holding fixed prices of other products as well as income and tastes
PED
give ab example of finding PED from cobb douglas
YED and example
XED and example
Complements
commodity pairs that the consumer likes to consume jointly
Substitutes
Commodity-pairs whre one commodity is consumed to the exclusion of the other
How does complementary nature effect relative price changes
Less sensitive as what matters is the price of the bundle.
What are the 2 main effects when a price changes
- Price Ratio Changes: one good cheaper relatively (substitution effect)
- Consumer feels richer or poorer (income effect)
What is the Hicksian method of decomposition
Hicksian: Take new budget line and move it parallel till it hits the original indifference curve. Creates new point (A’)
From A —> A’ will be just substitution effect (as price ratio same)
From A’ –> B will be just income
What is the slutsky method of decomposition
- Start with original budget line and move it parallel until you can afford original consumption
- Reoptimise to form a new optimal consumption bundle
move from A –> A’ as substitution effect as income eliminated
Move from A’ –> B is income effect
what are the effects of income and substitution on quantity consumed
Substitution: always go for cheaper product
Income: dep. on YED
Combined effect depends on which is stronger (if opposing)
Decompose this with the Hicksian method.
Determine the effects of the income and substitution effect, and thus wherever each good is a normal or inferior good.
How is a Giffen Good defined in income and substitution effects
If the income effect outweights the substitution effect
draw the graph of sandwhich and sushi when sushi is an inferior good and sandwhich is a normal good
Draw the effect of a an increase in the price of sushi if sushi is a giffen good
What are the 3 main ways to measure the effect that the price change had on the consumer
- Compensating Variation - ‘How much money should we give the consumer so that they will be exactly as well off as before the price change’
- Equivalent Variation - ‘How much money would the consumer be willing to pay to avoid the price change’
- Consumer Surplus
What is the difference between compensated and uncompensated demand and how they are calculated
- Uncompensated (Marshallian) Demand maximises utility given prices and income - x1(p1,p2,m)
Fix income + prices (fix budget line). Then get onto highest possible indifference curve
- Compensated (Hicksian) Demand minimises the cost of obtaining utility at prices - h1(p1,p2,u)
FIx utility and prices to fix indifference curve and gradient of budget line. Get onto lowest possible budget line.
How can the substitution effect be quantified
Change in x1 through substitution is approximately
dh1/dp1 * change in p1
How can the income effect be quantified
Price rise –> income falls by x1* change in price
dx1/dm(x1change in price)
Considering the quantification of income and substitution effects, how do you combine this
substitution effect - income effect
When is consumer surplus=compensating variation=equivalent variation
price change is small
No income effect
In general, consumer surplus is in between the the measures
what is the base weighted price indicies formula
When production function q(l,k) is used, what is the total costs equation
W = wage rate, r= capital rental price, L= quantity of labour, k= quantity of capital
C= wl + rk
What are the conventional fixed and variable costs
Convential to take k as fixed and L as variable
(distinguish between fixed and sunk costs)
What is total cost in the short run
C(q) = F + wl(q)
F= rk0 = fixed costs
(plant size)
what is the short run variable cost function
V(q) = C - F
thus, V(q) = wl(q)
what is the marginal cost function in SR and what is it equivalent to in terms of MPL and wage
What are the Average Total Costs (ATC)
What are the Average Variable Costs (AVC)
What happens when q=0 for costs
- At q=0, total costs equals fixed costs C=F
- AC= infinity, AVC=MC
Draw the TC and VC graph
How to see long run total cost?
there is one short run total cost curve for each value of k
Plot all SRTC curves croeesponding to all possivle valuies of K and define LRTC as the mioonimum cost at whicha ny given level of output can be produced when all inputs can be varied.
How can we find the lowest AC on the LRTC
Draw lines from LRTC points to origin
One with the smallest angle has the lowest AC
LRAC and LRMC graph
What do we assume firms choose
doesnt matter as both effect each other.
but we assume they choose quantity
What are the different revenue functions for a price-taker and monopoly
Price-Taker Firm:
Revenue(q) = P * q
Monopoly:
Revenue(q) = P(q) * q
For a price taker, describe how to find the profit maximissation price and quantity
FOC:
Profit(q) = p * q -C(q)
Profit’(q) = 0 –> p-C’(q) = 0
p = mc
SOC justify maximum:
Profit’‘(q)<0 –> -C’‘(q)<0
BORDER CONDITION:
Is q=0 or the shutdown price better than solution?
For a simple monopolist, describe how to find the profit maximisation price and quantity
Profit= p(q) * q - C(q)
FOC:
Profit’(q)=0 —> R’(q)=C’(q)
SOC:
R’‘(q)-C’‘(q) < 0
Border Condition:
Is q=0 or shut-down price better than solution?
What is first degree price discrimination
Charge each citizen according to their willingness to pay for beer - captures entire consumer surplus
What is second degree price discrimination
charging consumers a different price for the amount or quantity consumed
what is third degree price discrimination
charging different types of consumers a different price
Draw a firm and highlight the supply curve and how to calculate starting point and break even
How is labour related to MC mathematically
MC = W * dL/dQ
MPL = Marginal Productivity of Labour
MPL = dQ/dL
What is the wage equal to when profit is maximised
Wage = MVPL (Marginal Value of the Productivity of Labour)
MVPL= MPL * Price
essentially the same as MRPL lol
answer part a)
answer b)
answer c)
what 3 factors is the demand for labour reliant on
- Plant Size
- Output Price
- Wage Rate
Draw the labour demadn curve at certain fixed levels of capital
Assumptions of labour supply
- Allocating time between paid employment and leisure
- Enjoys both leisure and consumption (income)
- Marginal utility of both income and leisure are positive but diminish
- Both are complements in consumption
Individual utility depends on income (I) and daily leisure (R=hours)
U=U(I,R)
Individual requires a minimum numbner of leisure hours
How can the effects of a wage increase be decomposed
- Substitution Effect (always negative)
as wage goes up, leisure is more expensive
- Income Effect (positive if income and leisure are normal goods)
Assuming the individual is endowed with non-labour income (=V) and willing to work as much as they can. Build a model with budget constraint and indifference curves to find the optimal position
Max U=U(I,R) subject to I=V + w * L
0<L<L max
slope of -w
how do we derive an individuals labour supply curve from this model
Hicksian Decompose the effect of an increase in the wage rate if leisure is a normal good
How does the net effect of a wage increase an individuals supply of labour change
- At low levels of income, substitution effect outweighs income effect
- At high level income effect outweights substitution
causes backward bending blah blah
What are the 2 main potential effects of robots
- Displacement Effect- displalcing workers from previously performing tasks
- Productivity Effect-Other industries/taks increase labour demand as workers become more productive
What is Separation Theorem 1
When credit markets are perfect inndividuals can first calculate optimal investments using NPV and then calculate optimal consumption plan
What are the conditions for perfect credit markets
- Interest Rate for Borrowing = Interest Rate for Lending
- No constraints on how much you can borrow as long as it is within your means
- Perfect and costless –> ensures no one takes on loans that they cannot repay aand that all debts are repaid
What is separation theorem 2
When credit markers are imperfect
The decisions to save or borrow are interdependent so NPV is not enough to calculate the optimal investment plan
What is the model of intertemporal consumption
Individual makes plans for today and future in terms of how much they want to consumer at each period and how much they want to save/borrow
What are the model assumptions of intertemporal consumption
- 2 time periods
- Income in 2 periods y0 and y1
- Saving and borrowing possible at interest rate r
- Consumer derives utility from consumption in the 2 periods with preferences described u(c0,c1)
Choose c0 and c1 to maximise utility subject to a intertemporal budget constraint and non-negatiity constraints
Form the equation for the intertemporal budget contraint
Period 0: savings s0= y0 - c0> 0
(or borrowing if < 0)
Period 1: dissaving c1 = y1 + (1+r)s0
(or repaying debt)
Combining:
c1 = y1 + (1+r)(y0 - c0)
Rearranging:
c1 = (y1 + (1+r)y0) - (1+r)c0
What is the nature of the graph of the intertemporal budget constraint
Straight line with gradient -(1+r)
Draw the intertemporal budget contraint graph, identifying the saving, borrowing, endowment points and axis intercepts
What are the 2 main ways the intertemporal budget constraint is expressed
general assumptions of borrowing and saving decisions
- Typical consumer pref - completeness,transitivity,continuity –> U(c0,c1)
- Maximises U(c0,c1) subject to intertemporal budget constraint and non-negativity constraints
- Assume non-satitation and convesity assumptions are satisifed
What is the key result of an interest rate rise
- never makes a saver worse off
- usually makes a borrow worse off
draw the effect of an interest rate rise on a borrower
Hicksian Decompose the substitution and income effect of the increasses in the interest rate. Explain the effect of both.
Why is the saver always better off after a rate increase (show graphically)
Decompose the income and substitution effect of an increase in the itnerest rate for a saver
Show how a borrower could become a saver after the rate change
How do imperfect credit markets impact the intertemporal budget contraint
Rate of borrowing (Rb) > rate of saving (Rs)
causes kinked budget line
borrowing seg. gr: = -(1 + Rb)
Saving seg. gr. = -(1+Rs)
how does the credit limit in imperfect credit markets impact a borrowers utility - show graphically
PV and FV formulae
FV= (1+r)PV
PV= FV/(1+R)
What are the implications of Credit Market Imperfections (CMI) such as Rb>Rs and credit limits
- Consumption and investment decisions are imperfect
- Investment can be below its optimal level
- Can generate poverty traps
What are the more realistic assumptions of Behavioural Economics
- People do make decisions like in the ‘rational’ model but they have preferences that differ from those typically assumed by economists
- They make mistakes, they have different procedures to make decisions
What are some common fallacies
- People are imperfect statisticians
- Illusory superiority - rating yourself abive average
- Hot Hand- attributing ability to luck
What is the evidence for the hot hand fallacy
- Tversky found no statistical difference in the probability of a next shot being successful after a series of successful shots compared to a series of unsuccessful shots
- HOWEVEr by looking at data that starts with a series of unsuccessful shots you introduce a selection bias
tldr;
no statisitical difference in probabilities actually is evidence for a hot hand in data
How does behavioural economics relate to the assumption of preferences
People can still be rational agents, just have different preferences to the typical assumptions
e.g. Altruism: gain utility from others wellbeing
What is the decision and experience utility
Decision Utility: Utility when making the consumption decision - hot state
Experience Utility: Utility at the time of consumption itself - cold state
Consider a consumer with income ‘m’ facing prices p1=p2=1 with u(x1,x2) = Y* x1 + x2
find the solution at hold and cold states (where y varies)
What are the hot and cold states
Refer to emotional states
Hot states - getting excited, instinct
Cold states - thinking thoughtfully
What happens to welfare if decision making is in the hot state and consuption in the cold state
Cold state = true ‘experience utility’: u(x1,x2)= y * x1 + x2
- Actually selected x1=m, utility ym<m
- Should’ve selected x2=m, utility m
welfare optimising bundle (x1,x2)=(0,m)
Implications of hot and cold state
- Market free choice not optimal
- Market exploits states e.g. tempting advertising
How can taxes fix this negative externality of different utilities. What are the issues with it?
Taxes can cause people to switch pref.
but hurts individuals who’s hot and cold self like the same good so pareto improvement is not possible
How can nudges influence A type people without distorting B type people
- Create a default option of x1=0
- Allow A-types to opt out to choose x1>0 but requires effort
From these preferences, work out:
- Intertemporal budget constraint
- Uncompensted demand
Use these to draw a relaionship of saving when young, consumption at young and old
Draw the different old and young preferred position on a graph
Primitives of simultaneous move games
- Set of players: N= (1,2,…,n)
- For each player i in N, a set of actions
Ai= (a,b,…)
Profile of actions is a vector (a1,a2,… an) specifying for each player i in N an action ai in Ai
- A preference over the set of all profiles of actions, ‘>’
Define Nash Equilibrium
Nash Equilibrium is when neither player has an incentive to change their decision for a more profitable payoff
What is a strictly dominanted action
For any belief of a player about the actions of other players, this action is never taken as another action leads to a strictly higher payoff
Rational players will never take a strictly dominated action.
Find Nash Equilibriums
BB, SS
?
Steps to find MNE of matching pennies
- Focus on probability of other player
- Work out probability of other player impacting this players payoffs
- Indifference, thus equivalence
Key Idea: Player 1 chooses her probability of odds to make the blue player indifferent
How does prisonners dilemma relate to firms choice of competition or collusion
Describe the process of Bertrand Competition with these premises
Each firm decreases price to just below competitiors price
eventually equilibrium at p1=p2=MC, no player can deviate
Describe the process of Cournot Competition
- Work out each firms best response to another firm choosing q1/2
- Done by maximising profit, then putting in terms of firms quantity
- With 2 best responses, equate to find nash equilibrium
- Find profit max price + quantity. Split profit.
Describe Stackelberg Competition
One firm has a first mover advantage in choosing quantity.
Utilise backward induction to find SPE:
- Find Firm 2’s best response to Firm 1s choice (FOC)
- Substitute FOC of Firm 2 into Firm 1s quantity function
- Optimise Firm 1 Choice with FOC
do mon ami
Find the nash equilibrium of the hoteling location game
always has choice for guaranteeing half the business by going middle.
Both vendor 1 and 2 can have >=1/2
but V1+V2=1
Thus v1=v2=1/2
–> implies either equidistant from centre or in centre
but equidistant not NE as profitable deviation is middle
nash equilibrium is to go to the same location and split
How does the hotelling game apply to politics - median voter theorem
By shifting to the middle, can grab more of the voters of the other side than before.
Each player knows this so moves to centre –> no profitable payoff possible
What is a first price auction
sealed bid, highest bid wins and pays that
Second price auction
sealed bid, highest bid wins and pays the 2nd highest bid
write a payoff table for each scenario and find the equilibrium
do first and second price auctions provide the same revenue
yes, so do english and dutch, as long as each bidder knows their own valuation
how do you model entry of the market as a sequential game
2 stages:
1. Potential entrant chooses wether to enter
2. Incumbent chooses wether to fight
extensive form games are analysed using a game tree
Solve this
Analyse by backward induction, work out last player option and how the previous player responds to that and so on…
Eventually achieve Subgame Perfect Equilibrium- set of strategies which constitute a NE in everygame.
solution: Starbucks enter as then cafe will quit
this is as by backward induction we can see that the threat is not credible
How does a finite reprtition of games impact cooperation in the prisoners dilemma
finite repitition -> backward induction
Period before last no cooperation –> thus no credible cooperation throughout due to backward induction
How does infinite repitition help solve the problem of cooperation in the prisoners dilema
- Can no longer do backward induction
- But can do subgame perfect equilibria –> find long term strat that will benefit you the most
- This could be to cooperate - dep. on firm no. and discount rate
How do you calculate if you should cheat or collude in an infinitely repeated game
let d = 1/(1+r) be firms discount factor
- If firm cheats, other firms adopts a grim trigger strategy with a minmax punishement (often P=MC)
Optimal for collusion IF:
Present discounted value of collusion stream > Present discount value of cheating stream
What is a grim trigger strategy
Collude but responds to cheating with punishment forever
What is a minmax punishment
Worst punishment that one player can do to the other, given that the punished is responding optimally to its punishment
General equation to determine if collusion worth it
number of firms < total collusion income/cheat income * (1-discount)
What is taste-based discrimination
Preference for certain traits when interacting or choosing wether to interact with different people
What is belief-based discrimination
Individuals might believe that individual with different traits might behave differently
What is search intensity
likelihood the police will search a driver of a particular race
What is the hit rate
The likelihood that upon a search drugs are found in the vehicle of a driver of a particular race.
With this set up, draw the matrix and determine the equilibriums
There is only a mixed-strategy equilibrium
Races may differ in their payoffs and how may the police differ if they are taste based discriminating
If taste based:
* cost of searching race x < cost of searching race y
If not taste based
Cx=Cy, but police have different beliefs about hit rates of different races so engage in belief based discirmination
For hypothesis 1 with no taste-based discrimination. Find the hit rates from this matrix. What is the conclusion
h is such that the police should be indifferent between searching and not
h=c/v for both–> only belief based discrimination –> hit rates equalised across all races
Find the hit rates of hypothesis 2 taste-based discrimination when cx< cy
Model of Employer taste-based discrimination with different races
Model of Belief-Based Discrimination on productivity type of worker based on race
what are isoquants
indifference curve for the combination of inputs (labour or capital) such that a given quantity of output q could efficiently be produced with.
for any level of output q’, what will the isoquant do?
connect all the combinations (l,k) such that q(l,k)=q’
Draw isoquants for a fixed coefficient production function
Draw isoquants for variable production function
properties of isoquant
- negative slope
- non-intersection
- Coverage of (l,k) space
- Convex to origin
What is the MRTS (marginal rate of transformation)
- Gradient Function of isoquant
‘With fixed output - suppose i use one more unit of labour, how many units of capital can i forgo or vice vera’
MRTS calc
What are isocost lines
‘budget line’
incorporate wages and cost of capital
C = rK + wL
How is altruism a possible explanation for cooperation
Depending on extent, payoff includes payoff of others –> show cooperation as rational choice
What is reciprocal altruism
Positive Reciprocity- People want to help those who are nice to them
Negative Reciprocity- harm those who are nasty to them
draw a matrix with positive reciprocity
What about the Dictators Game might suggest that altruism isnt the only influence for cooperation
Dictators game, out of 10 quid avg kept 7.5
not altruism as giving away for benefit of a < 1
in theory can offer 1p, yet people usually reject offers below 20%
what does rationality imply
implies revealed preferences
What is the common solution to these problems:
How do we put normative value on the distributions of outcomes in society, how do we balance consumer and producer surplus
Pareto Efficiency
Define Pareto Efficiency
When comparing two different distributions of utilities enjoyed by individuals in society.
A Pareto Dominates B if under A all individuals are better off than under B + at least one individual is strictly better off
When is a distribution of utilities by individuals in a society Pareto Efficient
if there is no other feasible situation that Pareto dominates is
what does pareto efficiency imply for wealth distribution
wealth should be distributed to maximise the sum of utilities (surpluses) will lead to a Pareto Efficient Scenario
What is the issue of aiming for Pareto Efficiency (maximising consumer surplus)
consumer surplus does not take into account distributional aspects
What nuances are there in using utility to evaluate policies
‘Decision’ vs ‘experience’ utility? which to use
What is libertarain Paternalism
Base assumption of revealed preferences - preferences and choices are one and we can only infer preferences by looking at choices
(e.g. consumer surplus)
However hot + cold state imply that consumers dont make their choice their real preference.
Governments ‘paternally’ nudge consumers to their real preference, helping them make their optimal choice
