Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

●

Supply​ ​and​ ​Demand​ ​(w/partial​ ​derivatives)
○ Graphing​ ​a​ ​market​ ​(graphing​ ​supply​ ​and​ ​demand)
○ Graphs​ ​are​ ​statistical​ ​representations​ ​of​ ​dynamic​ ​markets​ ​under​ ​the​ ​following
assumptions
■ Product:​ ​uniform​ ​definition​ ​of​ ​a​ ​commodity,​ ​service,​ ​etc
...
​ ​derived​ ​demand

●

Law​ ​of​ ​Demand
○ Stated:​ ​the​ ​price​ ​of​ ​a​ ​good​ ​varies​ ​inversely​​ ​with​ ​its​ ​quantity,​ ​all​ ​else​ ​held​ ​constant
■ Partial​ ​differentiation

●

●

●
●

●
●
●

Q​ ​=​ ​D(p,p​ ​sub​ ​s,​ ​p​ ​sub​ ​c,​ ​Y)
○ p​ ​is​ ​the​ ​price​ ​of​ ​the​ ​good
○ p​ ​sub​ ​s​ ​is​ ​the​ ​price​ ​of​ ​substitutes
○ P​ ​sub​ ​c​ ​is​ ​the​ ​price​ ​of​ ​compliments
○ Y​ ​is​ ​income
■ p​ ​sub​ ​s​ ​might​ ​be​ ​beef​ ​or​ ​chicken
■ p​ ​sub​ ​c​ ​might​ ​be​ ​BBQ​ ​sauce
Ex:​ ​Q​ ​sub​ ​d​ ​=​ ​171​ ​-​ ​20p​ ​+​ ​20p​ ​sub​ ​b​ ​+​ ​3p​ ​sub​ ​f​ ​+​ ​2Y
○ p​ ​is​ ​pork,​ ​b​ ​is​ ​beef,​ ​f​ ​is​ ​fish,​ ​Y​ ​is​ ​income
○ Beef​ ​=​ ​4$/kg,​ ​fish​ ​=​ ​3
...
33))​ ​+​ ​((2)(125))
Q​ ​sub​ ​d​ ​=​ ​286​ ​-​ ​20p
○ Endogenous​ ​variable​ ​-​ ​a​ ​variable​ ​that’s​ ​within​ ​the​ ​model​ ​p​ ​in​ ​the​ ​above​ ​equation
○ Exogenous​ ​variable​ ​-​ ​the​ ​other​ ​variables​ ​outside​ ​the​ ​model
-​ ​in​ ​above​ ​equation:​ ​p​ ​sub​ ​b,​ ​p​ ​sub​ ​f,​ ​Y
Del​ ​Q​ ​sub​ ​d/del​ ​p​ ​=​ ​-20​ ​(Endogeneous​ ​effect)
Del​ ​Q​ ​sub​ ​d/del​ ​Y​ ​=​ ​2​ ​(Exogenous​ ​effect)

Law​ ​of​ ​Supply
○ Stated:​ ​ ​the​ ​price​ ​of​ ​a​ ​good​ ​varies​ ​directly​​ ​with​ ​its​ ​quantity,​ ​all​ ​else​ ​held​ ​constant
■ Partial​ ​Equilibrium​ ​Effect

Partial​ ​Equilibrium​ ​Effect
● Q​ ​=​ ​S(p,p​ ​sub​ ​f)
○ p​ ​is​ ​price
○ p​ ​sub​ ​f​ ​is​ ​production​ ​factors
● Ex:​ ​Q​ ​sub​ ​s​ ​=​ ​178​ ​+​ ​40p​ ​-​ ​60p​ ​sub​ ​h
○ p​ ​is​ ​pork
○ p​ ​sub​ ​h​ ​is​ ​hogs
○ Assume​ ​p​ ​sub​ ​h​ ​=​ ​1
...
30
○ Q​ ​sub​ ​e​ ​=​ ​220
What​ ​if​ ​P​ ​sub​ ​h​ ​is​ ​now​ ​=​ ​$1
...
30
■ Q*​ ​=​ ​220
○ E​ ​=​ ​-20(3
...
3
Classifying​ ​elasticities
○ Shapes​ ​of​ ​demand​ ​(supply)​ ​curves​ ​indicate​ ​their​ ​elasticity
■ Elastic​ ​(E​ ​<​ ​-1),​ ​unitary​ ​elastic​ ​(E​ ​=​ ​-1),​ ​or​ ​inelastic​ ​(0​ ​>​ ​E​ ​>​ ​-1)
● Perfectly​ ​inelastic​ ​(E​ ​=​ ​0)
● Perfectly​ ​elastic​ ​(E​ ​=​ ​-infinity)
Special​ ​Cases
○ Linear​ ​demand​ ​curve
■ The​ ​usual​ ​depiction,​ ​but​ ​really​ ​only​ ​a​ ​special​ ​case
○

●

●

“Instantaneous”​ ​comparative​ ​statics​ ​show​ ​equilibrium​ ​responses
for​ ​small​ ​changes​ ​in​ ​exogenous​ ​variables
Also​ ​more​ ​general:​ ​useful​ ​when​ ​supply​ ​&​ ​demand​ ​curves​ ​are
nonlinear
○ Q​ ​sub​ ​d​ ​=​ ​D(p)
○ Q​ ​sub​ ​s​ ​=​ ​S(p,​ ​a)
■ a​ ​is​ ​p​ ​sub​ ​h​ ​in​ ​our​ ​example
■ a​ ​represents​ ​a​ ​supply​ ​variable​ ​(shock)
○ D(p*(a))​ ​=​ ​S(p*(a),​ ​a)
■ dp/da​ ​=​ ​???​ ​←​ ​what​ ​question​ ​is​ ​asking/what​ ​we
need​ ​to​ ​find​ ​out/​ ​what​ ​we​ ​are​ ​looking​ ​for
■ (dD/dp*)(dp*/da)​ ​=​ ​(del​ ​S/del​ ​p*)(dp*/da)+(del​ ​s/​ ​del
a)
■ dp*/da​ ​=​ ​(del​ ​s/​ ​del​ ​a)/​ ​((dD/dp*)​ ​-​ ​(del​ ​S/​ ​del​ ​p*))
● dp*/dp​ ​sub​ ​h​ ​=​ ​-60/​ ​((-20)​ ​-​ ​(40))​ ​=​ ​1

Constant​ ​elasticity​ ​of​ ​demand​ ​curve
■ Regardless​ ​of​ ​supply​ ​curve,​ ​E​ ​sub​ ​Q,d​ ​is​ ​constant
● Q​ ​=​ ​ap^-b,​ ​E​ ​=​ ​(delQ/delp)(p/Q)​ ​=​ ​(-bap^(-b-1))(p/Q)​ ​=
-b((ap^-b)/p)(p/Q)​ ​=​ ​-b(Q/p)(p/Q)​ ​=​ ​-b
○ Revenue​ ​=​ ​(p)(Q)​ ​=​ ​p​ ​time​ ​Q(p)
■ delR/delp​ ​=​ ​p​ ​(dQ/dp)​ ​+​ ​Q(dp/dp)​ ​=​ ​p(dQ/dp)​ ​+​ ​Q
● Convert​ ​to​ ​elasticity
○ =​ ​Q(p/Q)(dQ/dp)​ ​+​ ​Q​ ​=​ ​QE​ ​+​ ​Q​ ​=​ ​Q(E​ ​+1)
Related​ ​Elasticities,​ ​etc
...
5psubjuice​ ​+​ ​2psubmilk​ ​+​ ​5Y
■ Q​ ​sub​ ​s​ ​=​ ​100​ ​-​ ​20p​ ​-​ ​30psubHFCS(high​ ​fructose​ ​corn​ ​syrup)
■ Q​ ​is​ ​millions​ ​of​ ​oz​ ​of​ ​SSB
■ p​ ​is​ ​price​ ​(pennies)​ ​per​ ​oz
● The​ ​equilibrium:​ ​p*​ ​=​ ​5
...
33
● n(aeda)​ ​=​ ​(dQ/dp)(p/Qsubs)​ ​=​ ​(20)(5
...
33)​ ​=​ ​0
...
17/218
...
2366
● dp/dtao​ ​=​ ​0
...
4733-(-0
...
66667​ ​=​ ​⅔

Tax​ ​incidence​ ​on​ ​consumers
■ On​ ​producers​ ​=​ ​1-⅔​ ​=​ ​⅓
Specific​ ​tax​ ​effect​ ​described
■ Specific​ ​tax​ ​effect​ ​features
● Depends​ ​on​ ​both​ ​the​ ​price​ ​elasticity​ ​of​ ​demand​ ​and​ ​the​ ​price
elasticity​ ​of​ ​supply
● Can​ ​separately​ ​calculate​ ​its​ ​effects​ ​on​ ​consumers​ ​and​ ​producers
■ Tax​ ​effects​ ​are​ ​shared:
● Between​ ​consumers​ ​and​ ​producers
● If​ ​levied​ ​on​ ​producers,​ ​the​ ​tax​ ​incidence​ ​on​ ​consumers​ ​is​ ​equal​ ​to
dp/dtao,​ ​and​ ​tax​ ​incidence​ ​on​ ​producers​ ​is​ ​1-(dp/dtao)
Ad​ ​valorem​ ​tax
■ Represented​ ​by​ ​a​ ​rotation,​ ​rather​ ​than​ ​a​ ​shift,​ ​of​ ​the​ ​demand​ ​curve,​ ​but
comparative​ ​static​ ​approach​ ​is​ ​similar
● See​ ​graph​ ​in​ ​lecture​ ​2​ ​(second​ ​to​ ​last​ ​slide)
Binding​ ​price​ ​ceiling​ ​creates​ ​excess​ ​demand
Binding​ ​price​ ​floor​ ​creates​ ​excess​ ​supply
○

○

○

○
○



---