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Economics & Policy > Key Equations > Flashcards

Key Equations Flashcards

1
Q

F = P(G/P)(E/G)*(F/E)

A

The Kaya identity
Traces changes in CO2 emissions to pop growth (P), the per capita economic activity (G/P), the energy intensity (E/G), and the carbon intensity of energy consumption (F/E)

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2
Q

C + I + GS + NE
C + G + I + X - M

A

GDP and SAM (social accounting matrix)
Consumption + Investment + Government Spending + Net Exports
Consumption + Government + Investments + Exports - Imports
Main economic drivers of a country’s growth, subject to other drivers

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3
Q

I = P * A * T

A

Environmental impact = Population x Level of affluence x Technological Coefficient
IPAT is an identity equation useful to understand the complex factors influences changes in environmental impact. Factors/drivers are interdependent. Accounts for impacts of production.

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4
Q

DE = P * GDP/P * DE/GDP

A

Domestic extraction

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5
Q

DMC = DE + PTB

A

Domestic material consumption = Domestic extraction + Physical trade balance
Measures materials consumed in a national economy

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6
Q

PTB = M - X

A

Physical trade balance = physical imports - physical exports
Shows whether a country is a net importer or exporter of materials

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7
Q

Parallel lines bowed downward mapping equivalent preferences shows an _____

A

indifference curve

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8
Q

Qd = a - b(P) or P = a - b(Q)

A

Resource demand function
Number of units demanded (Qd) and inverse demand curve
Qd varies with price charged for it
Inverse demand used for total and marginal revenue functions

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9
Q

P = a + bS or Qs = b(P - a)

A

Supply (P) and inverse supply curve
Units supplied varies with price

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10
Q

”% change in quantity divided by % change in price” is the generic formula for ________.

A

price elasticity of demand

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11
Q

When all independent values can increase by the same proportion equally they are ______ functions

A

Homogenous

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12
Q

U^AsubX = partial of U^A/X^A

A

Marginal utility or U

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13
Q

MP^YsubL = partial of Y/L^Y

A

Marginal product = MP; partial derivative of production curve

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14
Q

MRUS^A

A

Marginal rate of utility substitution for a good A
Rate at which X can be substituted for Y i.e. how much food or how many clothes can you buy?

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15
Q

MRTSsubx

A

Marginal rate of technical substitution in the production of X, holding output constant, substituting inputs - give up some factor x to use more of another y

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16
Q

MRTsubL

A

Marginal rate transformation of commodities: shifting labor to make more X or Y

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17
Q

W = W(U^A, U^B)

A

Social welfare function (SWF)
Same form as utility function
helps optimize along the utility possibility frontier
states technical possibilities and constraints available at a time

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18
Q

(Wsuba / Wsubb) = (U^Bsubx / U^Asubx) = (U^Bsuby / U^Asuby)

A

Condition for welfare maximization
SWF indifference curve slope = point on utility possibility frontier

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19
Q

Π = TotalRevenues − TotalCosts, which enables Marginal Revenue (MR) = Marginal Cost (MC)

A

Monopoly profit function

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20
Q

NSB = B - C
Measured at period t

A

Net social benefit with extraction costs C = cR

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21
Q

Q = AK^alpha*L^beta where a + b = 1

A

Cobb-Douglas PRODUCTION function
Expresses the quantity Q of output as a function of capital K and labor L

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22
Q

Ct = cRt

A

Total extraction costs

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23
Q

S-bar = R0 + R1

A

Initial stock of a resource

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24
Q

Rt

A

Quantity of a resource extracted and consumed in time t
Found in the area under the curve

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25
Q

W = W(U0,U1)

A

Social utility discount rate
Helps understand future trends in today’s terms

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26
Q

If the social utility discount rate is _____, consumption is favorable

A

high

27
Q

W = (U0 + U1) / (1 + rho)

W = NSB0 + NSB1 / 1 + rho

A

Socially optimal considerations
If costs are large, benefit is small and opposite

28
Q

(P0 - c)(1 + rho) = (P1 - c)

A

Hotelling rule
An efficient extraction program requires the net price of the resource to grow at the same rate as the social utility discount rate

29
Q

K e - a R = U(R)

A

Marginal social utility

30
Q

St = S-bar - integral over time 0 to t Rtdt
S-dot = ds/dt

A

Remaining stock of resources
Change in stock wrt time aka FLOW

31
Q

Pt = a - bRt
P0 and P1

A

The inverse demand function in the two-period model for non-renewable resources

32
Q

1/2 * Smax

A

Smsy

33
Q

G(S), G is 0 at S = 0 or = Smax and G = H

A

Biological growth as a function of stock

34
Q

NG = G - H

A

Net growth = biological growth - harvest
Part of economic sub-model

35
Q

NB = B - C

A

Net benefit = Gross benefit - Cost
Also for fishing profit

36
Q

B = PH

A

Revenue obtained from a harvest

37
Q

PH = wE

A

Price*Harvest = total cost per unit of harvest effort * Effort
Yield-effort relationship for open-access steady-state equilibrium
Has ZERO economic profit

38
Q

Same constraints as before, p = P - i also constant ⊓ is site value of land
⊓ = [pSsub(t1 - t0)e^-i(t1 - t0) - k]

A

Infinite rotation model

39
Q

PvsubR = R / r

A

Present value where R = annual rent and r = discount rate, this equation holds if all Rs are the same

40
Q

U(D) = U(h(D), z(D))

A

Urban land rent
Seeks to maximize utility, subject to constraints of budget and distance

41
Q

⊓ = psubzasubif(L,F) - wL - p^h(F)
At equilibrium, ⊓ = 0, but p^h(F) is positive

A

Profits per hectare

42
Q

Zsubi = Zsubi / h

A

Output per hectare with Zsubi = crop production

43
Q

Zsubi = asubi(L, h, F)

A

Crop production function

44
Q

p^h(D)

p^h(D) = (psubzi - ssubsziD)asubif(L) - wL

A

Von Thunen model: rent of land is function of distance, neither D nor F influence crop production BUT D influences in profits (intensity)

45
Q

When D > Dmax
When Dmax is at Psubzi / Ssubzi

A

Land rent is 0

46
Q

Bid-rent function graph

A

Indifference slope, intersects agricultural rent function where residential city is bounded (DsubA)

47
Q

y1 = a1w1 ; y2 = a2w2

A

Efficient allocation principle

48
Q

y2 = a2 (w = y1/a1)

A

Production possibility frontier for efficient allocation

49
Q

____ = pop. * gdp/pop. * energy/gdp * CO2/energy

A

Total CO2 emissions

50
Q

Shared ____ pathways describe illustrative scenarios for emissions of CO2

A

socioeconomic

51
Q

The 5 SSPs:

A

[FIRMS]
Sustainability
Middle of the road
Regional rivalry
Inequality
Fossil fueled development

52
Q

Physical and human impacts of climate change (4)

A

[ASHC]
Agricultural production
Heat-related human mortality
Storm damage
Costs of coastal protection

53
Q

Climate change effects with rising curves (4)
y = e^x
convex curve
y = x^3
parabolic y = x^2

A

[WEt StD CCP]
Water - y = e^x
Extreme temps - convex curve
storm damage - cubic, y = x^3
costs of coastal production - parabolic y = x^2

54
Q

Climate change effect with u-shaped curve

A

Heat-related human mortality

55
Q

Climate change effect with an inverse parabola (hill)

A

Agricultural production

56
Q

Y(t) = F (K, L, E)

A

Impacts of climate change on economic growth

57
Q

What is an inverse function?

A

A function that describes a variable solving another function

58
Q

SMC = PMC + MEC

A

Social marginal cost = private marginal cost + marginal external cost (aka willingness to pay)

59
Q

W-bar allocated to F1 and F2: W-bar = w1 + w2

A

Fairness criteria for sustainable water supply (W-bar)

60
Q

SWF minimized [y1, y2]

A

Strict equality

61
Q

SWF = y1 + y2

A

Individual welfare from income and their consumption

62
Q

Horizontal line denoted by (1 − h)x, where x is the raw abstraction and h · x are the return flows after usage.

A

Periodic abstraction of human settlement in the catchment area (e.g. water)

63
Q

Negatively sloped line for water resources

A

Replenishment rate

Economics & Policy (2 decks)

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