Key Equations

Question 1

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

Answer 1

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)

Question 2

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

Answer 2

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

Question 3

I = P * A * T

Answer 3

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.

Question 4

DE = P * GDP/P * DE/GDP

Answer 4

Domestic extraction

Question 5

DMC = DE + PTB

Answer 5

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

Question 6

PTB = M - X

Answer 6

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

Question 7

Parallel lines bowed downward mapping equivalent preferences shows an _____

Answer 7

indifference curve

Question 8

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

Answer 8

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

Question 9

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

Answer 9

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

Question 10

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

Answer 10

price elasticity of demand

Question 11

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

Answer 11

Homogenous

Question 12

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

Answer 12

Marginal utility or U

Question 13

MP^YsubL = partial of Y/L^Y

Answer 13

Marginal product = MP; partial derivative of production curve

Question 14

MRUS^A

Answer 14

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?

Question 15

MRTSsubx

Answer 15

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

Question 16

MRTsubL

Answer 16

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

Question 17

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

Answer 17

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

Question 18

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

Answer 18

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

Question 19

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

Answer 19

Monopoly profit function

Question 20

NSB = B - C
Measured at period t

Answer 20

Net social benefit with extraction costs C = cR

Question 21

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

Answer 21

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

Question 22

Ct = cRt

Answer 22

Total extraction costs

Question 23

S-bar = R0 + R1

Answer 23

Initial stock of a resource

Question 24

Rt

Answer 24

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

Question 25

W = W(U0,U1)

Answer 25

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

Question 26

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

Answer 26

high

Question 27

W = (U0 + U1) / (1 + rho) W = NSB0 + NSB1 / 1 + rho

Answer 27

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

Question 28

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

Answer 28

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*

Question 29

K e - a R = U(R)

Answer 29

Marginal social utility

Question 30

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

Answer 30

Remaining stock of resources Change in stock wrt time aka FLOW

Question 31

Pt = a - bRt P0 and P1

Answer 31

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

Question 32

1/2 * Smax

Answer 32

Smsy

Question 33

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

Answer 33

Biological growth as a function of stock

Question 34

NG = G - H

Answer 34

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

Question 35

NB = B - C

Answer 35

Net benefit = Gross benefit - Cost Also for fishing profit

Question 36

B = PH

Answer 36

Revenue obtained from a harvest

Question 37

PH = wE

Answer 37

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

Question 38

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

Answer 38

Infinite rotation model

Question 39

PvsubR = R / r

Answer 39

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

Question 40

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

Answer 40

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

Question 41

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

Answer 41

Profits per hectare

Question 42

Zsubi = Zsubi / h

Answer 42

Output per hectare with Zsubi = crop production

Question 43

Zsubi = asubi(L, h, F)

Answer 43

Crop production function

Question 44

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

Answer 44

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

Question 45

When D > Dmax When Dmax is at Psubzi / Ssubzi

Answer 45

Land rent is 0

Question 46

Bid-rent function graph

Answer 46

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

Question 47

y1 = a1w1 ; y2 = a2w2

Answer 47

Efficient allocation principle

Question 48

y2 = a2 (w = y1/a1)

Answer 48

Production possibility frontier for efficient allocation

Question 49

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

Answer 49

Total CO2 emissions

Question 50

Shared ____ pathways describe illustrative scenarios for emissions of CO2

Answer 50

socioeconomic

Question 51

The 5 SSPs:

Answer 51

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

Question 52

Physical and human impacts of climate change (4)

Answer 52

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

Question 53

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

Answer 53

[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

Question 54

Climate change effect with u-shaped curve

Answer 54

Heat-related human mortality

Question 55

Climate change effect with an inverse parabola (hill)

Answer 55

Agricultural production

Question 56

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

Answer 56

Impacts of climate change on economic growth

Question 57

What is an inverse function?

Answer 57

A function that describes a variable solving another function

Question 58

SMC = PMC + MEC

Answer 58

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

Question 59

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

Answer 59

Fairness criteria for sustainable water supply (W-bar)

Question 60

SWF minimized [y1, y2]

Answer 60

Strict equality

Question 61

SWF = y1 + y2

Answer 61

Individual welfare from income and their consumption

Question 62

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

Answer 62

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

Question 63

Negatively sloped line for water resources

Answer 63

Replenishment rate