Key Equations Flashcards
F = P(G/P)(E/G)*(F/E)
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)
C + I + GS + NE
C + G + I + X - M
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
I = P * A * T
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.
DE = P * GDP/P * DE/GDP
Domestic extraction
DMC = DE + PTB
Domestic material consumption = Domestic extraction + Physical trade balance
Measures materials consumed in a national economy
PTB = M - X
Physical trade balance = physical imports - physical exports
Shows whether a country is a net importer or exporter of materials
Parallel lines bowed downward mapping equivalent preferences shows an _____
indifference curve
Qd = a - b(P) or P = a - b(Q)
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
P = a + bS or Qs = b(P - a)
Supply (P) and inverse supply curve
Units supplied varies with price
”% change in quantity divided by % change in price” is the generic formula for ________.
price elasticity of demand
When all independent values can increase by the same proportion equally they are ______ functions
Homogenous
U^AsubX = partial of U^A/X^A
Marginal utility or U
MP^YsubL = partial of Y/L^Y
Marginal product = MP; partial derivative of production curve
MRUS^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?
MRTSsubx
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
MRTsubL
Marginal rate transformation of commodities: shifting labor to make more X or Y
W = W(U^A, U^B)
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
(Wsuba / Wsubb) = (U^Bsubx / U^Asubx) = (U^Bsuby / U^Asuby)
Condition for welfare maximization
SWF indifference curve slope = point on utility possibility frontier
Π = TotalRevenues − TotalCosts, which enables Marginal Revenue (MR) = Marginal Cost (MC)
Monopoly profit function
NSB = B - C
Measured at period t
Net social benefit with extraction costs C = cR
Q = AK^alpha*L^beta where a + b = 1
Cobb-Douglas PRODUCTION function
Expresses the quantity Q of output as a function of capital K and labor L
Ct = cRt
Total extraction costs
S-bar = R0 + R1
Initial stock of a resource
Rt
Quantity of a resource extracted and consumed in time t
Found in the area under the curve
W = W(U0,U1)
Social utility discount rate
Helps understand future trends in today’s terms
If the social utility discount rate is _____, consumption is favorable
high
W = (U0 + U1) / (1 + rho)
W = NSB0 + NSB1 / 1 + rho
Socially optimal considerations
If costs are large, benefit is small and opposite
(P0 - c)(1 + rho) = (P1 - c)
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
K e - a R = U(R)
Marginal social utility
St = S-bar - integral over time 0 to t Rtdt
S-dot = ds/dt
Remaining stock of resources
Change in stock wrt time aka FLOW
Pt = a - bRt
P0 and P1
The inverse demand function in the two-period model for non-renewable resources
1/2 * Smax
Smsy
G(S), G is 0 at S = 0 or = Smax and G = H
Biological growth as a function of stock
NG = G - H
Net growth = biological growth - harvest
Part of economic sub-model
NB = B - C
Net benefit = Gross benefit - Cost
Also for fishing profit
B = PH
Revenue obtained from a harvest
PH = wE
Price*Harvest = total cost per unit of harvest effort * Effort
Yield-effort relationship for open-access steady-state equilibrium
Has ZERO economic profit
Same constraints as before, p = P - i also constant ⊓ is site value of land
⊓ = [pSsub(t1 - t0)e^-i(t1 - t0) - k]
Infinite rotation model
PvsubR = R / r
Present value where R = annual rent and r = discount rate, this equation holds if all Rs are the same
U(D) = U(h(D), z(D))
Urban land rent
Seeks to maximize utility, subject to constraints of budget and distance
⊓ = psubzasubif(L,F) - wL - p^h(F)
At equilibrium, ⊓ = 0, but p^h(F) is positive
Profits per hectare
Zsubi = Zsubi / h
Output per hectare with Zsubi = crop production
Zsubi = asubi(L, h, F)
Crop production function
p^h(D)
p^h(D) = (psubzi - ssubsziD)asubif(L) - wL
Von Thunen model: rent of land is function of distance, neither D nor F influence crop production BUT D influences in profits (intensity)
When D > Dmax
When Dmax is at Psubzi / Ssubzi
Land rent is 0
Bid-rent function graph
Indifference slope, intersects agricultural rent function where residential city is bounded (DsubA)
y1 = a1w1 ; y2 = a2w2
Efficient allocation principle
y2 = a2 (w = y1/a1)
Production possibility frontier for efficient allocation
____ = pop. * gdp/pop. * energy/gdp * CO2/energy
Total CO2 emissions
Shared ____ pathways describe illustrative scenarios for emissions of CO2
socioeconomic
The 5 SSPs:
[FIRMS]
Sustainability
Middle of the road
Regional rivalry
Inequality
Fossil fueled development
Physical and human impacts of climate change (4)
[ASHC]
Agricultural production
Heat-related human mortality
Storm damage
Costs of coastal protection
Climate change effects with rising curves (4)
y = e^x
convex curve
y = x^3
parabolic y = x^2
[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
Climate change effect with u-shaped curve
Heat-related human mortality
Climate change effect with an inverse parabola (hill)
Agricultural production
Y(t) = F (K, L, E)
Impacts of climate change on economic growth
What is an inverse function?
A function that describes a variable solving another function
SMC = PMC + MEC
Social marginal cost = private marginal cost + marginal external cost (aka willingness to pay)
W-bar allocated to F1 and F2: W-bar = w1 + w2
Fairness criteria for sustainable water supply (W-bar)
SWF minimized [y1, y2]
Strict equality
SWF = y1 + y2
Individual welfare from income and their consumption
Horizontal line denoted by (1 − h)x, where x is the raw abstraction and h · x are the return flows after usage.
Periodic abstraction of human settlement in the catchment area (e.g. water)
Negatively sloped line for water resources
Replenishment rate
