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Policy Analysis in Welfare and Policy Spaces: Applications to the Labyrinthine U.S. Ethanol Policy Literature

  • David S. Bullock EMAIL logo and Anabelle Couleau


We discuss the analysis of policy in three “spaces”: the customary (q, p) space, “policy space,” and “welfare space.” Specific advantages of conducting policy analysis in welfare and policy spaces are as follows: (1) it makes clearer the distributional consequences of policy change instead of focusing solely on the aggregate welfare consequences of policy change; (2) it facilitates covering a very wide array of available policy options, instead of examining just a few; (3) it is a powerful tool for analyzing the effects of simultaneous use of multiple policy instruments; and (4) it clarifies what it means for policies to be more/less “efficient,” and for policy instruments to make each other more/less “efficient.” We demonstrate the usefulness of our framework in comparing and critiquing various conclusions recently expressed in the U.S. ethanol policy literature.

Online Appendix

Please see the accompanying Mathematica program, presented in a pdf file.


Variables in italics, vectors in boldface.

x = (x1,…, xm)

: a vector of generic policy instrument


: set of feasible policies

α = (α1,…, αz)

: the model’s parameters that change how welfare is a function of policy

i = 1,…, I

: index for mutually exclusive groups representing economics agents in the model, W = {1,…, I}: the model’s set of groups

hi: X × A → R

: function that defines how group i’s welfare is dependent on policy and market parameters


: the model’s welfare correspondence


: welfare manifold of an economic model that has policy space X and is parameterized by α


: for generic subsets XsubX and WsubW, the welfare submanifold of an economic model that has policy space X and is parameterized by α

In (q, p)-space

: value of the target price for an investigated year (policy instrument on commodity market)


: value of the ethanol tax credit for an investigated year (policy instrument on ethanol market)

tc(PT, α)

: minimum ethanol tax credit that is effective when the corn target price is PT


: vector of parameter values in the investigated crop year

DNEdom(z, αyear)

: domestic demand for corn in non-ethanol uses

DNE(z, αyear)

: total demand (domestic demand plus foreign excess demand) for corn in non-ethanol uses

SC(z, αyear)

: domestic corn supply curve,

ESC(z, PTyear, αyear)

: domestic corn-supplied-to-ethanol curve

ESF(z, α03)

: foreign excess-supply-of-fuel curve

PCSyear, PCDyear

: producer (S) and consumer (D) corn price


: equilibrium corn price


: world fuel price

ΔPSc(PTyear, tyear, αyear)

: change in corn producers’ surplus

ΔCTdom(PTyear, tyear, αyear)

: change in domestic corn consumers’ surplus

DWdom(PTyear, tyear, αyear)

: deadweight costs

In policy space

: a non-intervention policy (na stands for no-action by government)


: observed policy in year y

X = XnaX1X2X3

: the union of four non-intersecting subsets, each subset represents the combination of effective policy instruments

In welfare space
h(PT, t, α)≡(ΔCTdom(PT, t, α), ΔPSc(PT, t, α))

: the correspondence h maps any (target price, tax credit, parameter vector) ordered triple (PT, t, α) onto welfare space

H(YZ, αyear), which we denote STC(PT, t, αyear)

: the surplus transformation curve for the set YZ (here is an example), which is a set of policy instruments


: welfare outcome for a given combination of policy instruments


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Published Online: 2014-10-21
Published in Print: 2014-1-1

©2014 by De Gruyter

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