Welfare:
Consumer and Producer Surplus
and Internal Rate of Return
Daniel Mason-D’Croz
Sherman Robinson
Welfare Analysis
• We need to compute benefits and costs
associated with policy choices
– Benefits and costs occur over long time periods
• “Discounting” to compute present value of a time
stream of benefits and costs
• “Social” versus “market” benefits and costs
– Externalities and non-market costs and benefits
– We will focus on direct and indirect, measurable,
costs and benefits
Benefits: Consumer Surplus
• Measurable gains to demanders from changes
in supplies of goods due to projects
– Idea of “Consumer Surplus” (CS): the total amount
demanders would be willing to pay for a given
amount of commodities
• Changes in CS across all markets affected by a
“project” measure the benefits attributable to
that project
– Direct and indirect effects
Benefits: Producer Surplus
• Producer surplus measures the net benefits to
producers from a “project”: the change in
total revenue minus the change in total costs
of production of all producers
– Direct and indirect effects
• The sum of changes in Consumer and
Producer Surplus measures the total benefits
arising from a project
Costs
• Total costs associated with a project include
both the direct costs of the “project” (e.g.,
developing a new seed variety) and the
indirect impact on costs of linked producers
– We will measure only the “direct” financial costs
associated with a project
– Changes in costs of linked sectors will be captured
by changes in producer surplus, which are
measured from the net benefit side.
Consumer Surplus
PC
Reference Consumer Surplus
PIntsimulation
Simulation Consumer Surplus
PIntref
Income Effect
Price Effect
Both Income and Price Effect
(gains from income changes
lost to price changes)
Psimulation
Pref
Qref
Q*
Qsimulation
QF
“Virtual” Supply Curves
• Need to generate a “virtual” supply curve, given
yield and land area equations
– “Virtual” because it is not generated from a fully
specified cost function
• Yield and area are both functions of producer
prices, with constant elasticities
– Supply elasticity is the sum of these two elasticities
– Constant is the product of the two constants
Producer Surplus
PP
Psimulation
Agricultural Revenue
Producer Surplus
Total Cost
Qsimulation
QS
Producer Surplus
• We need to find the area under a non-linear,
constant-elasticity supply curve.
• After some algebra, that area is equal to:
𝑃 × 𝑄𝑆
𝑃𝑆 = 𝑃 × 𝑄𝑆 =
1+𝜀
• Which is equal to total revenue times 1 over 1
+ the elasticity of supply.
Benefit-Cost Analysis
• Can use CS and PS to measure benefits of
introducing some change such as a new
technology
• Need to discount CS and PS over time and
compute net present value (NPV) of benefits
• Need cost data over time to compute NPV of
costs
Net Present Values
𝑇
𝑁𝑃𝑉 𝐶𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =
𝑡=1
𝑡
𝑁𝑃𝑉 𝑃𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =
𝑡=1
𝑡
∆𝐶𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
1+𝑟 𝑡
𝑡
∆𝑃𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
1+𝑟 𝑡
Net Present Values
𝑁𝑃𝑉 𝑇𝑜𝑡𝑎𝑙 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =
𝑁𝑃𝑉 𝐶𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 + 𝑁𝑃𝑉 𝑃𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑇
𝑁𝑃𝑉(𝐶𝑜𝑠𝑡𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 ) =
𝑡=1
𝑡
𝐶𝑜𝑠𝑡𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
1+𝑟 𝑡
Benefit-Cost and Internal Rate of
Return
𝑁𝑃𝑉(𝑇𝑜𝑡𝑎𝑙 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 )
𝑁𝑃𝑉(𝐶𝑜𝑠𝑡𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 )
𝑁𝑃𝑉
𝑇
=
𝑡=1
𝑡
𝑡
𝑡
(∆𝐶𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
+ ∆𝐴𝑅𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
) − 𝐶𝑜𝑠𝑡𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
=0
𝑡
1 + 𝑖𝑟𝑟
Internal Rate of Return
• IRR calculation is done by using the GAMS
solver to find a solution to the equation
• If NPV of costs exceeds NPV of benefits, the
IRR does not exist
– We check for this condition and do not try to solve
for the IRR in this case
Technology Adoption and Costs
• Technology Adoption Pathway Module
– Pre-processing module the creates data to be read
in by IMPACT food module
– Allows users to specify regions, and timing for
technology adoption
• Critical to test several adoption scenarios, to
inform ex-ante analysis of different
technologies
Technology Adoption and Costs
• Costs are currently exogenous and supplied by
the users
• Technology adoption costs comes in 3 forms:
– Global Costs: Not tied to a specific country (e.g. CGcenter investments)
– National R&D Costs: Costs incurred at the country
level to develop and implement a technology (e.g.
National Research centers)
– Extension Costs: Costs incurred at country level to
implement a technology in the field
• Multiple cost scenarios should be used to test
cost sensitivity in the benefit-cost analysis