Welfare: Consumer and Producer Surplus and Internal Rate of Return

Daniel Mason-D’CrozSherman 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

QF

Pref

Psimulation

PIntref

PIntsimulation

Qref Q* Qsimulation

Reference Consumer Surplus

Simulation Consumer Surplus

Income Effect

Price Effect

Both Income and Price Effect (gains from income changes lost to price changes)

“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

QS

Psimulation

Qsimulation

Agricultural Revenue

Producer Surplus

Total Cost

Producer Surplus

• We need to find the area under a non-linear, constant-elasticity supply curve.

• After some algebra, that area is equal to:

• Which is equal to total revenue times 1 over 1 + the elasticity of supply.

𝑃𝑆=(𝑃×𝑄𝑆 )= 𝑃 ×𝑄𝑆1+𝜀

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

𝑁𝑃𝑉 (𝐶𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 )=∑𝑡=1

𝑇 ∆𝐶𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑡

(1+𝑟 )𝑡

𝑁𝑃𝑉 (𝑃 𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 )=∑𝑡=1

𝑡 ∆ 𝑃𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑡

(1+𝑟 )𝑡

Net Present Values

𝑁𝑃𝑉 (𝐶𝑜𝑠𝑡 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛)=∑𝑡=1

𝑇 𝐶𝑜𝑠𝑡𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑡

(1+𝑟 )𝑡

Benefit-Cost and Internal Rate of Return

𝑁𝑃𝑉 (𝑇𝑜𝑡𝑎𝑙𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛)𝑁𝑃𝑉 (𝐶𝑜𝑠𝑡𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛)

𝑁𝑃𝑉=∑𝑡=1

𝑇 (∆𝐶𝑆𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑡 +∆ 𝐴𝑅𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛

𝑡 )−𝐶𝑜𝑠𝑡 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑡

(1+𝑖𝑟 𝑟 )𝑡=0

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. CG-center 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