The World Bank is considering financing the construction of a micro dam in semi-arid Burkina Faso. The

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Question:

The World Bank is considering financing the construction of a micro dam in semi-arid Burkina Faso. The dam will serve to collect run-off water for irrigation purposes.
As an economist, you are asked to evaluate the welfare benefit from the dam. You are told the following (obviously, these are simplified assumptions):

(i) The total cost of building the dam is $50,000. In order to bring the construction equipment to the dam site, a dirt road to the village is built (cost included in the total cost of the dam).
(ii) The village has 200 hectares of arable land. Each household owns 1 hectare of land. The dam will flood 100 hectares of arable land but will permit irrigated agriculture on 40 hectares currently used for rain-fed agriculture.
(iii) One hectare of non-irrigated land yields on average 500 Kg of sorghum or 200 Kg of tomatoes per year.
(iv) One hectare of irrigated land yields on average 2000 Kg of sorghum or 4000 Kg of tomatoes per year.
(v) Before the dam is built, the price of sorghum is $1 per Kg and the price of tomato is $0.30 per Kg.
(vi) After the dam is built, the price of sorghum is expected to fall to $0.80 per Kg due to reduced transport costs (the village is a deficit producer) but to increase the price of tomatoes to $0.50 per Kg.
(vii) The price of manufactures is expected to fall by 15% due to reduced transport to the road.
(viii) Villagers spend 70% of their income on sorghum, the rest on manufactures. They do not eat tomatoes, which they prefer to sell for urban consumption.
(ix) Each household receives $200 a year in remittances from migrant relatives.
(x) Agricultural production costs are $100 per hectare per year for non-irrigated land and $200 per hectare for irrigated land.

You are asked to make a rapid estimate of the welfare benefit of the dam. Do the social benefits generated by the dam justify the cost of building it? (Hint: use a Cobb-Douglas utility function as approximation.) What if the World Bank only built the road? The cost of the road alone is $2000. The effect on prices would be the same but no land would be flooded/made suitable for irrigation. Is building the road a potential Pareto improvement?