Question

3. The Happy Valley Water Control Board (HVWCB) will undertake an irrigation project which will provide 10 million gallons of water annually to 100 wheat farms of 100 acres each. The HVWCB will charge $0.02 per gallon for the water, which will be distributed equally among the 100 farms. It is estimated that: i. land rent in Happy Valley will rise by $70 per acre per annum; ii. 50 farm labourers will be attracted to work on Happy Valley farms, at the market wage of $2000 per annum, from the vineyards of nearby Sunshine Valley; ii. production of wheat on Happy Valley farms is subject to constant returns to scale Assuming the Referent Group is the economy as a whole, work out the annual Referent Group benefit of the irrigation project in terms of areas defined by demand and supply curves for output or inputs. Explain your answer

Answer 1

As stated in the case, returns of scale are constant. This means that output will change in the same proportion of input. If input is doubled, then output will also double. Thus, in this case, value of additional output will be equal to the value of additional income generated.

Additional annual incomes generated are as below:

Land Rent = $70 * 100 farms of 100 acres each

= $70 * 10000 acres of land

= $700000

Labour wages = $2000 * 50 labour

= $100000

Water charges of HVWCB = $0.02 * 10,000,000 gallons

= $200000

Value derived by additional wheat production = Land Rent + Labour wages + Water charges

= $700000 + $100000 + $200000

= $1000000

As labours are diverted at market rate, the same would have been earned by them at Sunshine Valley also. Hence, opportunity cost of shifting of labour = $100000

Annual social benefit from irrigation project = Value derived by additional wheat production – Opportunity cost of labour shifting

= $1000000 - $100000

= $900000