Milk Payment Scheme Choice for a Rajasthan Cooperative
A milk cooperative in Rajasthan collects 1,200 litres of milk per day from 200 farmers and operates for 300 days a year. Scheme A pays a flat ₹34 per litre. Scheme B pays ₹33 per litre, plus a ₹2 per litre bonus on every litre whose fat content is at least 4%. Under Scheme B, the cooperative must test every litre at a cost of ₹0.30 per litre. At present, only 30% of the daily collection meets the 4% fat threshold. The cooperative wants to know which scheme gives farmers a higher annual payout, and at what share of qualifying milk Scheme B would become equal to Scheme A. The board can invest in feed advice that may raise the qualifying share, but any change will take one year. Assume no other costs and a 300-day year.
1. Calculate the annual net payout under each scheme at the current 30% qualifying share, and state which scheme is better for farmers.
Read the worked answer
Scheme A: 1,200 L/day × ₹34/L × 300 days = ₹1,22,40,000. Scheme B base: 1,200 × ₹33 × 300 = ₹1,18,80,000. Qualifying milk = 30% of 1,200 = 360 L/day. Bonus = 360 × ₹2 × 300 = ₹2,16,000. Testing cost = 1,200 × ₹0.30 × 300 = ₹1,08,000. Net Scheme B = ₹1,18,80,000 + ₹2,16,000 − ₹1,08,000 = ₹1,19,88,000. Difference = ₹1,22,40,000 − ₹1,19,88,000 = ₹2,52,000. So Scheme A pays farmers ₹2.52 lakh more per year at the current 30% qualifying share. The bonus does not yet offset the lower base price and testing cost.
2. Find the qualifying share at which Scheme B matches Scheme A. Show the equation.
Read the worked answer
Let x be the qualifying share. Bonus = 1,200 × x × ₹2 × 300 = ₹7,20,000x. Testing cost is fixed at ₹1,08,000. Net B = ₹1,18,80,000 + ₹7,20,000x − ₹1,08,000 = ₹1,17,72,000 + ₹7,20,000x. Set equal to A: ₹1,17,72,000 + ₹7,20,000x = ₹1,22,40,000. Then ₹7,20,000x = ₹4,68,000, so x = 0.65 = 65%. Scheme B breaks even only if 65% of milk qualifies for the bonus, up from 30% now. That is a 35-percentage-point improvement, which is a large change for one year of feed advice.
3. If testing cost rises to ₹0.50 per litre, what is the new break-even share? What should the cooperative recommend?
Read the worked answer
New testing cost = 1,200 × ₹0.50 × 300 = ₹1,80,000. Net B = ₹1,18,80,000 + ₹7,20,000x − ₹1,80,000 = ₹1,17,00,000 + ₹7,20,000x. Set equal to ₹1,22,40,000: ₹7,20,000x = ₹5,40,000, so x = 0.75 = 75%. The break-even share rises from 65% to 75%. Since current qualifying share is only 30%, Scheme B is even less attractive. The cooperative should recommend Scheme A unless it has strong evidence that feed advice can push qualifying milk above 75% within the year, and even then it should pilot the testing and bonus system before switching all farmers.