Water-Limited Dry-Season Cropping Choice in Magway
In Magway Region, a farm household holds 10 acres but has irrigation water for only 6 acres in the dry season. It must choose between sesame and green gram on those 6 acres. Sesame gives 14 baskets an acre at 45,000 kyat a basket, with cash costs of 180,000 kyat an acre and 50 person-days of labour. Green gram gives 8 baskets an acre at 65,000 kyat, cash costs of 160,000 kyat an acre and 25 person-days. The family can supply 200 person-days; hired labour costs 6,000 kyat a day. It has 300,000 kyat cash and must pay 120,000 kyat school fees this season. Borrowing costs 3 percent a month. Last year unseasonal rain destroyed three acres of sesame. The household wants the highest expected income but fears debt and crop failure.
1. Calculate the net return per acre and per person-day for each crop, and state the opportunity cost of using one acre for sesame instead of green gram. Does the household have enough family labour and cash to plant all six acres to the crop with the higher net return? Show your calculations.
Read the worked answer
Sesame: revenue = 14 × 45,000 = 630,000 kyat/acre. Net before family labour = 630,000 − 180,000 = 450,000 kyat/acre. Per person-day = 450,000 ÷ 50 = 9,000 kyat.
Green gram: revenue = 8 × 65,000 = 520,000 kyat/acre. Net before family labour = 520,000 − 160,000 = 360,000 kyat/acre. Per person-day = 360,000 ÷ 25 = 14,400 kyat.
The opportunity cost of one acre of sesame is the 360,000 kyat net return from green gram given up, plus the 25 extra person-days. Sesame earns 90,000 kyat more per acre, but it uses labour that could grow more green gram or be hired out.
All six acres to sesame needs 300 person-days. Family supplies 200, so 100 days must be hired at 6,000 = 600,000 kyat. Cash required = 6 × 180,000 + 600,000 + 120,000 school fees = 1,800,000 kyat. With only 300,000 kyat, the household must borrow 1,500,000 kyat.
All six acres to green gram needs 150 person-days, so no hired labour. Cash required = 6 × 160,000 + 120,000 = 1,080,000 kyat, so borrowing is 780,000 kyat. Thus the household cannot plant all six acres to sesame without both hired labour and much more debt; even green gram requires credit.
2. Advise the household on an acreage split. Use expected net income after cash costs, the borrowing requirement, interest, and the risk of sesame failure. A split that maximizes gross revenue is not necessarily the best choice.
Read the worked answer
Compare feasible splits after cash costs and school fees, before interest:
- 0 sesame / 6 green: revenue 3,120,000; cash costs 960,000; fees 120,000; net 2,040,000; borrowing 780,000; labour 150 days.
- 1 sesame / 5 green: revenue 3,230,000; cash costs 980,000; fees 120,000; net 2,130,000; borrowing 800,000; labour 175 days.
- 2 sesame / 4 green: revenue 3,340,000; cash costs 1,000,000; fees 120,000; net 2,220,000; borrowing 820,000; labour 200 days exactly.
- 3 sesame / 3 green: revenue 3,450,000; cash costs 1,020,000; fees 120,000; hired labour 150,000 for 25 days; net 2,160,000; borrowing 990,000.
The 2/4 split gives the highest net income before interest and uses exactly the family’s 200 person-days, so no hired labour. It borrows only 40,000 kyat more than all green gram. At 3 percent a month for four months, interest is about 98,400 kyat, leaving about 2,122,000 kyat; all green leaves about 1,946,000 kyat after interest. The gain from two sesame acres is roughly 176,000 kyat.
However, sesame carries rain risk. If both sesame acres fail, the household loses about 900,000 kyat of net return and still owes the loan. A risk-averse household may prefer 1 sesame / 5 green: it still earns 2,130,000 kyat, borrows slightly less, and limits exposure. All sesame is clearly unwise because it needs 100 hired days and 1.5 million kyat of borrowing. My advice: 2/4 if the household can tolerate one failed crop and arrange a short loan; otherwise 1/5. Avoid the gross-revenue-maximizing 3/3, because extra hired labour and debt reduce its advantage.