Linear equations of farm level demand were obtained for milk used in six different products. These demand equations were used in several quadratic-programming analyses to determine levels of farm marketings of milk and cream or allocation among products that would have maximized farmers’ cash receipts from marketings of milk and cream in 1964. Each analysis computed farm and retail prices for milk used in various products, quantity used in each product and total cash receipts. In one quadratic program, the solution was unconstrained; i.e., no upper limit was imposed on prices, and no lower limit was imposed on quantities. The solutions of several quadratic programs were required to satisfy certain constraints. These constraints were upper limits on prices or lower limits on quantities available.
Most quadratic-programming solutions called for increases in retail prices. To estimate the effect of these on consumer welfare, average compensating variations in per-capita income were computed. Given a change in one or more retail prices, compensating variation for an individual consumer is the amount by which his income must change to leave him exactly as well off after the price change as before.
Ladd, George W. and Updegraff, Gail E.
"Allocation of milk among products to maximize gross income of the nation's dairy farmers under 1964 demand functions,"
Research Bulletin (Iowa Agriculture and Home Economics Experiment Station): Vol. 36
, Article 1.
Available at: https://lib.dr.iastate.edu/researchbulletin/vol36/iss567/1