The government of a country wants to decide what prices should be charged for its dairy products, milk, butter and cheese.[22] All these products arise directly or indirectly from the country’s raw milk production. This raw milk is usefully divided into the two components of fat and dry matter. After subtracting the quantities of fat and dry matter which are used for making products for export or consumption on the farms there is a total yearly availability of 600,000 tons of fat and 750,000 tons of dry matter. This is all available for producing milk, butter and two kinds of cheese for domestic consumption.

The percentage compositions of the products are given in Table 22.1.

For the previous year the domestic consumption and prices for the products are given in Table 22.2.

Price elasticities of demand, relating consumer demand to the prices of each product, have been calculated on the basis of past statistics. The price elasticity of a product is defined by

For the two makes of cheese there will be some degree of substitution in consumer demand depending on relative prices. This is measured by cross-elasticity of demand with respect to price. The cross-elasticity from a product A to a product B is defined by

The elasticities and cross-elasticities are given in Table 22.3.

The objective is to determine what prices and resultant demand will maximize total revenue.

It is, however, politically unacceptable to allow a certain price index to rise. As a result of the way this index is calculated this limitation simply demands that the new prices must be such that the total cost of last year’s consumption would not be increased. A particularly important additional requirement is to quantify the economic cost of this political limitation.