8. On farmer Jones' farm, only honey is produced. There are two ways to make honey:...

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8. On farmer Jones' farm, only honey is produced. There are two ways to make honey: with and without bees. A bucket of artificial honey, absolutely indis- tinguishable from the real thing, is made out of syrup with one unit of labour. If the same honey is made the old fashioned way (with bees), then a > 1 total units of labour are required (including beekeeping) and 3 bees are required per bucket. Either way, farmer Jones has the capacity to produce up to a finite number H of buckets of honey on his farm. The neighbouring farm, belonging to Silvia, produces apples. A worker can produce a bushel of apples. However, if bees are present on Jones' farm, less labour is needed because the bees (rather than the workers) pollinate the apple blossoms. For this reason, bees in effect replace one worker in the task of pollinating. Up to a finite number A of bushels of apples can be grown on Silvia's farm. The market wage rate is w. Each farmer produces the maximum output at the cheapest cost to her/him. (a) Is the production of honey and apples going to be efficient? Explain. (b) How does the level of inefficiency depend on a, 3, y and w? (c) Give an intuitive explanation of your results in parts (a) and (b). (d) Up to how much would Silvia be willing to pay Jones to produce honey with bees rather than syrup? (e) What would happen to efficiency if Silvia acquires Jones' farm and hence both farms belong to one owner? 8. On farmer Jones' farm, only honey is produced. There are two ways to make honey: with and without bees. A bucket of artificial honey, absolutely indis- tinguishable from the real thing, is made out of syrup with one unit of labour. If the same honey is made the old fashioned way (with bees), then a > 1 total units of labour are required (including beekeeping) and 3 bees are required per bucket. Either way, farmer Jones has the capacity to produce up to a finite number H of buckets of honey on his farm. The neighbouring farm, belonging to Silvia, produces apples. A worker can produce a bushel of apples. However, if bees are present on Jones' farm, less labour is needed because the bees (rather than the workers) pollinate the apple blossoms. For this reason, bees in effect replace one worker in the task of pollinating. Up to a finite number A of bushels of apples can be grown on Silvia's farm. The market wage rate is w. Each farmer produces the maximum output at the cheapest cost to her/him. (a) Is the production of honey and apples going to be efficient? Explain. (b) How does the level of inefficiency depend on a, 3, y and w? (c) Give an intuitive explanation of your results in parts (a) and (b). (d) Up to how much would Silvia be willing to pay Jones to produce honey with bees rather than syrup? (e) What would happen to efficiency if Silvia acquires Jones' farm and hence both farms belong to one owner?

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