Homework #5 Key Econ 460 section A Fall 1996 Kilkenny

re: "Never Confuse Production with Productivity" Chapter 5 in Sacred Cows and Hot Potatoes: Agrarian Myths in Agricultural Policy by Browne, Skees, Swanson, Thompson, and Unnevehr (1992) Westview Press (on reserve in Heady Hall reading room).

1. Are larger farms more efficient than smaller farms? First, remember that efficiency is defined as the rate of output per unit of input. Let Q denote output and X denote input. The ratio (Q/X) is the rate of output per unit input, or, the farm's productivity. Productivity and efficiency refer to the same thing; a RATE not a level.

A study by Ahearn, et. al. is cited in Sacred Cows Ch. 5. They report that "productive efficiency, as measured by lower costs per bushel, levels out very quickly as farm size increases." To make it clear that your answers are FACTS, not just your personal opinion or religious belief, you should always refer to the research and name the persons who report the research.

The implication is that small and large farms have the same minimum average costs of production.

We assume farmers choose input levels "X*" optimally to produce their profit maximizing level of output Q*. At input prices W, the total cost of production is W@X. Average cost of production is defined TC/Q; so this is (W@X*)/Q*. NOTICE that average cost of production information includes everything we need to measure productivity or efficiency. When AC^large is the same as AC^small (as long as both farms pay the same prices for inputs); then (X/Q)^large = (X/Q)^small and (Q/X)^large = (Q/X)^small.

2. A graph that shows equally productive small and large farms cost curves would have a few important features. (1) both farm's u-shaped AC curves have their lowest points at the same price level. That illustrates the finding by Ahearn, et. al., that the lowest costs per bushel are on the same level for both sizes of farms.

(2) MC curve always crosses the AC curve at the minimum AC. That's why we call the Q chosen at the price that equals both MC and the minimum AC a long run optimal size. Only at that price are farms covering all costs, but there are no excess profits that would induce expansion or more farmers to enter.

(3) To show that a large farmer can take home a larger LEVEL of profit (rather than rate), choose any price (P') above that long run equilibrium price. Indicate Q*^small on the Q axis where P'= MC^small (i.e., relative to where P' crosses the MC^small curve.) Do the same P'=MC^large to find Q*^large.

Remember, profit is total revenues less total costs at Q*

= TR - TC

= P'@Q* - AC@Q*

= (P'-AC)@Q*

So, "boxes" with corners on (0,P'), (Q*,P'), (Q*,AC), and (0,AC) illustrate the profits of the farmers at P'. (Each point in the graph is identified by horizontal and vertical coordinates; in that order.)

Notice also that you can calculate dollars of profit simply by applying the formula for the area of a rectangle. For example, let P'=$3.00/bushel. At Q*^small, let AC^small = $2.10/bushel. At Q*^large, let AC^large = $2.10/bushel. But Q*^small = 160 bu/acre@200 acres = 32,000 bushels; while Q*^large is the same yield per acre for 1000 acres = 160,000 bushels. Calculate profits for each farmer.

Hints: The large farmer makes profit at the same rate ($0.90/bushel) but makes $115,200 more profit (level).