BUS 540 Module 3 Production and Cost Example

The Ninth Worker Costs More Than the Lettuce Is Worth: Production, Cost and Scale at a Hydroponic Greenhouse

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MBA Program, Aspen University

BUS 540: Managerial Economics

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Month Day, Year

The Ninth Worker Costs More Than the Lettuce Is Worth: Production, Cost and Scale at a Hydroponic Greenhouse

Circle City Greens, a composite hydroponic grower in Indianapolis, produces lettuce and leafy greens year-round in a 20,000-square-foot greenhouse and sells to grocery stores and restaurants. Its main product, a living butterhead lettuce, sells to grocers at $1.10 a head. Over the past year, the owners added workers to raise output, but profit barely changed. They are now considering a larger, more automated greenhouse. This paper analyzes the grower's production and costs to explain what happened and to evaluate the expansion.

The Short Run

In the short run, the greenhouse, its growing channels and its lighting are fixed. The only input the owners can change quickly is labor: workers who seed, transplant, monitor, harvest and pack. Baye and Prince (2022) describe the short-run production function, which shows output as a variable input increases with other inputs fixed, and the marginal product, the additional output from one more unit of the variable input. Because the greenhouse has a limited number of growing channels and a single packing line, each worker beyond a certain point has less to do productively.

Output and Marginal Cost

Each worker costs $900 a week in wages and benefits. The table shows weekly output with four to ten workers, based on the grower's records over the past year.

Marginal product falls steadily as workers are added. The fifth worker adds 2,800 heads; the tenth adds only 200, because the growing channels are full and workers wait for space on the packing line. This is diminishing marginal product, a consequence of adding labor to a fixed greenhouse.

The Hiring Rule

A firm maximizes profit by adding workers as long as the value of the output each one adds exceeds the cost, equivalently, as long as marginal cost is below the price. At a price of $1.10, the eighth worker produces lettuce at a marginal cost of $0.75 a head and is worth hiring. The ninth worker's marginal cost of $1.50 exceeds the price, so hiring the ninth and tenth workers, which the grower did last summer, lost money on every head they added. The grower should operate with eight workers.

Average Cost and Profit

Marginal cost tells the grower how much to produce; average total cost tells whether producing is profitable at all. Fixed costs, including the greenhouse lease, base energy and equipment, total about $9,000 a week. Other variable costs, such as seeds, nutrients and packaging, add $0.18 a head. At eight workers and 17,800 heads, labor costs $7,200, other variable costs $3,204 and fixed costs $9,000, for a total of $19,404, or about $1.09 a head. With a price of $1.10, the grower earns about one cent a head, or roughly $180 a week. The business covers its costs but barely. Profit did not rise as workers were added because diminishing returns pushed marginal cost above price, and the fixed costs of a small greenhouse keep average cost close to price even at the best staffing level.

The Long Run and Economies of Scale

In the long run, the owners can change the size and design of the greenhouse. A proposed 45,000-square-foot facility with automated seeding, moving growing channels and a faster packing line would cost about $4.2 million. Engineering estimates from the equipment supplier, adjusted by the owners, suggest it could produce about 50,000 heads a week with 14 workers, at an average total cost of about $0.86 a head including financing. The lower cost reflects economies of scale: automation reduces labor per head, and fixed costs such as management and climate control are spread over more output.

Learning by Doing

Costs also fall with experience. Lieberman (1984), studying 37 chemical products, found that unit costs declined substantially as cumulative industry output grew, and that learning was associated with both experience and investment in new plants. For Circle City, the experience gained in the current greenhouse, such as nutrient formulas and harvest timing, would carry into the new one, and costs in the larger facility should fall further as staff learn the automated system. This supports the engineering estimate but also warns that the first year in a new facility may cost more than the estimate.

Testing the Scale Assumption

Engineering estimates can be optimistic. Stigler (1958) proposed a simple test of efficient size: observe which sizes of firms grow their share of an industry over time, since sizes that survive and grow are likely the efficient ones. In controlled environment agriculture, several very large indoor farms have closed in recent years while mid-sized greenhouses serving regional grocers have expanded. Applied loosely, Stigler's test suggests that a mid-sized greenhouse like the proposed facility, rather than a much larger one, is a reasonable scale for a regional market.

What the Owners Missed

The owners' records showed rising output after each hire, which seemed to justify the hiring. They were looking at total output, not the change in output per added worker, and at average cost across the whole crop, which fell slightly at first and then rose. Neither measure revealed the point at which a worker cost more than the lettuce he or she added. A weekly report showing output per worker and marginal cost per head would have flagged the problem after the ninth hire.

Recommendation

Circle City should immediately return to eight workers, cutting labor costs by about $1,800 a week with almost no loss of output. It should proceed with the larger greenhouse only if it secures supply contracts for at least 35,000 heads a week at prices of at least $1.00, so that the new facility can operate near its efficient scale from the first year.

Conclusion

Diminishing marginal product explains why adding workers stopped adding profit: beyond eight workers, each added head cost more than it sold for. Average cost shows that the current greenhouse barely breaks even. Economies of scale and learning suggest a larger facility could lower costs, but only if the grower can sell its output. Economic analysis turned frustration into two clear decisions.

References

Baye, M. R., & Prince, J. T. (2022). Managerial economics and business strategy (10th ed.). McGraw Hill.

Lieberman, M. B. (1984). The learning curve and pricing in the chemical processing industries. RAND Journal of Economics, 15(2), 213-228. https://doi.org/10.2307/2555676

Stigler, G. J. (1958). The economies of scale. Journal of Law and Economics, 1, 54-71. https://doi.org/10.1086/466541