Question

​Kroger, the​ country's leading​ grocery-only chain, added a line of private label organic and natural foods call Simple Truth to its stores. If​ you've priced organic​ foods, you know they are more expensive. For​ example, a dozen conventionally farmed​ Grade-A eggs at Kroger costs consumers$1.81​,whereas Simple Truth eggs are priced at $4.1 per dozen. One study found​ that, overall, the average price of organic foods is 85 percent more than that of conventional foods.​ However, if prices get too​ high, consumers will not purchase the organic options. One element of sustainability is organic​ farming, which costs much more than conventional​ farming, and those higher costs are passed on to consumers. Suppose that a conventional egg​ farmer's average fixed costs per year for​ conventionally-farmed eggs are​ $1 million per​ year, but an organic egg​ farmer's fixed costs are five times that amount. Further assume that the organic​ farmer's variable costs of​$2.22.2per dozen are twice as much as conventional​ farmer's variable costs.

Most large egg farmers sell eggs directly to retailers. Using​ Kroger's prices, what is the​ farmer's price per dozen to the retailer for conventional and organic eggs if​ Kroger's margin is

25 percent based on its retail​ price?

The price the farmer sells a dozen of conventional eggs is ​$_______________

Answer 1

First look at how profit margin is calculated as a percentage.

Revenue is the price at which the retailer sells one unit of a product.

Cost of goods sold (COGS) is the cost of 1 unit to the retailer ( the amount paid by the retailer to buy one unit).

The gross profit earned by the retailer is then Revenue - COGS, and the profit margin is given by the formula

.

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To find the farmer's price per dozen (or the COGS) to the retailer for a dozen of conventional eggs:

Revenue per dozen = $1.81 ( given in the question).

Let the COGS per dozen be $ x.

Profit margin = 25.

Substitute all the above data in the formula for profit margin.

Solving the equation, we find .

The price the farmer sells a dozen conventional eggs for is $1.3575.

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Repeat the same calculation to find the price for which the farmer sells a dozen organic eggs.

Revenue per dozen = $4.1.

Let the price per dozen to the retailer be x.

Profit margin = 25.

Again using the formula for profit margin

Solving the equation, we find .

The price the farmer sells a dozen organic eggs for is $ 3.075.