This is an appeal from a conviction and sentence for presenting false statements and making false claims to the United States Department of Agriculture in connection with the food stamp program. Concluding that there was sufficient evidence to support the jury's verdict, we shall affirm the conviction. We shall vacate the sentence and remand the case for resentencing, however, because of an error in the calculation of the loss caused by the defendant's conduct.

* The defendant, Patricia Arnous, and her husband, Bassam Arnous, owned a number of convenience stores in Memphis, Tennessee. Mr. Arnous was primarily responsible for operating the stores, and Mrs. Arnous did the bookkeeping. Some of the business licenses, beer permits, and food stamp authorizations for the stores were registered in the name of Mrs. Arnous; she said that this was due to her husband's immigrant status.

Mr. and Mrs. Arnous opened the Stop One Market in 1994. Mr. Arnous testified at trial that in September of that year he filled out an application for authorization to accept food stamps at the store, naming his wife as the owner. He testified that he presented the application to his wife for her signature and that she signed the document without reading it. Mrs. Arnous testified that she did not recall having read the application. Her signature, however, was affixed directly beneath the following statement: "I swear the information on this application is true, and I did read the penalties and the warning above."

One of the questions on the application form was whether the store owner or any immediate family member had been convicted of a crime. The "No" box was checked in response to this question. Mr. Arnous had in fact been convicted of a felony, however, as Mrs. Arnous knew. Under the governing regulations, the felony conviction disqualified both spouses from participation in the food stamp program.

Because of the false answer in the application, Mr. and Mrs. Arnous were able to obtain an authorization number that allowed them to participate in the program. Mrs. Arnous personally submitted seven food stamp redemption claims using the authorization number, and other individuals submitted nine additional claims using the number.

Mrs. Arnous was indicted on one count of violating 18 U.S.C. § 1001 by making a false statement in the application for approval to participate in the food stamp program. She was also indicted on 16 counts of violating 18 U.S.C. § 287 by presenting false food stamp redemption claims. The district court dismissed the counts involving redemption claims submitted by persons other than Mrs. Arnous, but denied a motion for acquittal with respect to the remaining counts.

The jury returned a verdict of guilty on counts one through eight, and Mrs. Arnous was sentenced to imprisonment for a total term of 15 months. (The court recommended to the Bureau of Prisons that six months of "shock incarceration" be substituted for the 15 months.) A three year period of supervised release was to follow the prison term, during which time Mrs. Arnous was prohibited from participating in any business or activity involving the food stamp program. She was also ordered to pay an assessment of $400 and to make restitution of $3,274. Mrs. Arnous has perfected a timely appeal.

Under the government's theory of the case, as the parties agree, the jury could not have found that Mrs. Arnous submitted false claims in violation of 18 U.S.C. § 287 unless it also found that she made a false statement in violation of 18 U.S.C. § 1001. The validity of all eight convictions turns on the sufficiency of the evidence offered to show a violation of § 1001.

To prove that § 1001 has been violated, the government must establish that the defendant knowingly and willfully made a material false statement that pertained to an activity within the jurisdiction of a federal agency. United States v. Steele, 933 F.2d 1313, 1318-19 (6th Cir.), cert. denied, 502 U.S. 909, 112 S. Ct. 303, 116 L. Ed. 2d 246 (1991). Mrs. Arnous concedes that she signed an application pertaining to an activity within the jurisdiction of a federal agency, and she concedes that the application contained a material false statement; her sole contention is that the government did not present evidence sufficient to enable a rational jury to find beyond a reasonable doubt that the false statement was made knowingly and willfully.

The evidence on this point seems sufficient to us. Mr. Yousef Nahhas, a business associate of Mr. and Mrs. Arnous, testified that in April or May of 1994 Mrs. Arnous showed him how to fill out forms to obtain the necessary licenses for a convenience store. Among the forms was the same type of food stamp application at issue here. Mr. Nahhas testified that he saw Mrs. Arnous read the instructions sent by the Department of Agriculture and that he saw her review the application. He and Mrs. Arnous went over the application point by point, he said, and he specifically testified that he recalled the question about prior convictions. A jury could properly find, on the basis of this testimony, that Mrs. Arnous was aware that the application asked whether the store owner or an immediate family member had been convicted of a crime.

Whether or not Mrs. Arnous read the food stamp application for the Stop One Market before signing it, the jury had a reasonable basis for finding that she knew the application contained material false information. The district court instructed the jury that it could find the element of knowledge if it believed that Mrs. Arnous had "deliberately ignored a high probability that the form contained material false information." See United States v. Lee, 991 F.2d 343, 351 (6th Cir.1993) (approving the use of such an instruction). The evidence regarding Mrs. Arnous' prior knowledge of the contents of the application form was sufficient to support a finding that she deliberately ignored a high probability that the form contained a material false statement.

In calculating Mrs. Arnous' guideline sentence range, the district court found that her conduct had caused a loss of $30,891--the total amount of the food stamp redemption claims submitted by the Stop One Market under the fraudulently obtained authorization number. On the strength of this finding, the offense level was increased by four pursuant to U.S.S.G. § 2F1.1(b). Mrs. Arnous contends that there should have been no increase, her conduct having caused no loss.

Application Note 7(d) to § 2F1.1 provides that "[i]n a case involving diversion of government program benefits, loss is the value of the benefits diverted from intended recipients or uses." The government presented two theories as to the benefits Mrs. Arnous diverted from their intended use. First, it asserted that some of the food stamps redeemed by the Stop One Market were probably not exchanged for authorized products. In a deposition in a civil case, Mrs. Arnous testified that the Stop One Market had sales of no more than $700 dollars per day and that food stamps accounted for between 40 and 50 percent of the daily sales. On several occasions, however, Mr. Arnous or a market employee submitted over $1,000 in food stamp redemption certificates, using the fraudulently obtained authorization number. This discrepancy between the store's gross sales and its food stamp redemptions may suggest that the store exchanged cash or unauthorized products for food stamp coupons.1 See United States v. Barnes, 117 F.3d 328 (7th Cir.1997).

When food stamp coupons are exchanged for cash or unauthorized products, the coupons are diverted from their intended use--the purchase of specified food products. The loss caused by the defendant's conduct under such circumstances is the face value of the coupons exchanged. Id. In the case at bar, however, the district court made no finding that the Stop One Market had exchanged any food stamps for cash or unauthorized products. Rather, the court relied on the government's second theory of loss, which was that the food stamps would have been used at other stores if they had not been used at the Stop One Market. The government argued, and the district court found, that other stores would have received an additional $30,891 in food stamp business but for Mrs. Arnous' crime.

One problem with this theory, as we see it, is that the theory ignores the factor known in the accounting world as "cost of goods sold." If other stores had received the food stamps which were used at the Stop One Market, the other stores would have had to part with inventory having a retail value of $30,891. The net loss (aside from any lost opportunity to make additional sales) was the difference between the cost of the inventory to the other stores and the face amount of the food stamps. Cf. United States v. Parsons, 109 F.3d 1002, 1004 (4th Cir.1997) (holding that the profit made by a defendant is an appropriate proxy for loss in certain cases).

A second potential problem is that even the profits lost by stores eligible to receive food stamps may not be cognizable under U.S.S.G. § 2F1.1. As noted above, Application Note 7(d) provides that loss is the value of the government benefits diverted from intended recipients or uses. It is debatable whether retail establishments are intended recipients of the benefits of the food stamp program.

We think that the government wins this debate. The Supreme Court has stated that the only authorized use of food stamps is "to purchase food in retail food stores which have been approved for participation in the food stamp program at prices prevailing in such stores." Liparota v. United States, 471 U.S. 419, 426, 105 S. Ct. 2084, 2088, 85 L. Ed. 2d 434 (1985). In Barnes the Seventh Circuit defined "intended use" as "the purchase of specified food products from authorized retailers." 117 F.3d at 335. It would seem to follow that by fraudulently obtaining an authorization number and accepting food stamps pursuant to that number, Mrs. Arnous diverted food stamps from their intended use--the purchase of food products from properly authorized retailers. The amount of the loss caused by such diversion was the amount of the profits that properly authorized retailers failed to realize as a result of the business having gone to the Stop One Market instead of to them.

The conviction is AFFIRMED, the sentence is VACATED, and the case is REMANDED for resentencing.