Citrus greening, retail fruit prices, and household welfare: A demand system approach

Abstract

Pests and diseases like citrus greening that threaten agricultural productivity also pose a risk to consumers. Reductions in food supply due to outbreaks and spread could increase food prices. We model U.S. household fruit demand using a Quadratic Almost Ideal Demand System and data from Circana’s 2020 and 2021 household panel. Price and income elasticity estimates reveal how household behavior might adjust with shocks to citrus and other fruit prices. Shocks to retail fruit prices can be from either citrus greening or other phenomena such as adverse weather. We also use compensating variation to estimate the impact that changes in fruit prices could have on consumer welfare.

Introduction

Pests and diseases that threaten agricultural productivity and output also pose a threat to consumers. The Animal Plant Health Inspection Service (APHIS), an agency within the U.S. Department of Agriculture (USDA) responsible for monitoring and managing threats to all types of crops and animal agriculture, lists dozens of these diseases and pests on its website (USDA-APHIS, 2022a). Citrus greening, officially known as Huanglongbing (HLB), is among the diseases negatively affecting U.S. agriculture (APHIS, 2022b; University of Florida Citrus Research and Education Center, 2022a). It is spread by an insect, the Asian citrus psyllid. Trees can fall victim to HLB if infected insects feed on them. Symptoms include yellow shoots, leaf mottle, and small lopsided fruit that taste bitter and appear green at the stylar end. The tree will eventually die. HLB originated in Asia but has spread globally to Africa, South America, and North America. It was first detected in the U.S. in Florida in 2005. ¹

Reductions in agricultural output associated with HLB, much like those associated with adverse weather events and other phenomena, can negatively affect consumer welfare. How much consumer welfare decreases will depend on the size of any increase in retail prices as well as consumer demand for affected products. The more consumers demand of those products and the less elastic their demand for them, the greater is the potential welfare loss.

A variety of techniques exist for detecting HLB, mitigating its effects, and controlling spread of the disease. ² However, a cure has not yet been found. Thakuria et al (2023) provide a review of existing detection and management options while Zapata et al (2022) examine the disease’s impact on grower profitability. Application of Zapata et al’s (2022) method to a hypothetical grapefruit grove in Texas reveals that growers should expect a substantial reduction in profits once their trees become infected regardless of the strategy they implement.

Citrus fruits represent a substantial portion of U.S. total fruit consumption and damages to these crops may adversely affect consumer welfare. In 2021, U.S. per capita fruit consumption totaled about 193 pounds on a retail equivalent weight basis (USDA ERS, 2023). About 68 percent of this fruit (132 pounds) was marketed in fresh form, 24 percent (46 pounds) was sold as juice, and 8 percent (15 pounds) was sold in frozen, canned, or dried form. Citrus fruits, including oranges, tangerines, grapefruit, lemons, and limes, among others, represented 19 percent of all fresh fruit consumption and 54 percent of all fruit juice consumption.

In this study, we focus on citrus fruit, a market facing biological threats, and begin with a brief review of evolving supply and demand conditions in the U.S. market. We then present and estimate a fruit demand system. This is necessary in order to understand how demand might respond to any retail price changes. Estimation of a Quadratic Almost Ideal Demand System (QUAIDS) provides income and conditional expenditure elasticities as well as own- and cross-price elasticities of demand. Household-level data from Circana’s (formerly IRI’s) 2020 and 2021 National Consumer Panel (NCP) are used to estimate the demand system including: (1) citrus fresh (all whole or cut fresh citrus fruit), (2) citrus liquid (citrus juices and drinks including frozen types), (3) other fresh (all non-citrus cut or whole fresh fruit), (4) other liquid (non-citrus juices and drinks including frozen types), and (5) all others (all frozen excluding frozen liquid, dried, or canned fruit products). Finally, we use compensating variation (CV) to estimate the impact that a change in fruit prices could have on consumer welfare. Our method for calculating CV uses compensated (Hicksian) price elasticities that we obtain from our QUAIDS model. This method is easier to use than other procedures requiring estimation of the cost function. Welfare calculations presented in the study for a few scenarios are based on historic data and could be adapted to account for food price shocks that may occur in the future.

U.S. citrus fruit market dynamics and the spread of HLB

U.S. growers harvested $2.91 billion worth of citrus fruit during the 2021–2022 growing season (USDA, NASS, 2022). Largest among them was the orange crop valued at about $1.47 billion followed by the tangerine and mandarin crops ($0.70 billion), the lemon crop ($0.58 billion), and the grapefruit crop ($0.17 billion).

U.S. citrus fruit growers have faced many challenges in recent decades including the spread of HLB, adverse weather events, and competition from imports (Luckstead and Devadoss, 2020). U.S. production of oranges for juicing and other forms of processing has been trending downward since the mid-2000s when HLB was first detected in the country (USDA ERS, 2022b). Growers in Florida accounted for over 90% of U.S. oranges harvested for processing in the early 2000s. Due in part to HLB, production in Florida fell from 6.4 million short tons in 2004/05 to 1.7 million short tons in 2020/21, a 72% decrease.

U.S. consumers have also been drinking less orange juice over time. U.S. per capita orange juice consumption fell 53% from 0.175 to 0.083 cups per day between 2005 and 2021 (USDA, ERS, 2023). ³ Healthcare providers, who once encouraged children to drink 100% fruit juice as a source of nutrients and extra water, have become worried about the amounts of calories and sugar in fruit juice (Heyman and Abrams, 2017). The American Academy of Pediatrics now recommends that caregivers promote whole fruit, water, and low-fat/nonfat milk as alternatives (Heyman and Abrams, 2017), even though there remains little evidence that fruit juice consumption contributes to obesity or obesity-related diseases (Auerbach et al., 2018). ⁴

U.S. grapefruit production and consumption have also been declining steadily (USDA ERS, 2022b and 2023). During the 2004–2005 growing season, Florida and Texas growers accounted for a combined 82% of U.S. production. However, combined production in those two states fell from 808,000 short tons in 2004/05 to 196,000 short tons in 2021/22, a 76% decrease. For consumption, grapefruit fell 75% from 0.016 to 0.002 cups per day between 2008 and 2021 nationally.

Warnings have been issued against consuming grapefruit and grapefruit juice with certain medications as consumption of this type of citrus fruit can interfere with the performance of those drugs, including some common prescription and over-the-counter drugs for managing blood pressure and cholesterol. The U.S. Department of Health and Human Services (DHHS), U.S. Food and Drug Administration (FDA) requires manufacturers of those drugs to label their products with warnings against drinking grapefruit juice or eating raw grapefruit while taking the product (DHHS, FDA, 2023).

Unlike grapefruit and oranges for processing, U.S. production and consumption of fresh market oranges, tangerines, and lemons has been steady (USDA ERS, 2022b and 2023). HLB has so far not been detected in commercial groves in California (USDA NASS, 2022). California currently accounts for about 92% of all fresh market oranges, 96% of all lemons, and 96% of all U.S.-grown tangerines and mandarins.

Governments around the world are investing in the fight against HLB. ⁵ Hopefully, breakthrough technologies will be developed soon to limit damage from the disease. Retail orange and grapefruit juice prices are already increasing. Data from the Florida Department of Citrus (FDOC) show that average retail prices for 100% orange juice purchased as frozen concentrate (FCOJ) increased about 51% from $3.57 per gallon during the 2004–2005 season to $5.38 per gallon in 2020–2021 (FDOC, 2021). ⁶ Average retail prices for 100% orange juice purchased as refrigerated, not-from-concentrate (NFC) juice simultaneously increased 62% from $5.49 per gallon during the 2004–2005 season to $8.92 per gallon in 2020–2021 with some of the largest price increases occurring during the most recent years. ⁷ Indeed, according to Dezember and Uberti (2023), average retail prices for NFC juice were up 20% in January 2023 over peak prices seen in 2016. This price spike occurred after Florida announced its smallest orange crop since 1937 due to the continued spread of HLB, hurricanes, and other adverse weather conditions. The size of the spike might have been even worse for consumers if imports were not also rising to offset some lost domestic production. Imported fruit accounted for 58.4% of U.S. orange juice supply in 2021 up from 14.9% in 2004 (USDA ERS, 2022b). Brazil is the world’s leading producer and exporter of oranges for processing (USDA FAS, 2022a). HLB is also pervasive in that country. ⁸ Any further spread of the disease, including California where the bulk of U.S. citrus fruit for consumption as fresh produce is grown, could further raise consumer-level prices for all types of citrus fruit products with negative implications for consumer welfare.

Modeling U.S. household fruit demand and potential welfare loss

U.S. households are vulnerable to food price shocks that may arise from the spread of diseases, pests, and other threats to agriculture. Up-to-date price and income elasticities of demand are needed to predict how households may adjust the mix of products they buy in response to food price shocks. A broad measure of overall household well-being is also needed. Compensating variation (CV) has been widely used in the literature to quantify changes in household welfare given a specific set of price changes. In this study, we consider a few scenarios: first we consider a 10% price increase in any individual fruit category, holding substitute prices constant, and second, we consider simultaneous price increases in fruit categories. ⁹

Several previous studies using data collected in the 1980s through the 2000s examine U.S. household demand for fruit. In general, it is found that fruit demand is inelastic. For example, Park et al.’s (1996) elasticity estimate for total fruit (aggregated) is −0.43 based on the 1987–1988 National Food Consumption Survey. Using the same data, Huang and Lin (2000) reported an estimate of −0.70. Using Nielsen Homescan data, Dong and Lin (2009) reported that the elasticity estimate for total fruits is −0.55. Price elasticities for specific fruit products are more elastic than those for the total aggregate but still are inelastic in most cases. For example, previously reported elasticity estimates for oranges are −0.85 (Huang, 1993), −0.67 (Brown and Lee, 2002), −0.79 (Durham and Eales, 2010), and −1.14 (You et al., 1997). Those for all citrus are −0.65 (Huang, 1993) and −1.10 (Okrent and Alston, 2012).

Existing studies also confirm that fruit is a normal and necessary good as the Engel curve relationship between income and total expenditure on fresh fruits is positive and less than 1. Using retail purchase data reported by Nielsen’s Homescan panel, Lin et al. (2009) found that households will increase their total fresh fruit expenditures by 0.19% given a 1% increase in income. They also investigate how changes in total fresh fruit expenditures will, in turn, affect spending on organic and conventional fresh fruits. For example, a 1% increase in fresh fruit expenditure is found to increase expenditures on organic fresh fruits by 0.81% to 1.03% (the expenditure elasticity). The estimated expenditure elasticities can be multiplied by the 0.19% Engel Curve effect to estimate how much organic fruit expenditures would rise with a 1% increase in income (the income elasticity).

Given ongoing changes discussed above in U.S. demand for citrus fruit, we desire updated estimates of how consumers may respond to price increases. Indeed, during the height of the COVID-19 pandemic in 2020, U.S. demand for orange juice increased but this boost in demand was short-lived and consumption fell in 2021 over 2020 as the pandemic subsided. ¹⁰ In this study, we separately model U.S. household fruit demand using both 2020 and 2021 NCP data. ¹¹ Results from both data sets are used to estimate the impact of an increase in retail prices on consumer welfare. To save space, we report a full set of results using 2021 data and only those essential to estimating welfare effects using 2020 data. Comparing results for the two years serves as a robustness check. It also illustrates how differences in demand conditions can lead to different estimates of how a given retail price increase might affect consumer welfare.

The NCP is an operational joint venture owned by Circana and The Nielsen Company (Muth et al. 2016). The data set includes households that participated for 12 full months and bought at least one fruit product during that year. Each household used a hand-held scanner to record its food purchases after shopping occasions at retail food stores (e.g., supermarkets, supercenters, and warehouse club stores). We identify and place each NCP household’s fruit purchases into one of 5 categories: (1) citrus fresh (all whole or cut fresh citrus fruit), (2) citrus liquid (citrus juices and drinks including frozen types), (3) other fresh (all non-citrus cut or whole fresh fruit), (4) other liquid (non-citrus juices and drinks including frozen types), (5) all others (all frozen excluding frozen liquid, dried, or canned fruit products). Finally, we calculate each household’s 2020 and 2021 annual fruit purchases within each category by aggregating over their daily purchases. This Circana data set enables us to measure fruit demand and consumer welfare at the household level.

Some NCP households reported no purchases of some fruit products in our demand system (Tables 1 and 2). For example, in 2021, among all 53,737 sampled households, about 23% bought no citrus fresh, 30% did not buy citrus liquid, 1% made no purchases of other fresh, 26% did not acquire other liquid, and 12% did not buy all others. The data are censored at zero. We cannot fully observe household demand in all cases.

Table 1. Household fruits expenditures, prices, and quantities, 2021

Note: (1) citrus fresh are all whole or cut fresh citrus fruits, (2) citrus liquid are citrus juices and drinks including frozen types, (3) other fresh are all non-citrus cut or whole fresh fruits, (4) other liquid is non-citrus juices and drinks including frozen types, and (5) all others are all frozen excluding liquid, dried, or canned fruit products. Total households in the sample = 53,732.

Table 2. Household fruits expenditures, prices, and quantities, 2020

Note: (1) citrus fresh are all whole or cut fresh citrus fruits, (2) citrus liquid are citrus juices and drinks including frozen types, (3) other fresh are all non-citrus cut or whole fresh fruits, (4) other liquid is non-citrus juices and drinks including frozen types, and (5) all others are all frozen excluding liquid, dried, or canned fruit products. Total households in the sample = 54,645.

Estimates of the prices that each household faced for all 5 products were derived as is necessary for the estimation of a demand system. For those fruit products that households reported buying, we use unit values calculated from the observed expenditure and purchase quantities. These data suffer from “data censoring” whereby some households purchase zero items in the target categories so prices and demand cannot be directly observed. Censoring is often unavoidable in household demand models but can be addressed with established methods. For missing price observations, which occur when households reported zero purchases of a product, we first use the average unit value paid by households in the same zip code. If no other households residing in the zip code made a purchase, we then use the average unit price paid by households in the same county, followed by households in the same state, and, finally, households across the nation. For the 2021 data, the average unit values paid for fruit are $0.139/oz for total fruit, $0.09/oz for citrus fresh, $0.07/oz for citrus liquid, $0.21/oz for other fresh, $0.06/oz for other liquid, and $0.23/oz for all others (Table 1).

The QUAIDS model introduced by Banks et al. (1997) is adopted in the study. The QUAIDS model is well suited for modeling annual U.S. household demand for a group of fruit products. This model extends Deaton and Muellbauer’s (1980) Almost Ideal Demand System (AIDS). The AIDS model is consistent with economic theory as it satisfies most axioms of consumer choice. However, it assumes a consumer’s purchases of each individual product to be loglinear in total expenditure on the group. The QUAIDS model further allows for the possibility that such consumer behavior is quadratic in log total expenditure. Additionally, it can also be adapted to correct for problems associated with use of scanner data, such as expenditure and price endogeneity and data censoring. Estimated elasticities from the QUAIDS model calculated with more recent data will generate superior CV estimates than relying on published, older estimates would have.

Fruit demand model

Following classic economic theory and previous analyses of U.S. food demand, we assume that households engage in a multistage budgeting process and fruits are separable from other goods. Households first allocate their income across housing, transportation, food away from home, and different food groups for food at home (FAH), such as fruits, vegetables, meats, and grains, among other needs and wants. Money allocated to a FAH group in the first stage is then divided among specific types of products in a second stage. It can be theorized that total FAH fruit expenditures are divided in the model’s second stage among the 5 fruit products mentioned above.

Empirical analyses of food demand typically focus on only one stage of a household’s budgeting process. In this study, we followed that same general approach. We focused on the second stage and did not attempt to estimate a complete first-stage system; rather, we simplified the first stage to a single equation that explains a household’s total FAH fruit expenditures in 2020 and 2021. In keeping with economic theory, we include household income in this equation. Based on a review of past studies, we also include selected demographic characteristics such as household size, education, and race (USDA ERS, 2022a; Hoy et al., 2017; Tichenor and Conrad, 2015; Drewnowski and Rheem, 2015). This single equation is called the Engel curve and it reveals the relationship between income and total fruit expenditures.

Following Dhar et al., (2003), we specify our total fruit expenditure equation in log form as:

(1) $$lnX = \delta 'Y + \eta$$

where X is average household-level FAH total fruit expenditures and Y is a J × 1 vector of explanatory variables. $\delta $ is a vector of parameters [J × 1], and $\eta $ is an error term. As mentioned above, we included in Y household income and other household demographic variables.

To model the second stage of the multistage budgeting process and explain how households spread their total fruit expenditures over the five categories of products, we estimated a demand model based on the QUAIDS first introduced by Banks et al. (1997). A basic system of five QUAIDS expenditure share equations is:

(2) $$W = \alpha + \gamma ln\;P + \;\beta \;ln \left( {{X \over {a\left( P \right)}}} \right) + {\lambda \over {b\left( p \right)}}{\left({ln \left( {{X \over {a\left( P \right)}}}\right) }\right)^2} + \varepsilon \;$$

where W is a 5 × 1 vector of expenditure shares, $lnP$ is a 5 × 1 vector of log product prices, $lnX$ is log total fruit expenditures, $ln a\left( P \right) = {\alpha _0} + \;\alpha 'lnP + \;{1 \over 2}\;{\left( {lnP} \right)^\prime }\gamma \left( {lnP} \right)$ ,, $b\left( P \right) = {e^{\beta 'lnP}}$ , and ε is a 5 × 1 vector of error terms where $\varepsilon \sim N\left( {0,\Sigma } \right)$ . The error term follows a joint normal distribution with a mean vector of 0 and a variance-covariance matrix $\Sigma $ .

The model contains a group of parameters to be estimated: ${{\rm{\alpha }}_0}\;\left[ {1\times1} \right]$ , ¹² $\alpha \;[ {5\times1} ]$ , $\;\beta \;\left[ {5} \times1 \right]$ , $\;\lambda \;\left[ {5} \times1 \right]$ , $\gamma \;\left[ {5\times5} \right]$ , and $\Sigma\left[ {5\times5} \right]$ . As shown in (2), W is quadratic in log total expenditure X if $\;\lambda $ is statistically significant. If not, the QUAIDS budget share equations reduce to the AIDS budget share equations and W is linear in log X.

To ensure the model conforms with economic theory, the following restrictions are placed on the parameters: $I\alpha = 1,\;{\bf{I}}\gamma = 0,\;\;I\beta = 0$ , $I\lambda = 0$ , $I\Sigma = 0,\;\;\gamma ' = \gamma $ where I is a 5×1 vector of 1’s. ¹³

We allowed for the likelihood that households’ fruits choices depended on their demographic characteristics in addition to prices and expenditures. It is possible to incorporate such variables into the above QUAIDS by transforming the intercept in equation (2), $\alpha $ , as: ¹⁴

(3) $$\alpha = {\vartheta _0} + {\vartheta _1}Z$$

where Z is [k $ \times $ 5] vector of demographics and k is the number of such variables. Inserting equation (3) into equation (2) completes the specification of our demand model for the second stage of a household’s budgeting process:

(4) $$W = {\vartheta _0} + {\vartheta _1}Z + \gamma lnP + \;\beta \;ln \left( {{X \over {a\left( P \right)}}} \right) + {\lambda \over {b\left( p \right)}}{\left(ln \left( {{X \over {a\left( P \right)}}} \right)\right)^2} + \varepsilon .$$

Following previous studies, we include in Z variables such as household size, age, race and ethnicity, and education (USDA ERS, 2022a; Hoy et al., 2017; Tichenor and Conrad, 2015; Drewnowski and Rheem, 2015). ${\vartheta _0}$ [5 $ \times $ 1] and ${\vartheta _1}$ [5 × k] are parameter vectors. ${\vartheta _0}$ and ${\vartheta _1}$ have the following restrictions: $I{\vartheta _0} = 1$ and $I{\vartheta _1} = 0$ .

The above household fruit demand model can be estimated using maximum likelihood techniques and the procedure in Wales and Woodland (1983) and Dong et al. (2004) to accommodate zero censoring as some households made no purchases of one or more of the 5 categories of fruit in our demand system as noted above (Tables 1 and 2). This procedure is unique among methods that account for data censoring because budget constraints are imposed in both the observed expenditure shares and the latent expenditure shares. Equations (1) and (4) are jointly determined. This approach helped to ensure parameter estimates were consistent as total fruits expenditure X in (4) may be endogenous (LaFrance, 1993). Marshallian price elasticities, total FAH fruit expenditure elasticities, and demographics elasticities can all be obtained using the estimate of equation (4) (Dong et al., 2004). The demographics included in Z and Y, as well as their summary statistics, are provided for our 2021 data in Table 3. Those for our 2020 data are available on request.

Table 3. Demographic variables in expenditure share and total expenditure equations, 2021

*indicates in both equations, and **indicates in total expenditure equation only.

Compensating variation (welfare analysis)

Economists commonly estimate demand systems to gain important insights on consumer demand behavior and well-being. Elasticity estimates with respect to the appropriate variables can shed light on how consumers might adjust their purchases with changes in prices, expenditures, or even their own demographic characteristics such as education or household composition. It is also possible to estimate how much a change in prices can affect a consumer’s overall well-being (utility). A utility function measures the well-being that a consumer experiences based on the amounts of products consumed. An indirect utility function measures optimized consumer utility based on the consumer’s utility-maximizing selection of products, which is in turn based on products’ prices and expenditures. For instance, higher prices imply a lower level of utility given any constant level of expenditures since prices determine the amounts of products that can be purchased and consumed with a fixed amount of money.

CV is a method for measuring changes in welfare given a change in product prices and it is based on the indirect utility function. The indirect utility function associated with a QUAIDS model (Banks et al.,1997) is:

(5) $$u\left( {X,P} \right) = {\left\{ {\left[{{\ln X - lna\left( P \right)} \over {b\left( P \right)}}\right]^{ - 1}} + L\left( P \right)\right\} ^{ - 1}}$$

where the variables and parameters are defined above and $L\left( P \right) = \lambda 'lnP$ . Given an initial level of total expenditure, X ₀, and an initial set of prices P ₀, $u\left( {X_0,P_0} \right) = {\left\{ {\left[{{\ln X_0 - lna\left( P_0 \right)} \over {b\left( P_0 \right)}}\right]^{ - 1}} + L\left( P_0 \right)\right\} ^{ - 1}}$ is the initial level of consumer utility. This will decrease if prices increase from P ₀ to P ₁ . The consumer could no longer afford as many goods as previously. Additional income would be required to keep the consumer’s level of utility unchanged. CV is the amount of additional income needed to restore utility to its original level given new prices faced by the consumer. Let X ₁ be the level of expenditures a consumer would need to attain the same level of utility as was attainable with X ₀ and P ₀ given the new price level, P ₁ . The CV can then be calculated as X ₁ - X ₀ where the value of X ₁ can be determined from the function (Attanasio et al., 2013):

(6) $${\left\{ {\left[{{{\it ln} {X_1} - lna\left( {{P_1}} \right)} \over {b\left( {{P_1}} \right)}}\right]^{ - 1}} + L\left( {{P_1}} \right)\right\} ^{ - 1}} = {\left\{ {\left[{{{\it ln} {X_0} - lna\left( {{P_0}} \right)} \over {b\left( {{P_0}} \right)}}\right]^{ - 1}} + L\left( {{P_0}} \right)\right\} ^{ - 1}}$$

However, this well-known procedure for calculating CV is not computationally friendly. Firstly, one needs to know or estimate all parameters of the cost function (5). Secondly, one needs to solve the highly non-linear equation (6).

An alternative procedure for calculating CV is desirable as the estimation of the cost function for a food demand system at the household level is difficult. By contrast, suppose we have only price elasticities without knowing the cost function, we can still calculate the CV from the following procedure: We begin by rewriting (5) with X as a function of u and P, i.e., $X\left( {u,P} \right)$ . This function is known as the expenditure or cost function and, as above, CV = X ₁ - X ₀ = $X\left( {u,{P_1}} \right)-\;X\left( {u,{P_0}} \right)$ is the amount of income a consumer would need to keep utility constant after an increase in P from P ₀ to P ₁ (Huang and Huang, 2012). Following Huang and Huang (2012), we then derive the needed expenditure changes for each of the five fruit products (CV for individual products) to keep the original utility level from the expenditure function approach as below:

(7) $$EX = \left( {{P_1}{Q_0}} \right)\left[ \psi{\;\left( {dP/{P_0}} \right)} \right] + \left( {{P_0}{Q_0}} \right)\left( {dP/{P_0}} \right)\;$$

where EX is a 5 × 1 vector of the needed individual expenditure changes or the individual CV of each product in the system, $\psi $ is a [5 × 5] matrix of Hicksian price elasticities which can be calculated from the Marshallian price elasticities using the Slutsky equation after the QUAIDS model has been estimated and parameters in (4) are known, $\;{P_0}$ is a 5 × 1 vector of original prices, ${P_1}$ is a 5 × 1 vector of prices after the change, ${\rm{d}}P = {P_1} - {P_0}$ , and ${Q_0}$ is a 5 × 1 vector of original quantities purchased. CV is the sum of the 5 elements in EX.

Equation (7) takes advantage of the compensated (Hicksian) price elasticities and, in practice, should be easier to estimate than equation (6) after we have those estimates. ¹⁵ Different from the traditional indirect utility approach, in addition to CV, this approach can also provide EX, the expenditure changes in each individual product in the system (individual CV) to keep the original utility level given the price changes. ¹⁶

Results

We estimated a QUAIDS model for U.S. household fruit demand using both 2020 and 2021 NCP data as described above. The quadratic parameter ( $\lambda $ ) was statistically significant at the 5% level using both data sets. A quadratic relationship between total fruit expenditures and all 5 budget shares is appropriate. A QUAIDS specification better explains household behavior than a traditional AIDS would have. Parameter estimates based on our 2021 data for both the first and second stage of a household’s multistage budgeting process are reported in the appendix tables (Tables A1 and A2). Those based on our 2020 data are available on request. Results based on the two data sets are expected to differ somewhat given differences in fruit product demand in 2020 and 2021. As shown above in Tables 1 and 2, U.S. households purchased slightly less fruit in 2021 (1,684.39 oz) than in 2020 (1,692.65 oz). Citrus juices, such as orange juice, were among the products they bought in greater quantities during the height of the COVID-19 pandemic (19.59 oz in 2020 versus 18.42 oz in 2021). Below, we begin by reporting the estimated own- and cross-price elasticities. We then examine demand elasticities with respect to total fruit expenditures and income before turning to those with respect to a household’s key demographic characteristics. Finally, we examine results for a series of simulations that show how price shocks might alter consumer welfare.

Price elasticities

Results confirm that U.S. household demand for fruit is generally inelastic with respect to own price. As shown in Tables 4 and 5, which reports the estimated Marshallian (uncompensated) price elasticities for 2021 and 2020, respectively, the own-price demand elasticities range from −0.377 for all other fruits to −0.843 for citrus fresh (Table 4 for 2021) and −0.320 for all other fruits to −0.737 for citrus fresh (Table 5 for 2020). These numbers also show that own-price elasticities are slightly smaller in magnitude in 2020 than in 2021, indicating household purchases were less responsive to price changes during the height of the COVID-19 pandemic. However, results for both years continue to be consistent with estimates reported for total fruit in previous studies: −0.43, −0.70, and −0.55 reported by Park et al. (1996), Huang and Lin (2000), and Dong and Lin (2009), respectively. Estimates previously reported for all citrus fruit include −0.65 (Huang, 1993) and −1.10 (Okrent and Alston, 2012). Estimates reported in the literature for specific types of fruit are notably higher. For example, those reported for oranges include −0.85 (Huang, 1993), −0.67 (Brown and Lee, 2002), and −0.79 (Durham and Eales, 2010).

Table 4. Marshallian price and expenditure elasticities of fruits, 2021

Note: Bold numbers represent “significant” at 5 percent or above.

Table 5. Marshallian price and expenditure elasticities of fruits, 2020

Note: Bold numbers represent “significant” at 5 percent or above.

The Hicksian (compensated) price elasticities contained in Tables 6 and 7 are essential input information in quantifying the consumer welfare effects of price changes. These are calculated using the Slutsky equation from the Marshallian price elasticities and the total expenditure elasticities and hold utility constant. The compensated own-price elasticities are smaller in magnitude than their Marshallian (uncompensated) counterparts and range from −0.155 for all other fruits to −0.749 for citrus fresh for 2021. Similar to the Marshallian price elasticities, these Hicksian own-price elasticities are smaller in magnitude in 2020 than their counterparts in 2021.

Table 6. Hicksian price elasticities of fruits, 2021

Note: Bold are statistically significant at the 5-percent level or above.

Table 7. Hicksian price elasticities of fruits, 2020

Note: Bold are statistically significant at the 5-percent level or above.

U.S. households also have only a limited willingness to substitute between different types of fruit when prices change. Positive off-diagonal values in Table 4 or 5, indicate that two types of fruit are gross price substitutes. For example, a 10-percent increase in the price of citrus liquid would increase purchases of other liquid by 1.76% for 2021 (Table 4). The Hicksian (compensated) cross-price effects reported in Tables 6 and 7 are slightly larger than their gross counterparts. A 10-percent increase in the price of citrus liquid would increase compensated purchases of other liquid by 2.96% percent for 2021. Other liquid and other fresh are also substitutes.

Conditional expenditure and income elasticities

The estimated income and expenditure elasticities for 2021 reported in Table 8 reveal how changes in income may affect U.S. household fruit demand. Results for the first stage of a household’s multistage budgeting process confirm a positive Engel curve relationship between income and total fruit expenditures. A 1% increase in income increases total fruit spending by 0.18%, on average, which is very close to Lin et al (2009)’s finding of 0.19%. This result is also statistically significant at the 1% level. Results for the second stage of a household’s budgeting process are reported in the first column of Table 8 and further reveal how a change in conditional expenditures, in turn, affects demand for each type of fruit in the system. A 1% increase in total fruit expenditures increases citrus fresh spending by 1.09%, spending for citrus liquid by 1.11%, spending for other fresh by 0.94%, spending for other liquid by 0.84%, and spending on all others 0.89%. Finally, our first and second-stage results are combined to estimate unconditional income elasticities of demand. Each expenditure elasticity in the first column is multiplied by the 0.18% Engel Curve effect. As shown in the second column of Table 8, a 1% increase in income increases a household’s expenditures on citrus fresh by 0.19%, and citrus liquid by 0.20%. Results for 2020 are similar and available upon request.

Table 8. Fruit Income Elasticities of Sampled Households, 2021

Household demographic elasticities

In addition to prices and income, U.S. fruit demand also varies across households with their demographic characteristics. Following past studies, as mentioned above, we account for a variety of these demographic characteristics. Elasticities with respect to those variables for 2021 are provided in Table 9. Household size is found to have a positive effect on demand for citrus liquid but a negative effect on demand for other liquid. Education negatively (positively) affects demand for citrus (other) liquid. Results for 2020 are similar and available upon request.

Table 9. Demographic elasticities of fruit expenditure shares, 2021

Note: Bold numbers are significant at the 5-percent level or above. Numbers for the dummy variables are the percentage change in the shares when the variables change from 1 to 0. The region base is Northeast.

Household welfare simulations

Any further spread of HLB or other diseases or pests could negatively affect US fruit production. Parallel changes in overseas production would serve to amplify any impacts on domestic production. Below, using equation (7), we calculate the change in household welfare associated with some retail price increase scenarios. Our estimated welfare changes are in nominal dollars and will depend on initial prices, initial quantities, and our assumed demand elasticities as shown in the formula. We report two sets of simulations for the purpose of comparison. The first shows the impact on household welfare if the retail price increases were to occur when demand conditions are similar to those observed in 2021. It is based on our results using 2021 NCP data and the initial conditions reported in Table 1 for that same year. The second shows the impact on household welfare if the price increases were to instead occur in an environment more like 2020. It is based on our results using 2020 NCP data and the initial conditions reported in Table 2. Fruit prices were generally higher in 2021 ($0.139 per ounce) than in 2020 ($0.136 per ounce) (Tables 1 and 2). However, on average, U.S. households purchased slightly less fruit, including less citrus juices, such as orange juice, in 2021 than in 2020.

For our first price change scenario, we consider a 10% increase in the price of any single fruit category, holding other fruit prices constant (Tables 10 and 11). As mentioned above, retail juice prices were up to more than 20% in early 2023 over peaks reached in 2016. To be conservative, we simulate the impact of 10% price increases. Shown in the first column of Tables 10 and 11 are the effects of a 10% increase in the price of only citrus fresh. The total welfare (CV) is $0.90 for 2021 and $0.77 for 2020. Bringing households back to their initial level of utility would require increasing their average total fruit expenditures by these amounts. For 2021, this includes a $0.34 increase in compensated expenditures (individual CV) for citrus fresh (due to its compensated own-price effect), $0.33 for citrus liquid (due to its compensated cross-price effect), −$0.22 for other fresh, $0.22 for other liquid, and $0.22 for all others. The negative compensated expenditure change for other fresh (−$0.22) is due to the negative compensated cross-price elasticity between citrus fresh and other fresh, a complement relationship between the two. An increase in only citrus liquid prices would have a similar impact on household welfare as shown in the second column of Table 10 for 2021. Increasing the price of these products by 10% would reduce household total welfare by $1.13. This includes a $0.48 increase in compensated expenditures for citrus liquid (due to its compensated own-price effect), $0.32 for citrus fresh (due to its compensated cross-price effect), −$0.51 for other fresh, $0.69 for other liquid, and $0.15 for all others.

Table 10. Change in compensated expenditures (compensating variation) needed to maintain household utility after A 10% price increase in individual fruits ($), 2021

Table 11. Change in compensated expenditures (compensating variation) needed to maintain household utility after A 10% price increase in individual fruits ($), 2020

By comparing Tables 10 and 11, we see that the simulated welfare losses for 2021 and 2020 are generally similar in size. One notable difference between the two sets of simulations is the effects of an increase in citrus liquids prices. This is due in large part to households’ greater demand for citrus juices in 2020 as compared with 2021.

For our second price change scenario, we examine the loss in consumer welfare that could occur if price for all or some types of fruit were to simultaneously increase. Thus, we calculated the CV for each of the fruits for two scenarios: (1) when prices of all five fruit product categories increased by 10%, and (2) when prices of two products, citrus fresh and citrus liquid, increased by 10% at the same time. The results are provided in Tables 12 for 2021 and 13 for 2020. In scenario (1), the consumer welfare loss is $17.05 for 2021 and $16.92 for 2020. In scenario (2), the consumer welfare loss is $1.89 for 2021 and $1.83 for 2020. The welfare loss in these two scenarios for 2021 and 2020 are again similar.

Table 12. Change in compensated expenditures (compensating variation) needed to maintain household utility after A 10% price increase in all or combined fruits ($), 2021

Table 13. Change in compensated expenditures (compensating variation) needed to maintain household utility after A 10% price increase in all or combined fruits ($), 2020

Conclusions

Researchers around the world are working to cure and mitigate the effects of HLB while U.S. states with commercial citrus production do their best to control spread of the disease. Any further spread of HLB could reduce supply of US domestic as well as foreign-grown citrus fruit while any cure could increase supply. It is currently unknown what the future holds. As such, in this study, we estimate a QUAIDS model for U.S. household fruit demand to provide the information needed to understand households’ likely responses to future fruit price changes as well as the tools needed to calculate how their welfare might be affected. The method we present for calculating CV in this study can be adapted using the reported Hicksian elasticities to account for actual future events. It does not require calculating the expenditure function. Overall, the welfare losses reported in this study are relatively small compared to those reported by Dong et al. (2022) for meat products, which reflects differences in U.S. household demand for each type of food. For example, if demand conditions for fruit were like those in 2021, a 10% increase in cut or whole citrus fruit prices would reduce U.S. household welfare by $0.90. Looking to the future, as the size and direction of coming price changes may be different, it may be necessary to accordingly re-calculate the CV.