Hicksian Elasticities Research Articles

Validating LA/AIDS model in the food market of Pakistan

The study aims to conduct a consumer demand analysis of the food market of Pakistan by estimating its own price and cross-price elasticities. This study also examines expenditure and income elasticities to show the influence of relative change in price, total expenditure, and income on the relative change in demanded quantities of the selected food products. The study takes meat, vegetables, fruits, and pulses as different food baskets and estimates income elasticities, including uncompensated (Marshallian) and compensated (Hicksian) own price and cross-price elasticities. The findings are concluded based on Marshallian elasticity as it provides more accurate images of substitutes and complements compared with Hicksian elasticity. The study applies the Linear Approximate Almost Ideal Demand System model to estimate the results by acquiring data from a household integrated economic survey of Pakistan from 2018 to 2019. The findings of expenditure elasticity (uncompensated own price elasticity) reveal that vegetables and pulses are normal (inelastic) goods, whereas meat and fruits are luxury (elastic) goods. The results of uncompensated cross-price elasticities reveal that vegetables and meat, and vegetables and fruits are substitutable commodities. In addition, pulses and vegetables, and pulses and meat are complementary goods. The study suggests fruitful implications for food policymakers.

Demand for selected plant-based protein among the staff of a tertiary institution in Nigeria

Increasing demand for animal protein has a negative consequences human health and the environment. Thus, the need for a replacement of animal protein with plant-based protein in human diet. The demand for selected plant-based protein (PBPs) (soybean, mushroom, potato, and cowpea) was therefore assessed. Data collected from 343 staffers of university of Ibadan were analysed using descriptive statistics and Quadratic Almost Ideal Demand System. Mushroom and soybean were luxury goods but demand for mushroom was more elastic than soybean. Potato was considered a necessary good. Expenditure elasticity for cowpea was however found to be just unitary. The selected plant-based proteins were normal goods. Furthermore, all the compensated own-price elasticities (except mushroom) were less than one (in absolute terms) indicating that they are price-inelastic. They ranged between (-0.14) for soybean and (-0.62) for potato. Hicksian elasticities showed that mushroom was a substitute for cowpea and potato. Cowpea and potato were also substitutes to each other. Socio-economic factors influencing demand were years of schooling, access to market, prices of the PBPs and marital status of the respondent.

The substitutability of slaves: Evidence from the eastern frontier of the Cape Colony

ABSTRACT The substitutability of the economic institution of slave labour has often been assumed as a given. Apart from some capital investment to retrain slaves for a different task, essentially their labour could be substituted for any other form of labour. This paper questions that assumption by using a longitudinal study of the Graaff-Reinet district on the eastern frontier of South Africa’s Cape Colony. We calculate the Hicksian elasticity of complementarity coefficients for each year of a 22-year combination of cross-sectional tax datasets (1805–1828) to test whether slave labour was substitutable for other forms of labour. We find that slave labour, indigenous labour and settler family labour were not substitutable over the period of the study. This lends credence to the finding that slave and family labour were two different inputs in agricultural production. Indigenous khoe labour and slave labour remain complements throughout the period of the study even when khoe labour becomes scarce after the frontier conflicts. We argue that the non-substitutability of slave labour was due to the settlers’ need to acquire labourers with location-specific skills such as the indigenous khoe, and that slaves may have served a purpose other than as a source of unskilled labour, such as for artisan skills or for collateral.

Food Price Subsidy and its Effects on Poverty in Khyber Pakhtunkhwa, Pakistan

We estimate the effect of food price subsidy on poverty in Khyber Pakhtunkhwa, Pakistan in this paper. The study uses Linear Approximate Almost Ideal Demand System for the estimation of compensated and uncompensated price and expenditure elasticities of food using Household Integrated Economic Survey. The estimated own and cross price Hicksian elasticities are used for estimating the changes in the quantity of food consumed, expenditure on food and its effect on poverty. The study uses two recent available poverty lines for estimation, showing that the scheme of food price subsidy increase real income of the households which has a decreased poverty state. The analysis shows that the subsidy program marginally decreases poverty in the province. The study recommends targeted food price subsidy for poverty alleviation and eradicating chronic hunger.

Aggregating Elasticities: Intensive and Extensive Margins of Women's Labor Supply

We show that there is substantial heterogeneity in women's labor supply elasticities at the micro level and highlight the implications for aggregate behavior. We consider both intertemporal and intratemporal choices, and identify intensive and extensive responses in a consistent life‐cycle framework, using US CEX data. Heterogeneity is due to observables, such as age, wealth, hours worked, and the wage level, as well as to unobservable tastes for leisure: the median Marshallian elasticity for hours worked is 0.18, with corresponding Hicksian elasticity of 0.54 and Frisch elasticity of 0.87. At the 90th percentile, these values are 0.79, 1.16, and 1.92. Responses at the extensive margin explain about 54% of the total labor supply response for women under 30, although this declines with age. Aggregate elasticities are higher in recessions, and increase with the length of the recession. The heterogeneity at the micro level means that the aggregate labor supply elasticity is not a structural parameter: any aggregate elasticity will depend on the demographic structure of the economy as well as the distribution of wealth and the particular point in the business cycle.

Endogenous capital depreciation and technology shocks

I examine the dynamic impact of capital maintenance on key aggregates through the depreciation rate. I find that two factors are crucial for the short-run effects of Total Factor Productivity and Investment-Specific shocks: (i) the marginal efficiency of maintenance and its connection with the rate of utilization, and (ii) the interplay between the intertemporal effect of maintenance and the substitution effect between maintenance and utilization. The latter is expressed by the relative size of the elasticity of maintenance to the Hicksian elasticity of complementarity between maintenance and utilization. These theoretical results suggest that to match the observed responses of the macroeconomic aggregates the sign of the cross derivative should be negative and that the relative size of the Hicksian elasticity should be smaller than the maintenance elasticity of marginal depreciation. Finally, the model suggests that the main macroeconomic aggregates react procyclically, with the exception of maintenance, the behavior of which depends on the type of the shock.

Subsistence, Substitutability and Sustainability in Consumption

We propose a representation of individual preferences with a subsistence requirement in consumption, and examine its implications for substitutability and sustainability. Specifically, we generalize the standard constant-elasticity-of-substitution (CES) utility specification for manufactured goods and environmental services, by adding a subsistence requirement for environmental services. We find that the Hicksian elasticity of substitution strictly monotonically increases with the consumption of environmental services above the subsistence requirement, and approaches the standard CES value as consumption becomes very large. Whether the two goods are market substitutes depends on the level of income. We further show that the subsistence requirement may jeopardize the existence of an intertemporally optimal and sustainable consumption path. Our results have important implications for growth, development and environmental policy.

Discussion

Discussion

Abstracts

Abstracts

Subsistence and Substitutability in Consumer Preferences

We propose a representation of individual preferences with a subsistence requirement in consumption, and examine its implications for substitutability and sustainability. Specifically, we generalize the standard constant-elasticity-of-substitution (CES) utility specification for manufactured goods and environmental services, by adding a subsistence requirement for environmental services. We find that the Hicksian elasticity of substitution strictly monotonically increases with the consumption of environmental services above the subsistence requirement, and approaches the standard CES value as consumption becomes very large. Whether the two goods are market substitutes depends on the level of income. We further show that the subsistence requirement may jeopardize the existence of an intertemporally optimal and sustainable consumption path. Our results have important implications for growth, development and environmental policy.

Does Indivisible Labor Explain the Difference between Micro and Macro Elasticities? A Meta-Analysis of Extensive Margin Elasticities

Macroeconomic calibrations imply much larger labor supply elasticities than microeconometric studies. One prominent explanation for this divergence is that indivisible labor generates extensive margin responses that are not captured in micro studies of hours choices. We evaluate whether existing calibrations of macro models are consistent with micro evidence on extensive margin responses using two approaches. First, we use a standard calibrated macro model to simulate the impacts of tax policy changes on labor supply. Second, we present a metaanalysis of quasi-experimental estimates of extensive margin elasticities. We find that micro estimates are consistent with macro evidence on the steady-state (Hicksian) elasticities relevant for cross-country comparisons. However, micro estimates of extensive-margin elasticities are an order of magnitude smaller than the values needed to explain business cycle fluctuations in aggregate hours. Hence, indivisible labor supply does not explain the large gap between micro and macro estimates of intertemporal substitution (Frisch) elasticities. Our synthesis of the micro evidence points to Hicksian elasticities of 0.3 on the intensive and 0.25 on the extensive margin and Frisch elasticities of 0.5 on the intensive and 0.25 on the extensive margin.

Sistemas de equações de demanda por carnes no Brasil: especificação e estimação

Especificações alternativas do sistema de demanda quase ideal (AIDS) foram utilizadas para estimar as demandas agregadas das carnes bovina, suína e de frango e outros bens de consumo e as suas elasticidades no Brasil. Detectada a necessidade de se utilizar a variável tendência nas equações dos modelos, observou-se uma tendência de crescimento da demanda por carnes e de decrescimento da demanda por outros bens de consumo. A variável dummy para o Plano Real indicou que o mesmo não afetou as demandas. Com base nas elasticidades próprios-preços Marshallianas, as demandas por carnes são inelásticas e a demanda por outros bens de consumo é elástica. As elasticidades preços-cruzados Marshallianas e Hicksianas confirmaram que as carnes bovina, suína e de frango são bens substitutos. As elasticidades-gasto indicaram que todos os bens são normais, exceto a carne suína que é um bem inferior. Como é provável que o gasto com o consumo das famílias aumente ao longo do tempo, ceteris paribus, as elasticidades gasto indicam que a demanda por carnes perderá importância para os outros bens de consumo, que o consumo de carne bovina perderá importância para a carne de frango e que o consumo de carne de porco perderá importância para as outras carnes.

Optimal commodity taxation for reduction of envy

This paper derives optimal commodity taxes in a two-class economy based on λ-equitability. An allocation is λ-equitable if no agent envies a proportion λ of the bundle of any other agent. We examine the properties of Pareto undominated allocations in a class of λ-equitable allocations. We first show that the consistency between envy reduction and enhancement of the low-skilled agent’s utility depends on 1) the income elasticity of leisure 2) the degree of preference and skill differences. On the optimal tax rule, we can show the following. When the envy constraint is binding, ceteris paribus, the goods preferred by the low skilled agent and of high Hicksian elasticities are taxed more heavily. The optimal commodity tax is uniform if, in addition to weak separability, sub-utility of the goods is homothetic.

Optimal non-linear income taxation for reduction of envy

This paper examines the optimal non-linear income taxation problem based on λ-equitability. An allocation is λ-equitable if no agent envies a proportion λ of the bundle of any other agent. We examine the properties of Pareto undominated allocations for various λ-equitability requirements. When there is one output, the marginal income tax rate can increase only if leisure is a luxury. In a multi-commodity model with commodity taxes, the goods preferred by the low skilled agent and/or those with high Hicksian elasticities are taxed more heavily. When preferences exhibit quasi-linearity, we can show that the introduction of the λ-equitability constraint increases the marginal income tax rates of the entire population.

Unemployment as a constraint on labour supply and goods demand in Spain

In this paper the implications of unemployment on labour supply and goods demand functions in Spain are analysed during the period 1964–91. To this end, the labour supply and goods demand is jointly modelled using a dynamic linear expenditure system under the condition that labour supply has been rationed due to the increasing number of unemployed in the last three decades. After proof that the model exhibits neither autocorrelation nor dynamic heteroscedasticity problems, it is found that food, beverages and tobacco, gross rent, fuel and power and miscellaneous goods are necessities, while other goods are luxuries. Labour has an expenditure effect below zero. The own-price Marshallian and Hicksian elasticities are negative for consumption goods and positive for labour, and indicate that all consumption goods are price inelastic. Finally, the cross-price values indicate that the goods are complementary.

The Structure of Forestry Production: Short-Run and Long-Run Results

Abstract This paper extends the study of regional forestry production to address long-run production possibilities using a restricted profit function approach. The model consists of two outputs, sawtimber and pulpwood; one variable input, regeneration effort; and two quasi-fixed inputs, land and growing stock. Estimation is performed using cross-sectional data of industrial timber production in the southeastern United States. Estimated values include own- and cross-price elasticities between inputs and outputs, Hicksian elasticities of substitution, shadow prices of the quasi-fixed factors, and long-run Marshallian elasticities. While short-run supply elasticities are consistent with earlier studies, long-run results show much greater supply responses as land and management inputs are given time to adjust. These results also suggest that ambiguous results regarding pulpwood and sawtimber substitutability found in previous studies can be explained by a shift from complementarity in the short run to substitutability in the long run. For. Sci. 37(2):540-551.

A Revenue-Function Approach to the Measurement of Output-Substitution Possibilities in Agriculture

The purpose of this article is to calculate Hicksian and Marshallian estimates of output-substitution possibilities in an agricultural industry. The Hicksian elasticities or net substitution possibilities are measured within a revenue-maximizing framework holding input levels constant. The Marshallian elasticities that encompass both net substitution and expansion effects are measured within a profit-maximizing framework allowing both output and input levels to vary. The results are empirically reasonable and consistent with the duality theory for revenue and profit maximizing behavior. A notable empirical result is that, in the very short run or market period with input levels held constant, there exists considerable scope for changing the output composition between crops and cattle on cattle farms.

Estimating Substitution and Expansion Effects: Reply

Hertel's major point is that some of my estimates (Lopez) would violate predicted outcomes based on economic theory. These outcomes correspond to the so-called normal case as discussed by Hicks and others. Two types of normal outcomes are violated by my results, namely the gross input complementarity condition and the requirement that gross or Marshallian own-price elasticities need to be larger (in absolute values) than compensated or Hicksian elasticities. The gross complementarity condition does not follow from the theory of the profit-maximizing firm. It rather arises from assumptions regarding second derivatives of the production or transformation functions (i.e., cross-second derivatives among inputs are positive). The second set of conditions does follow from the theory of the firm, and its violation may suggest inconsistency between the estimated results and the underlying model. Therefore, these two sets of conditions are based on fundamentally different sources: the former depends on superimposed assumptions about the production technology on the profit maximization model, while the latter is inherent to the model. Hence, the evaluation of estimated elasticities using the first set of conditions is a dubious procedure since there is no a priori reason to assume that the technological assumptions underlying these conditions are of general validity, particularly in the multi-input, multi-output context.' Rather, the more reasonable approach would be to use empirical estimates to verify the degree of generality of such assumptions. With respect to the second set of conditions, I believe that they constitute sensible criteria for the evaluation of empirical estimates that are based on the profit-maximizing model. Their violation may reflect that the profit-maximizing model is inadequate, data problems, aggregation problems, etc. In my estimates this condition is not satisfied by the land and structures input when its own-price elasticities are evaluated at mean values of the variables. As discussed in the 1984 article (p. 364) the land and structures input is likely to suffer from measurement problems. It appears that the adjustments for land and structure quality were insufficient mainly due to the lack of data on qualitative aspects of structures. It is also interesting to indicate, however, that this condition is not violated at all sample points. In fact, when the elasticities are evaluated at about 25% of the sample points, the own gross-price elasticities of land and structures are greater in absolute value than the compensated elasticities, as the profit-maximization hypothesis implies.