Existence of competitive equilibrium in a single-sector growth model with heterogeneous agents and endogenous leisure

We prove the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents and elastic labor supply. The method of proof relies on exploiting the existence of Lagrange multipliers in infinite dimensional spaces and the link between Pareto-optima and competitive equilibria.Optimal growth model, Lagrange multipliers, single-sector growth model, competitive equilibrium, elastic labor supply.

Response of prime lambs to dietary omega-3-rich oils: impact on meat quality

This thesis investigated the responses of confined and grazing weaner prime lambs to dietary omega-3 (n-3) polyunsaturated fatty acids (PUFA)-rich oil supplementation with regards to animal performance, carcass characteristics, feed conversion efficiency, feed costs and fatty acid profiles of longissimus dorsi muscle, liver, kidney and heart. The primary objectives were to systematically investigate and collect scientific evidence on the nutritional enhancement of health beneficial omega-3 long chain polyunsaturated fatty acids (n-3 LC-PUFA) content of confined and grazing weaner lambs supplemented with or without canola, rice bran, flaxseed, rumen-protected and safflower oil-infused pellets and to evaluate the cost of producing premium quality lamb relative to liveweight gain. Two on-farm experiments representing both indoor lot-fed and outdoor grazing production systems, were conducted to achieve the overarching objectives of the thesis. In Experiment 1 (indoor confined production system), seventy-two, 6 months old, White Suffolk x Corriedale first-cross weaner prime lambs were randomly assigned to six treatment groups: (1) Control: Lucerne hay only; wheat-based pellets infused with 50 ml/kg dry matter (DM) of oil from (2) rice bran (RBO); (3) canola (CO); (4) rumen-protected (RPO), (5) flaxseed (FSO) and (6) safflower (SO) dietary sources in a completely randomized experimental design. All lambs had ad libitum access to lucerne hay and clean fresh water and supplemented lambs were fed 1 kg of pellet/head/day for 10 weeks after three weeks of adaptation. Data on daily dry matter feed intake, weekly liveweight and body conformation measurements were recorded. At the end of the feeding trial, all lambs were humanely sacrificed at a commercial abattoir, carcass characteristics evaluated and samples of the longissimus dorsi muscle, heart, liver and kidney were taken. Fatty acid profiles of sampled tissues and organs were analysed by gas chromatography and gas chromatography mass spectrometry. All data were analysed in SAS utilising both general linear (PROC GLM) and mixed model (PROC MIXED) procedures with repeated measures that adjusted for fixed, random and interaction effects. Supplementation of confined lambs resulted in improvement of dry matter feed intakes, lamb performance and carcass characteristics. RBO and CO treatments had lower feed costs and similar indices of lamb performance, carcass characteristics and over the hooks trade (OTH) incomes compared with other treatment groups. Eicosapentaenoic acid (EPA, 20:5n-3) and docosahexaenoic acid (DHA, 22:6n-3) contents of the longissimus dorsi muscle of lambs supplemented with CO, FSO, SO and RPO were above the 30 mg per standard serve threshold for omega-3 "source" claim under the Foods Standard Australia and New Zealand (FSANZ) guidelines. The ≥C₂₀ n-3 LC-PUFA contents of the longissimus dorsi muscle did not differ among supplemented confined lambs. However, variation in fatty acid contents among and between different organs and tissues was observed and the liver and kidney could be labelled as 'good source' (above 60 mg per standard serve threshold) of n-3 LC-PUFA. From the results in Experiment 1, the following research questions needed to be answered: 1. Given that CO and RBO were the cheapest supplements, was there any added advantage of supplementing lambs grazing lucerne and cocksfoot pastures with CO and RBO oil-based pellets in enhancing EPA+DHA contents in the muscle tissue and organs? 2. Could animal performance, carcass traits, feed conversion efficiency and OTH trade incomes of grazing lambs be improved by additional supplementation with RBO and CO? Experiment 2 was designed to answer these questions. Therefore, forty-eight White Suffolk x Corriedale first-cross weaners were randomly allocated to one of the following four treatments in a split-plot experimental design: (1) Cocksfoot cv. porto (CFP) or lucerne pastures only (control); (2) CFP or lucerne pastures supplemented with pellets infused with oil from (3) canola (CO); (4) rice bran (RBO) or no oil pellets (NOP). Lucerne and CFP pastures were considered as the main plot effects and pellet supplementation as a sub-plot effect in a feeding trial that lasted for nine weeks. The findings demonstrated that animal performance and carcass characteristics of lucerne grazing lambs were not affected by pellet supplementation. However, lambs grazing CFP and supplemented with CO had lower feed conversion efficiency (FCE) and higher OTH trade income than CFP only grazing lambs. Lucerne grazing lambs had higher average daily gain, hot carcass weight and OTH trade income than CFP grazing lambs. The addition of pellets to the diet of grazing lambs generally decreased α-linolenic acid (ALA, 18:3n-3) and n-3 LC-PUFA contents and increased the n-6/n-3 ratio in the longissimus dorsi muscle. Different types of pastures and pellet supplementation affected the fatty acid profiles of organs and tissues of grazing lambs. For instance, ALA, 20:3n-6, EPA, PUFA, n-3 PUFA, and n-6 PUFA contents in longissimus dorsi muscle of lucerne grazing lambs were higher than in CFP grazing lambs. Variation in fatty acid contents in different organs of grazing lambs indicated that the liver and kidney can be used as 'good sources' of n-3 LC-PUFA. Cocksfoot cv. porto produced premium quality, healthy lambs with high contents of ALA and n-3 LC-PUFA. Taken together, dry matter feed intake, animal performance, carcass characteristics and fatty acid profiles of confined lambs were improved by supplementation with PUFA-rich, oil-infused pellets. RBO and CO can be used to improve n-3 LC-PUFA contents in the longissimus dorsi muscle of confined lambs at low feed costs, with comparable indices of animal performance and carcass characteristics with other sources of PUFA. Supplementation of CFP grazing lambs with CO can be used as a strategic nutrition tool for increasing OTH income with low FCE. CFP also demonstrated the potential for producing premium quality, healthy lambs. Recommended future studies should focus on: 1) Whole farm production cost-benefit analysis; 2) Marketing omega-3 labelled lamb products; 3) Investigating potential new pasture varieties for improving n-3 LC-PUFA content of grazing lambs; and 4) Better understanding of the rumen biohydrogenation pathways in grazing lambs

Existence of competitive equilibrium in an optimal growth model with heterogeneous agents and endogenous leisure

This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents, elastic labor supply and complete assets markets. The method of proof relies on some recent results concerning the existence of Lagrande multipliers in infinite dimensional spaces and their representation as a summable sequence and a direct application of the inward boundary fixed point theorem.Optimal growth model, Lagrange multipliers, competitive equilibrium, individually rational Pareto Optimum, elastic labor supply.

Non-convex Aggregate Technology and Optimal Economic Growth

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state equilibrium toward which the convergence of the optimal paths is monotone and asymptotic. When the discount rate is in some intermediate range, we find sufficient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, the optimal paths converge to one single appropriate equilibrium steady state. This state might be a poverty trap with low per capita capital, which acts as the extinction state encountered in earlier studies focused on S-shapes production functions. Second, we consider the case of linear utility and provide sufficient conditions to have either unique or two steady states when the discount rate is in some intermediate range . In the latter case, we give conditions under which the above critical value might not exist, and the economy attains one steady state infinite time, then stays at the other steady state afterward.Non-convex agreggative technology - optimal economic growth - steady state

Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor

The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.Single-sector growth model, heterogeneous agents, elastic labor supply.

Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor

The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.Single-sector growth model, heterogeneous agents, elastic labor supply, supermodularity