Essays on the Dual-Economy

UNIVERSITY OF BRITISH COLUMBIA Essays on the Dual- Economy This is a prospectus for a thesis in Economics Amlan Das Gupta 10/31/2011 I would like to gratefully acknowledge invaluable help and guidance from Dr Mukesh Eswaran in the making of this prospectus. This is a prospectus for a thesis which will contain three essays. Essay 1 Introduction This essay investigates some of the general equilibrium consequences of conspicuous consumption in a developing country. In 1899 in his book titled “The Theory of the Leisure Class” Thornstein Veblen introduced the idea of conspicuous consumption into economics. Although similar ideas were also voiced by Smith almost 150 years before that, Veblen was perhaps the first to realise the role of visible consumption as a signal of one’s status. Status seeking behaviour is very common amongst the human race and one of the most important determinants of status is wealth. While it is difficult to communicate one’s true wealth level by one’s appearance, visible consumption may provide hints that are easily picked up by others. In some cases people might even be able to make themselves appear wealthier than they really are. This status-seeking behaviour has potentially significant consequences for the economy. In particular when all members of society are pursuing status through conspicuous consumption they are likely to compete with each other, leading to a further escalation in such consumption. Such competition often has interesting effects. Coelho (1985) and Cooper et al (2001) have used this phenomenon to motivate economic growth in their models. Higher income leads a person to buy more status goods which in turn inspires more investment in them. Hopkins and Korienko (2004) in a theoretical model investigate the consequences of a change in income distribution in the presence of Veblen preferences. They show that when the society gets richer almost everybody consumes more of the Veblen good and utility declines at every income level. Empirical papers have also tested some implications of this phenomenon. Luttmer (2005) and Charles et all (2009) are examples of this. In the former Luttmer shows that happiness of a person is inversely related to the income of her neighbourhood. Charles et all use the fact that race is a negative signal for status and the so-called poorer races have to spend more on conspicuous consumption to make up for this handicap. As expected, they find that the differences in spending on visible consumption by race can be explained by the average incomes of the particular race. This paper is looking to investigate the effects of status-seeking behaviour in the context of a dual economy. The concept of dual economy, first introduced by Arthur Lewis in 1954, is frequently used to model developing economies. This classic model tells the story of development in dual economies where better technologies in the industrial sector draws out labour from the agricultural sector, eventually raising incomes in both sectors. This model naturally introduces heterogeneity in the economy which is a setting where Veblen competition becomes more potent. The most interesting question to investigate is what the consequences of growth are in the economy with status-seeking agents. Labour allocation across the sectors, consumption of the agricultural/industrial good and the welfare implications should all be affected. In this paper I investigate all these aspects. One interesting fall-out of conspicuous consumption is that with the rise in income, when the society’s consumption of the industrial/Veblen good is going up, agents might have to dig into their budget for food to try and keep up. This brings us to one of my main motivations behind this paper. In Deaton and Dreze (2009) the authors present empirical evidence that in India per-capita calorie consumption has been falling even as real incomes are increasing. This has been the case in spite of India being one of the fastest growing economies in the last two decades and in spite of the relative price of food remaining more or less constant. This is a very puzzling finding since the fall in calorie consumption is observed for almost all income groups. In our closed economy model we show that if the growth in the economy is such that the relative price of food remains constant we are going to have a fall in the food consumption of all income groups as long as all income groups are consuming at least some of the Veblen good. Although this is just one possible explanation for the calorie-puzzle it is worth considering since levels of conspicuous consumption in India are reaching disturbing levels, as reported by newspapers and the media. Next I extend our simple dual economy model to a small open economy setting. Here again I investigate the possibility of a fall in food consumption in response to rise in productivity. Here I find that calorie consumption falls as a response to any rise in productivity in either sector. The paper is arranged as follows: the second section presents the model, section 3 discusses the results and the last section concludes and talks about further questions that could be pursued. Model In this section I present a simple two sector general equilibrium model based on Eswaran-Kotwal (1993). There are two goods, food and some industrial good which is also used as a signal of wealth. Also there are two income groups given by landowners and simple labourers. In the first part of this section I discuss the preference structure that I assume. Preference Structure: The preference structure must reflect the characteristics of an agent living in a poor developing economy and also the tendency to seek status using conspicuous consumption. In order to account for the first aspect I use a quasi-linear preference which is linear in the industrial good. Here X is food and Z the industrial good; lower case denotes quantities of these goods. is an increasing and strictly concave function which is followed by a term linear in Z. The interesting characteristic of this utility function is that it implies that at lower levels of consumption of X marginal utility will be higher than that from the industrial good (which is a constant). So until agent’s marginal utility from X has fallen to there will be no consumption of Z. Also after the marginal utilities have been equalised, all extra income will go into consumption of Z. This feature is very apt description of preferences in poorer areas where initially agents devote all their income to subsistence requirements. Luxury goods and other non-necessary goods are consumed only after the basic needs have been fulfilled. In order to incorporate status seeking behaviour in the model I add another term to the utility function which depend on the average Z consumption of the economy . There are various ways to incorporate Veblen preferences (see Eaton and Eswaran 2009). The general function that we use here only says that utility of the agent falls with and rises with own Z consumption. But due to the assumed concavity it also means that the marginal utility from Z consumption rises with . As we shall see in more detail in what follows, this is the most important thing that we need for our results. Partial Equilibrium Analysis: In this section I present some insights that may be gained by examining the consequences of the above preference structure in a partial equilibrium setting. Here we assume that X is the numeraire good and the relative price of Z is given by p. Also assume that there are two income groups with incomes and is just the average Z consumption of the two groups. Proposition 1: Demand for the industrial good (food) of the poorer group is rising (falling) with the rise in the richer group’s income as long as the poor are consuming some industrial good. Proof: This can be shown for any general utility function of the form assumed above. The agent’s problem is as follows: Taking the Lagrange multiplier to be λ we have the first order conditions as follows: This of course assumes that the poor have enough money to consume some Z. Then we have: i v y2 The above is always positive given the assumptions on the utility function and that Z goes up with the agent’s own income. From the budget constraint the second part of the proposition follows. When goes up it increases the other agent’s demand for Z. This pushes up the marginal utility of Z consumption for the first agent and so drives down her threshold for the consumption of X. So if the agent was at her threshold previously she will now have some part of her income free to consume Z. So a rise in leads to lowering of the income level at which Z consumption begins for the poorer group. An off shoot of this is the next proposition: Proposition 2: The lowest income, at which an agent begins to consume industrial good, falls with income of the other agent. Proof: This can also be demonstrated using the general utility function described in proposition 1. If demand for Z is barely 0 then equation 1 above reduces to the following: So, Is the critical value of income at which the poor start consuming Z The above is again negative using the assumptions on the utility function and that Z is a normal good for all agents. From this point onwards I will be using the following specialized form for the utility function in order to simplify analysis: I should point out that the part representing utility from X has to be such that marginal utility from X falls fast and agents achieve satiation with grain.

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