Consumption Decision among Tobacco and Food
Introduction
Consumption behavior is a key issue in micro Economics. Utility theory and indifference curve are the fundamental tools in analyzing people’s consumption decision. This essay would take a simplified example, consumption decision in working place with only two goods, to explore how people allocate resource to different goods under different constraints.
Firstly, derive the budget constrain for both workers. Suppose they could consume X unit of food and Y unit of tobacco, and thus the expenditure should with the amount of allowance,
X + Y ≤ 100
In the following graph, X axis stands for the units of food consumed, while Y axis stands for the tobacco consumed, then the dash area represents the feasible consumption combination for the workers.
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For the worker who does not smoke, the situation is relatively simple. Because he does not smoke, his indifference curve is vertical, and he would spend all his allowance on food, and the feasible area shows that he could consume from 0 unit to 100 units of food. Since the consumption of food is the more the better, this worker would choose to consume 100 units of food, represented by point A.

For the worker who smokes, the situation is a little more complicated, for the indifference curve needs to be derived to determine his consumption decision. An indifference curve is the graph representing different consumption combination of goods that brings the same utility for the consumer, in other words, between which the consumer is indifferent (Kreps, 1990).For example, if the worker feels that consuming 20 unit of tobacco and 70 unit of food is indifferent to 30 units of each goods, the two point of consumption combination fall on the same indifferent curve. Since consumers are usually assumed to prefer diversified consumption, the indifference curves are convex (Varian, 1992). The following graph show the indifference curve for the worker who smokes. The higher indifference curve is prefered, because it means more consumption.

Therefore, the consumption decision for the worker who smokes is to choose a points falling on feasible area and the highest indifference curve, which is the tangent point between the budget line and indifference curve. The points B in the following graph represents the consumption decision by the worker who smokes. Notice that point C is unaffordable, and the other points do not maximize his utility.

After the ban on smoking, the feasible consumption area has changed for both workers. Since the tobacco is not available any more, the feasible area becomes a horizontal line on X axis, shown as the bold line in the following graph:

After the ban on smoking, the situation for the worker who does not smoke remains the same, so his optimal consumption combination point B’ is the same as the original point A.

For the worker who smokes, the situation has changed. He would still choose the available points on the highest indifference curve. As the following graph shows, his optimal choice now becomes point B’, which is the same as the worker who does not smoke.

For the worker who does not smoke, his consumption before and after the ban on smoking is the same, so he is not influenced by the policy.
For the worker who smokes, his consumption is forced to change. This worker is worse off, because the available area after the ban on smoking is within the available area before the ban on smoking, and does not includes the optimal point before the ban on smoking. As for how much he is worse off. From the perspective of consumer utility, his utility is reduced from the higher indifference curve to the lower one, and his lose is the gap between the utility level represented by the two indifference curve

From the perspective of amount of allowance, without the ban on smoking, the utility level of point B’ can be achieved with allowance less than $100. Graphically, draw a straight line with slop of -1 and tangent to this indifference curve. Its crossing point with X axis, P’, represent the amount of allowance that can achieve the same utility level if no ban on smoking. Therefore, he is worse off by (100-P’) if measured by amount of allowance.
The following alternative policy can also reduce the smoking level.
l  Higher tax on tobacco
IF higher tax is imposed on tobacco, the higher tax would be finally reflected on tobacco price, in other words, the price of tobacco is raised. For example, if the price of tobacco is raised to $2 per unit, the budget line is change as follow:
 

The feasible area has changed. Let’s see how the consumption decision by the worker who smokes changes. He still chooses the point that tangent to the highest indifference curve, which is point B₁.The graph shows that pont B₁ is lower than point B, which means that less tobacco is consumed. Notice that the indifference curve is lowered, meaning that the reduce on tobacco consumption is at the cost of consumers’ utility(Romer, 1996).

B1

l  Raise tobacco price and lower food price
The previous policy reduces the tobacco consumption at the cost of consumers’ utility. However, if the policy maker can increase the tobacco price, and at the meantime, properly reduce the price of food, the consumers’ utility can remains the same. Graphically, if the price change makes the budget line change to the following one, the new consumption point B₂ is on the same indifference curve as point B, which means that the utility level of consumers is not harmed, but point B₂ is lower than point B, which means that it does reduce the consumption of tobacco.

l  Discourage people from smoking
The government can discourage people from smoking by publicizing the harm to the smoker and other people brought by smoking. When people get aware of the harm of smoking, the utility of smoking may be reduced, for they may worry about the health issue. And the people around may dislike the smokers, which also serve as the negative utility for the smoker. In this way, the indifferent curve changes to reflect people’s attitude to smoking. The following graph illustrates how the indifference curves changes. And the optimal consumption combination now changes to point B₃, which means people consume more food and less tobacco.

Conclusion
No matter how the policy changes, the worker who does not smoke would spend all his allowance on food. For the worker who smokes, his consumption combination is influence by the policy, and his would always choose the feasible comsumption point that falls on the highest indifference curve.
 
Reference
Kreps, D. M. (1990).A course in microeconomic theory(pp. 577-660). New York: Harvester Wheatsheaf.
Romer, D. (1996). Advanced macroeconomics.New York, 52.
Varian, H. R. (1992).Microeconomic analysis(Vol. 2). New York: Norton.
 Australia：Consumption Decision among Tobacco and Food代写