# The Budget Constraint, Figure 1 displays the rational decision

The rational consumer theory is a frameworkfor understanding and modelling, economic and social behaviour. The theorystates that consumers will always make prudent and logical purchases, resultingin consumer satisfaction within the specific nature of good selected.  Thereby stating that consumers assess the optimal way to leverage theirpurchasing power, to maximize their utility and minimize opportunity coststhrough employing trade-offs.  Interestingly, there are real world implications that may disprove the rational consumertheory, which lead the consumer to make illogical and irrational choices. “Our irrational behaviours are neither random nor senseless;we all make the same types of mistakes over and over, because of the basicwiring of our brains” (Dan Ariely, Predictably Irrational – 2008).

Toexemplify the Budget Constraint, Figure 1 displays the rational decision makingof a consumer named Ashley, who is observing two branded refreshments from astore. The consumer’s income is £50 a week, and the cost of a Case of Coca-Colais £5 whilst the Case of Pepsi is £2.50. Therefore, Figure 1 illustrates themaximum bundle amount the consumer can purchase under Ashley’s budget. Forexample, if Ashley spends his total income on Cases of Coca-Cola, then thiswould result in Ashley obtaining 10 Cases of Coca-Cola, furthermore, if Ashleydecided to instead spend all of his income on Cases of Pepsi, then this wouldresult in having 20 Cases of Pepsi. These two items can then be combined aslong as it is in the budget constraint.

If Ashley willingly sacrificed a singleCase of Coca-Cola, then he would be able to purchase two Cases of Pepsi, thisis due to the slope of the budget constraint (B1) being -0.5= (-(10/20). ­As you can see in Figure 1, the budget constraint curve has now shiftedto the right (A2), this is due to there being a special offer of 20% off theprice of Cases of Pepsi. This shallthereby increase Ashley’s budget constraint for Cases of Pepsi by 20%, thediscount leads to further benefits such as increasing the variety of bundlesthat can be combined with Cases of Coca-Cola, and this is due to him having 20%more to spend on Cases of Pepsi. If his income w­­as allocated equally at £25for both shops, the offer would result in him having £5 more to spend on Casesof Pepsi. However, this does not increase the amount of units purchasable of Casesof Coca-Cola (y-axis) in the budget constraint, as the offer is exclusive to Casesof Pepsi. There is also an indifference curve displayed in figure1, this curve shall exhibit all of the combinations of two products, which yield the same level ofsatisfaction or utility t­­o the consumer. Firstly, the curve is quite steep meaningthat the marginal rate of substitution is high, thereforeAshley would be willing to give up a very large amount of y to obtain very little of x.

Ashley’s main objective when choosing what bundle toconsume, is to reach the highest level of utility , thereby achieving thehighest indifference curve possible. Therefore, if Ashley gains a pay rise, then his net utility willrise, resulting in an upward shifton the indifference curve from (I1)to (I2), thereby increasingconsumption of goods X and Y.  When considering both thebudget constraint and indifference curve, the ‘Optimal bundle point’ fromFigure 1 is where the circle is situated, meaning that the optimal point will bewhen Ashley purchases 20 Cases of Pepsi and 2 Cases of Coca-Cola. This shows thateven though Ashley’s has not fully utilised the 20% discount applied to Casesof Pepsi, he has allocated the optimal bundleof goods within this circumstance, in which shall providehim with the highest utility.

Overtime,Ashley’s preference towards Pepsi and Coca Cola have become equal. Therefore, fromFigure 2, Ashley’s change in preference makes both of these products perfectsubstitutes, hence making the indifference curve linear. Ashley shall thereforetry to gain the highest possible utility at the best possible price for him; andthis is the point whereby he is able to purchase the highest amount of goodsgiven his weekly budget. This is because the two products are perfectsubstitutes and therefore he will not have a preference regarding either good.

For example, in Figure 2, we can see Ashley will gain the highest utility atthe point where line B2 intercepts the I5, as he will be able to get 25 Casesof Pepsi and zero Cases of Coca Cola, thereby exploiting the 20% discount applied. Thisis a demonstration of the continuity and convexity axiomatic assumptions beingbroken.  Ashley has a brother named ‘Nathan’ who runs a local restaurant; therefore,he purchases Cases of Coca-Cola as well as Cases of Pepsi, as these therequired are supplies for his restaurant. Nathan perceives two goods ascomplementary as Good X would withhold little to no value when consumed alone,however when combined with good Y, would increase overall value of theoffering.

In Figure 3, we can see that the elbowsare collinear and the budget constraint intercepting them expresses the proportionin which each good needs to increase by, so that there is an increase in theutility.Figure 3, therefore, illustrates Nathan’s best bundle, which will give him maximumutility, where the highest point the indifference curve is interchanged withthe budget constraint. Nathan has an income of £50 a week, this optimal pointof utility is when Nathan purchases 6 units of ‘Cases of Coca-Cola’ and 6 unitsof ‘Cases of Pepsi’, this shall thereby use £45 of his budget, with a remainderof £5. There is a remainder of money because of both goods being non-separable,meaning that he is unable to maximise his budget. Furthermore, the 20% discountwill not be applied to the Cases of Pepsi due to the goods being perfectlycomplimentary.

In conclusion, a consumer acting upona rational basis would be enticed by the 20% discount offered on ‘Cases ofPepsi’. This is understandable as a rational consumer’s objective will be tomaximise their utility. These offers also aid companies in increasing theirshare in the market and hence their profits because consumers will be inclinedto purchase Pepsi, rather than substitute companies selling the same product atthe full price.

However, the only issue with this theory is that not allconsumers act with rational in reality; thereby a discount could lead to aprice inelasticity of demand, resulting in the offer being a failure to thecompany.