Yesterday I posted about kūmara prices increasing, and the impact of that on the markets for kūmara and potatoes. This week, my ECONS101 class will be covering constrained optimisation, and the main application of the general constrained optimisation model that we will be looking at is the consumer choice model. So, it seems timely to look at the effect of kūmara prices on consumer decision-making, using that model.
Consider the decision-making of a single consumer. [*] The model is shown in the diagram below. The consumer can choose to buy kūmara (measured along the x-axis) or 'all other goods' (AOG; measured along the y-axis). All of the points within the space on the diagram are combinations of kūmara and AOG, which we will refer to as bundles of goods. Now, the consumer's choice of how much of each good (kūmara and AOG) they will buy is constrained by their income (M). This is represented on the diagram by the straight-line budget constraint. The budget constraint starts at a bundle of goods with only AOG and no kūmara at all. At that point (at the top of the budget constraint), the consumer is spending all of their income on AOG, and nothing on kūmara. The maximum amount of AOG the consumer can buy is M/Pa (where Pa is the price of AOG). At the other end of the budget constraint is a bundle of goods with only kūmara and no AOG at all. At that point (at the bottom of the budget constraint), the consumer is spending all of their income on kūmara, and nothing on AOG. The maximum amount of kūmara the consumer can buy is M/Pk0 (where Pk0 is the price of kūmara). Now, the consumer can afford any bundle of goods (kūmara and AOG) that is on the budget constraint or underneath it (we refer to this as the feasible set). Now, for reasons we won't go into here, the slope of the budget constraint is equal to -Pk0/Pa (the relative price of the two goods). Any bundles of goods outside of the budget constraint cost too much for the consumer to afford. Next, we assume that the consumer is trying to maximise their utility. We represent utility on the diagram using indifference curves. So, the consumer is trying to get to the highest possible indifference curve, while choosing a bundle of goods that is in the feasible set. That happens at the bundle of goods E0, which is on the highest indifference curve I0, and which includes K0 of kūmara and A0 of AOG. The consumer can't get to any higher indifference curve than I0, because any higher indifference curve than I0 wouldn't be touching the budget constraint (and so there would be no bundles of goods on the higher indifference curve that are within the feasible set). That is the basic setup of the consumer choice model, and it shows what the consumer will buy given their income (M), the prices of the goods (Pk0 and Pa), and the consumer's preferences for the two goods (shown by the indifference curves).
Now, consider what happens when the price of kūmara increases (as discussed in yesterday's post) from Pk0 to Pk1. The budget constraint is affected first. If the consumer was only buying AOG and no kūmara at all, then the change in the price of kūmara would not affect them. The point at the top of the budget constraint remains the same. However, if the consumer were only buying kūmara (and no AOG at all), then they would now be able to buy less kūmara. This is represented by the new point M/Pk1, which is a smaller quantity of kūmara than M/Pk0. The budget constraint pivots inwards and becomes steeper. The steeper budget constraint makes sense, because its slope is now equal to -Pk1/Pa, which is a larger number (in absolute terms) than -Pk0/Pa (and larger numbers mean steeper slopes). The problem for the consumer is that they now can't afford the bundle of goods E0, because it is outside of the new feasible set (it is outside the budget constraint - the consumer can't afford to buy E0 any more). Instead, the consumer will choose the bundle of goods on the highest indifference curve that they can now reach. That is the indifference curve I1, and they will buy the bundle of goods E1, which includes K1 of kūmara and A1 of AOG.
In the consumer choice model, after the price of kūmara increases, the new bundle of goods that the consumer chooses to buy contains less kūmara. So, consumers will respond to the increase in the price of kūmara by buying less kūmara. This is what economists refer to as the Law of Demand, one of the most important empirical regularities in economics.
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[*] I haven't explained all of the moving parts of the consumer choice model here. In particular, I'm leaving a detailed discussion of indifference curves for a future post. However, if you need a bit more detail, try this explainer.
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