Corner solution

In non-technical terms, a corner solution is when the chooser is either unwilling or unable to make a trade-off between goods.

[3] Real world examples of a corner solution occur when someone says "I wouldn't buy that at any price", "Why would I buy X when Y is cheaper" or "I will do X no matter the cost", this could be for any number of reasons e.g. a bad brand experience, loyalty to a specific brand or when a cheaper version of the same good exists.

Such a solution lacks mathematical elegance, and most examples are characterized by externally forced conditions (such as "variables x and y cannot be negative") that put the actual local extrema outside the permitted values.

In the usual case, constrained utility is maximized on the budget constraint with strictly positive quantities consumed of both goods.

Furthermore, a range of lower prices for the good with initial zero consumption may leave quantity demanded unchanged at zero, rather than increasing it as in the more usual case.

To find a corner solution graphically one must shift the indifference curve in the direction which increases utility.

If you do not find a tangency point within the domain then the utility maximising indifference curve for the given budget constraint will be at an intersection between either the x or y axis (depending on whether the slope of the indifference curve is strictly greater than or less than the slope of the budget constraint) - this is a corner solution.

This diagram shows an example corner solution where the optimal bundle lies on the x-intercept at point (M,0). IC 1 is not a solution as it does not fully utilise the entire budget, IC 3 is unachievable as it exceeds the total amount of the budget. The optimal solution in this example is M units of good X and 0 units of good Y. This is a corner solution as the highest possible IC (IC 2) intersects the budget line at one of the intercepts (x-intercept). [ 1 ]