thumb|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).
In mathematics and economics, a corner solution is a special solution to an agent's maximization problem in which the quantity of one of the arguments in the maximized function is zero. In non-technical terms, a corner solution is when the chooser is either unwilling or unable to make a trade-off between goods.
In economics
In the context of economics the corner solution is best characterised by when the highest indifference curve attainable is not tangential to the budget line, in this scenario the consumer puts their entire budget into purchasing as much of one of the goods as possible and none of any other. When the slope of the indifference curve is greater than the slope of the budget line, the consumer is willing to give up more of good 1 for a unit of good 2 than is required by the market. Thus, it follows that if the slope of the indifference curve is strictly greater than the slope of the budget line:
<math>\text{Slope of indifference curve} > \text{Slope of budget line}; \ \forall \text{ values of the slopes}</math>
Then the result will be a corner solution intersecting the x-axis. The converse is also true for a corner solution resulting from an intercept through the y-axis.
Another example is "zero-tolerance" policies, such as a parent who is unwilling to expose their children to any risk, no matter how small and no matter what the benefits of the activity might be. "Nothing is more important than my child's safety" is a corner solution in its refusal to admit there might be trade-offs. The word "corner" refers to the fact that if one graphs the maximization problem, the optimal point will occur at the "corner" created by the budget constraint and one axis.
See also
- Indifference curve: Assumptions section
- Interior solution (optimization)