In a simple model of credit imperfections, when consumers borrow and lend at different interest rates, the budget line is kinked because

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In a simple model of credit imperfections, when consumers borrow and lend at different interest rates, the budget line is kinked because the consumer usually lends at a lower rate than they borrow due to credit market imperfections such as transaction costs, risk, and default. This leads to a kink in the budget line at the point where the consumer switches from being a borrower to being a lender, creating a discontinuity in the marginal rate of substitution.

In a Simple Model of Credit Imperfections, When Consumers Borrow