# Can budget lines be discontinuous?

It's been awhile since I've taken introductory microeconomics. I read budget lines can be discontinuous awhile ago but am suspicious as to such a concept being discussed in intro micro classes particularly calling them budget 'lines'.

The problem:

Say Jill likes food and clothing. Jill has 200 to spend on food and clothing. One unit of food costs \$1 while one unit of clothing costs$2.

Budget line is 200=F+2C

Say Jill receives an 80% discount on food but it applies up to 100 units.

New budget line is 200=0.2F+2C for 0-100 then same as old for 100 onward?

So it's discontinuous? So it's not really a budget 'line' right (though piecewise, it's a line, I guess).

• What you described seems to be a kink in the line (not a discontinuity), unless you mean that if she does not receive any discount at all in case she buys more than 100 units. – HRSE Feb 16 '16 at 8:59