A student has 70 days to allocate between work and free time. They earn a daily wage of $90. In addition to any wages earned, they receive a one-time, unconditional gift of $1,000. The relationship between their maximum consumption (c) and the number of free days they take (t) is represented by the equation: c = 90(70 - t) + 1,000. If the student decides to take 30 days of free time, what is their maximum possible consumption?

Calculating Free Days for a Consumption Target

A student has 70 days to allocate between work (at a wage of $90/day) and free time. After receiving a $1,000 gift, their budget constraint is represented by the equation c = 90(70 - t) + 1,000, where c is consumption and t is free days. The addition of this $1,000 gift increases the opportunity cost of taking an additional day of free time.

Evaluating a Financial Plan

A student has 70 days to allocate between work and free time, earning a daily wage of $90. If this student receives an unconditional gift of $1,000, how does this change the graphical representation of their budget constraint (with consumption on the vertical axis and free days on the horizontal axis)?

Comparing Income Changes on a Budget

A student's budget for a 70-day period is described by the equation c = 90(70 - t) + 1,000, where c is total consumption and t is the number of free days taken. Match each component of the equation to its correct economic interpretation.

Formulating a Budget Constraint Equation

A student's financial situation over a 70-day period is modeled by the budget constraint c = 90(70 - t) + 1,000, where c is total consumption and t is the number of free days. The $1,000 in the equation represents a one-time gift. How does this gift affect the student's maximum possible consumption and the maximum number of free days they can take, compared to a situation without the gift?

A student's budget over a 70-day period is determined by the equation c = 90(70 - t) + 1,000, where c is consumption and t is the number of free days. Based on this equation, the amount of consumption the student must give up to gain one additional day of free time is $____.