Suppose John is planning to join a sports club. Membership in the club will allow John to swim at the pool for half price. Normally swimming for an hour would cost $10. If John has an income of $1000, the club membership fee is $100, and we plot the number of visits to the pool on the horizontal axis and a composite "other goods" which have a price of $1 on the vertical axis, the slope of John's budget line after joining the club will be:

Question

Quizplus · Accepted Answer

Before joining the club, John's budget line can be expressed as:

10x + y = 1000

where x is the number of visits to the pool and y is the amount of "other goods" that John can consume.

After John joins the club, the cost of swimming is halved to $5 per hour. This means that John's new budget line can be expressed as:

5x + y = 900

where 900 is the amount of income remaining after John pays the membership fee of $100.

To find the slope of John's new budget line, we can rearrange the equation as:
y = -5x + 900

This is in the form y = mx + b, where m is the slope of the budget line. Thus, we can see that the slope is -5.

Therefore, the answer is B) -5. Before joining the club, John's budget constraint is:

10x + y = 1000

Where x is the number of swimming hours and y is the amount spent on other goods.

After joining the club, John's budget constraint becomes:

5x + y - 100 = 1000

Where 5x is the half price for swimming, and a membership fee of $100 is subtracted from John's income of $1000.

Now we can rewrite this equation as:

y = -5x + 1100

Which is in the slope-intercept form y = mx + b, where the slope (m) is -5. Therefore, the slope of John's budget line after joining the club is -5.

Suppose John Is Planning to Join a Sports Club −10- 10−10

Suppose John Is Planning to Join a Sports Club $- 10$