Here is a detailed step-by-step analysis to determine how many visits per week David should take to the gym at the discounted $3 price, based on marginal benefit principles:
First, I will recreate the provided table showing David's marginal benefits for each weekly gym visit:
Weekly Visits | Marginal Benefit (in $)
1st visit | $20\
2nd visit | $15
3rd visit | $10
4th visit | $4
5th visit | $3
6th visit | $0
To find the optimal number of visits per week, I need to compare the marginal benefit of each additional visit to the marginal cost, which is the $3 discounted price.
The marginal benefit of the 1st visit is $20, which exceeds the $3 marginal cost, so the 1st visit provides net benefit.
The marginal benefit of the 2nd visit is $15, which also exceeds the $3 marginal cost, so the 2nd visit also provides net benefit.
The marginal benefit of the 3rd visit is $10, which exceeds the $3 cost, so the 3rd visit provides net benefit as well.
However, the marginal benefit of the 4th visit is $4, which is less than the $3 cost. Therefore, the 4th visit does not provide net benefit.
Based on marginal analysis principles, David should take 3 gym visits per week when facing the discounted $3 price. The 3 visits provide positive net benefits of $20, $15, and $10 respectively, totaling $45 of net benefit to David. Additional visits beyond 3 provide less marginal benefit than marginal cost, reducing net benefits.
In summary, by comparing marginal benefits and marginal costs, the optimal number of weekly gym visits for David with the $3 discounted coupon is 3 visits. This maximizes his total net benefits.