4. The following is a cost function for clinic visits in a small inner city clinic.

Quantity of Visits Total Costs per Week Marginal cost
0 $10 0
1 15 5
2 25 10
3 45 20
4 75 30
5 115 40
6 165 50

a. Determine the marginal cost for each level of output
b. If the price per visit is given to be $25, at what level of visits will the maximum profit position be? What are the profits at this level? What is the quantity supplied
Quantity of Visits Price per visits Total costs per week Marginal cost
0 $25 10 250
1 $25 15 5
2 $25 25 10
3 $25 45 20
4 $25 75 30
5 $25 115 40
6 $25 165 50

a. To determine the marginal cost for each level of output, we need to find the change in total costs per week for each increase in the quantity of visits.

Marginal cost = Change in Total Costs per Week / Change in Quantity of Visits

For example, to find the marginal cost at level 2 of visits:
Marginal cost at level 2 = (Total Costs per Week at level 2 - Total Costs per Week at level 1) / (Quantity of Visits at level 2 - Quantity of Visits at level 1)
= ($25 - $15) / (2 - 1)
= $10 / 1
= $10

Using the same method, we can calculate the marginal cost for each level of output:

Marginal cost at:
Level 0: $0
Level 1: $5
Level 2: $10
Level 3: $20
Level 4: $30
Level 5: $40
Level 6: $50

b. To find the level of visits at which the maximum profit position will be achieved, we need to compare the marginal cost to the price per visit.

At a given level of visits, the profit can be calculated as:

Profit = (Price per Visit - Marginal Cost) * Quantity of Visits

We need to find the level of visits where the profit is maximized.

Using the given price per visit of $25, we can calculate the profit for each level of visits:

Profit at:
Level 0: ($25 - $0) * 0 = $0
Level 1: ($25 - $5) * 1 = $20
Level 2: ($25 - $10) * 2 = $30
Level 3: ($25 - $20) * 3 = $15
Level 4: ($25 - $30) * 4 = -$20
Level 5: ($25 - $40) * 5 = -$75
Level 6: ($25 - $50) * 6 = -$150

From the calculation, we can see that the maximum profit is achieved at level 2 of visits, where the profit is $30. At this level, the quantity supplied is 2 visits.