Please help me with this question!

QUESTION:
Heaven Sub, a subway shop, has the following marginal product curve points for its hourly product:

(0.5, 13)
(1.5, 17)
(2.5, 15)
(3.5, 11)
(4.5, 9)

i) When labour increases from 2 to 3 workers, total product increases by _____ subs per hour.

ii) Assume that if there are no workers, Heaven Sub does not have any output. Find the points in order to plot the production function.

iii) Find the points to the average product curve at 1, 2, 3,4 or 5 workers.

iv) Marginal product and average product curves always intersect at the ________ of the _____ curve.

MY ANSWERS:
i) 13 because when I graphed the points, the third input or worker intersected at (3, 13)

ii) I don’t know how to find the production function because I only know the change in quantity of workers and subs per worker. I don’t know how to work backwards.

iii) The AP formula is AP = quantity/number of inputs. The change in quantity of workers and subs per worker are given, and not the original values. So, again, I don’t know how to do this question..

iv) max, AP according to my notes and I don't really understand the theory of it.

An Excel spreadsheet would be very helpful for these questions

I looks like you need to "plot" total production. You are given the marginal product from adding each worker. Just convert that into total production. The first .5 workers gives 13 units of production (Q). The next worker adds 17 units, for a total of 30. The next worker adds 15, for a total of 45. And so on.
iii) AP = q/inputs. At .5 inputs, AP = 13/.5 = 26, at 1.5 AP=30/1.5=20, and so on.

iv) Max AP, what is the maximum AP value you get?

i) To find the increase in total product when labor increases from 2 to 3 workers, we need to find the difference in total product between these two levels.

Given the points:
(2.5, 15) and (3.5, 11)

Total product at 2 workers is 15, and at 3 workers is 11. Therefore, the increase in total product is:
11 - 15 = -4 subs per hour

So, when labor increases from 2 to 3 workers, total product decreases by 4 subs per hour.

ii) To plot the production function, we need to find the relationship between the quantity of workers (labor) and the quantity of subs produced.

Given the points:
(0.5, 13)
(1.5, 17)
(2.5, 15)
(3.5, 11)
(4.5, 9)

These points represent the marginal product of labor. To construct the production function, we need to find the total product values at each level of labor.

The total product values can be found by summing up the marginal products. Start with an initial value of total product (which is 0 if there are no workers), and then add each marginal product value sequentially.

For example, to find the total product at 0.5 workers:
Total product at 0.5 workers = 0 (Initial value) + marginal product at 0.5 workers = 0 + 13 = 13

Similarly, find the total product values for all the other levels of labor based on the given marginal product values.

iii) To find the average product at each level of workers, we need to divide the total product at that level by the number of workers.

For example, to find the average product at 1 worker, divide the total product at 1 worker by 1.

To find the average product at 2 workers, divide the total product at 2 workers by 2.

Repeat this process for all the other levels of workers given.

iv) Marginal product and average product curves always intersect at the maximum point of the average product curve.

This means that the point where the average product curve reaches its highest value is where the marginal product curve intersects it.

To find the maximum of the average product curve, you need to find the point where the average product is highest. This can be done by analyzing the trend of the average product values at each level of workers and identifying the peak value.

So, the marginal product and average product curves always intersect at the maximum point of the average product curve.