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1.The world is filled with technology and there is always a fear amongst people that machine will replace humans. Quiet true to some extent but not in all the sectors of the economy. For example when it come to the requirement of problem solving and leadership skills, machines can never replace a valuable employee.

1. Empathy

Though robots can perform surgeries, it cannot give moral support, encouragement to fight with the disease as doctor does. Empathy plays important role in recovery of the patient which machine can't.

2. Proactive Employees

Employees who are responsible and who take initiative to solve the problems and come up with better solution and ideas are extremely valuable to its employers. Machines may be good in processing commands but not in starting new tasks.

3. Creative Ideas

As humans get exposure to lot of things in day to day basis such as Photography, painting, writing, marketing, management, art and craft. They get inspired and influenced to create new by indulging in creative thinking which machines can't do.

4. Teamwork

With collaboration of the team companies are earning 21% profit. Though machines can do everything, they lack the sense of real collaboration.

5. Adjustment and shifts in dynamic environment

Machines are programmed in specific roles. Although they can function well in particular roles they cannot adjust and shift to new roles according to new requirement and demand. Humans have the ability to grow and adjust, train themselves for shifts in new roles.

6. Contribution of the community

Community play a significant role in businesses both local and online to make money. Small businesses thrive in small town and involves exchange of homegrown wealth. Employees contribute to local economy in creating jobs and nurturing the community.

7. Application

People are better at understanding the problems and situations outside data while machines can only work based on its data.

While machines can replace many jobs but it cannot replace every job. Creativity, nature and ingenuity cannot be replaced by machines as of now because machines work smart only with the inputs of people.

2.I'm denoting θ = a throughout the problem.

The production function is given as

Y = K^????a?????.(AN)^1-a

Now, A = 4.K/N

Putting this in the production function we get

Y = K^??????a.(N.4K/N)^1-a

or, Y = K^??????a+1-a.(4)^1-a

or, Y = (4)^1-a.K

Now, a = 0.5.

Hence, Y = (4)^1-0.5??.K

or, Y = 2.K

Hence, per capita output is

y = Y/L = 2.K/L

or, y = 2.k [k = per worker capital]

Now, from solow growth model, we get the identity,

dk = s.y - (n + d).k

Where, d = depriciation rate, n = population growth rate and s = savings rate

dk/k = s.(y/k) - (n + d)...........(1)

Now, we are given that, n = 0.02, d = 0.03 and s = 0.1. And, y/k = 2. Putting all these values in equation (1) we get

dk/k = 0.1×2 - (0.02+0.03)

or, dk/k = 0.15

And, from the production function we get

y = 2.k

or, dy = 2.dk

or, dy/y = 2.(dk/k).(k/y)

or, dy/y = 2×0.15×(1/2) [as y/k = 2]

or, dy/y = 0.15

Initial growth rates of y and k are

dy/y = 0.15 and dk/k = 0.15.

Now, population growth rate increases to 0.05.

Hence, n* = 0.05

d = 0.03, s = 0.1

Putting these again in equation (1) we get

dk/k = 0.1×2 - (0.05+0.03)

or, dk/k = 0.12

And, from production function we get

y = 2.k

or, dy/y = 2.(dk/k).(k/y)

or, dy/y = 2×0.12×(1/2)

or, dy/y = 0.12

Hence, after increase in population growth rate,

dy/y = 0.12 and dk/k = 0.12.

We can see that the per capita income growth reduced from 0.15 to 0.12.

? An increase in the rate of population growth will cause the rate of growth of per capita output to decrease.

3.Please use this google drive link to download the answer file.       

https://drive.google.com/file/d/1tEcmZU9gl1Y2Du-dIaxvkztaDoJNjR7T/view?usp=sharing

Note: If you have any trouble in viewing/downloading the answer from the given link, please use this below guide to understand the whole process. 

https://helpinhomework.org/blog/how-to-obtain-answer-through-google-drive-link