Suppose there is a consumer and a producer in an economy. The producer aims to maximize his profit by producing good x and his utility by consuming consumer good x. Benefit, cost and social welfare functions are as follows:

= () = () = ()

Also, f'() > 0,f''(u) < 0,f'() > 0andf''(c) > 0 these assumptions are valid

In this case:

a) Find utility maximization.

b) Find the profit maximization.

c) Find the first level conditions.

d) Combine the first level conditions. Explain the result.

e) Find the social welfare function.

f) Find the first level condition. Explain the result.

g) Describe your work with a graph.