We are looking at a company that offers its goods in a market with well-functioning competition. The company's cost function C (x) can be written

C = 0.5cx ^ 2 + F

Where x is production, F is fixed costs, and c is a given positive number

a)

Calculate the marginal cost (marginal cost) for this cost function.

b)

Does the cost function express a constant, decreasing or increasing scale yield?

The company's profit can be expressed by profit function n (x).

n (x) = Px - C (x) = Px - 0,5cx ^ 2 - F

where P is the product price.

Assume that the company maximizes profits

c)

Find your company's customization

d)

Find an expression of the company's profit as a function of the product price P, parameter c and fixed costs F

Show the effect on optimal production and on the company's profits from that

e) product price P increases

f) product price P and parameter c both increase by the same percentage

g) fixed costs F increase