A firm offers its goods in a market with well-functioning competition. The firm's cost function C(x) is

C(x) = 0.5cx² + F

Where

x = production

F = fixed costs

c = a given positive number

a. Calculate the marginal cost for this cost function

b. Does the cost function express constant, increasing, or decreasing returns to scale?

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a. My solution is MC = cx (derived the cost function). Is this correct?

b. Based on the graph from the cost function I made in GeoGebra, it is convex. Does it mean that the cost function has increasing returns on scale? Or do I have to find the production function first and look at this graph? If so, how do I find this?