Sarah's pretzel plant has the following short run cost function: C(q,K)= (wq^3)/(1000K^3/2)+50K where q is Sarah's output level, w is the cost of a labour hour and K is the number of pretzels machines Sarah rents. Sarah short run marginal cost curve is MC(q,K=(3wq^2/(1000K^3/2). At the moment, Sarah leases 10 pretzel machines, the cost of labor is $6.85 and she can sell all of the output she produces at $35 per unit.
A) what type of market is Sarah operating in?
B) what is the optimal level of output for Sarah and how much profit does she make at this level?
C) if the minimum wage increases, such as wage per labor hour rises to $7.50, what happens to Sarah optimal level of output and profits?