Please provide step by step solution with graph(s)

1st part

Suppose a certain city has a monopoly cable-television company. This company has total costs TC = 0.25Q² + 30Q + 70. (Hint: using calculus, this means MC = 0.5Q + 30 since MC is the derivative of TCwith respect to output.)

The demand in the community is approximated by the equation Q_d = 60 - P/2 (alternatively, you can write the demand equation as Q_d = 60 - 0.5P).

• Graphically depict the demand curve as well as the marginal cost (MC) curve.
• If the cable company is free to choose its own price P_m and quantity Q_m, graphically depict the monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome.
• Compute and state the exact monopolist equilibrium price P_m and quantity Q_m that you depicted graphically.

2nd Part

Continue with your analysis of the monopoly cable-television company from Question 3, with demand of Q_d = 60 - P/2 (alternatively, you can write the demand equation as Q_d = 60 - 0.5P) and MC = 0.5Q + 30.

• Reproduce the graph which shows your demand and marginal cost (MC) curves, as well as any other necessary curves.
• Graphically indicate the socially optimal output level, Q_soc, and compute the quantity and price associated with this output.
• Depict areas of consumer surplus (CS_SOC), producer surplus (PS_SOC), and any possible deadweight loss (DWL_SOC) associated with socially optimal outcome.(You do not need to determine the numerical size of CS, PS, and DWL, just show them graphically.)
• Depict areas of consumer surplus (CS_m), producer surplus (PS_m), and any possible deadweight loss (DW_mL) associated with monopoly. (You do not need to determine the numerical size of CS, PS, and DWL, just show them graphically.)
• Explain how you've determined the socially optimal output level. How does the socially optimal output compare to the monopolist output in terms of individual CS, PS, and DWL (e.g., compare CS_m and CS_SOC, and so on)? How does the total surplus (sum of consumer and producer surpluses) compare between the two situations? (Narrative response; suggested length of four to eight sentences or one to two paragraphs. It might be useful to create a table to contrast the two settings.)