Solaris is the sole supplier of solar panels in Sunnylandia. Solaris has no fixed costs and can supply solar panels at a constant marginal cost MC of $10 per panel. There are two different categories of customers of solar energy, business and residential. The businesses' demand for solar panels is Q_B(P) = 240 - 3P. The residential demand for solar panels is Q_R(P) = 80 - 5P.

Business market (B) (45 points)

a)Calculate the profit maximizing price and number of panels that Solaris will choose to sell to business clients, as well as the firm's profit .(10 points)

b)Use a diagram to illustrate the producer surplus PS_B that Solaris enjoys, the consumer surplus of the businesses CS_B, and the deadweight loss DWL_B in the business market. Then, compute CS_B and DWL_B.(10 points)

c)Tax per unit (TU): The government decides to tax Solaris at $2 per panel sold. Find the new optimal price and quantity that Solaris chooses, and compute its profit . Finally, compute the tax revenue TR_TU.(10 points)

d)Lump sum tax (LS): Instead of a tax per unit, the government imposes a lump tax of $204 on Solaris. Find the new optimal price and quantity that Solaris chooses, and compute its profit in this case.(9 points)

e)Suppose that the government is looking to tax Solaris to raise revenue for upgrading the power grid, and hires you to advise which one of the taxes above - a tax per unit or a lump sum - to implement: which one of the two taxes would you recommend? Explain why. (6 points)

Residential market (R) (30 points)

f)Calculate the profit maximizing price and number of panels that Solaris will choose to sell to residential clients, as well as the firm's profit .(10 points)

g)Use a diagram to illustrate the producer surplus PS_R that Solaris enjoys, the consumer surplus of the residential clients CS_R, and the deadweight loss DWL_R in the residential market. Then, compute CS_R and DWL_R.(10 points)

h)The government wants to encourage the production of solar panels for the residential market. In order to do so, it is willing to give to the monopoly a subsidy of s per panel, but the government wishes to calibrate this subsidy such that Solaris would supply an efficient quantity (that is, the same quantity as the one produced under perfect competition) in the residential market. Assuming that the government knows the demand and the costs that Solaris has, compute how much the subsidy s should be.(5 points)

i)Suppose the government wishes to finance the total cost of the subsidy given in h) to the residential market by taxing the panels sold in the business market. What is the minimum amount of tax per unit t that the government would have to charge Solaris for the panels sold in the business market in order to cover the total subsidy needed for the residential market?(5 points)

Combined market (C)(25 points)

j)Suppose that the government legislates that companies are no longer allowed to price-discriminate between the business and residential market customers; thus, the business and residential markets are combined. Show the combined demand using a diagram, then show and calculate the profit maximizing price and number of panels that Solaris will choose to sell in the combined market, as well as the firm's profit .(20 points)

k)Which category of customers (i.e., business or residential) benefits from the market being now combined? Justify your answer.(5 points)