Question 1 (70 marks) [This question includes 4 sections]

Shinra Electric Power Company is the only power company in Midgar prefecture, it controls the exploration of Mako energy which can be utilized for power generation on its own. It has    absolute control over power transmission and distribution, it meanwhile has significant              underhanded influence into societal, infrastructural, and political spheres.

1.    Identify the market structure of Shinra in Midgar; discuss how a firm like Shinra sets price and maximizes profits with mathematics wherever necessary. (10 marks)            

2.    Suppose Shinra’s power generation (Q) follows a production function  = √ , where L is the number of labour and M stands for the quantity of Mako required. The power demand in Midgar is given by  = 100 −  . The wage, w, is $1 per unit of labour and the exploration  cost of Mako, r, is $4 per unit.

a)    Derive the long-run total cost equation as a function of Q. (10 marks)

b)   What quantity maximizes this Shinra’s profit? (10 marks)

c)    What optimal input bundle produces the profit-maximizing quantity? (10 marks)

3.    Discuss how a regulator (e.g., the government of Midgar) regulates Shinra. (10 marks)

4.    A housewife in Midgar, Tifa Lockhart, only consumes two types of energy: electricity and LPG. Without loss of generality, assume Tifa has a constant elasticity of substitution (CES) cost function: for ∀(, ) ∈ (0, 1), (, ) = ( + (1 − ) )1/  =  +  . Where X is electricity demand (kWh), Y is the LPG demand (Mcf), E is electricity price ($/kWh), G is the LPG price ($/Mcf), and I represents the intermediate output index, which is an             increasing function of end-use demand. Please help Tifa derive her own-price elasticity for  electricity and LPG based on (, ). Show necessary key steps. (20 marks)

Question 2 (30 marks) [This question includes 2 sections]

Renewable power generation has grown rapidly in the last two decades in China, as is illustrated

by the figure below.

Discuss:

1.    The opportunities faced with renewable generation. Support your arguments with real-world examples and/or appropriate figures. (10 marks)

2.    How to delineate the incurred challenges of renewable generation, compared with  conventional generations. Support your arguments with real-world examples and/or appropriate models. (20 marks)