1 costsan electricity company estimates that its

Question

1 Costs

An electricity company estimates that its variable cost for producing electricity is given by the following ex- pression: C(q) = 25q2 + 2000q [$] where C is the total cost and q is the quantity produced (MWh)

• Derive an expression for the marginal cost of production
  Derive expressions for the revenue and the profit when the widgets are sold at marginal cost.

2 Welfare

There are two firms (producers) in the market and they are price takers.

Total Cost Function for firm 1: 0.65(Q1)2 + 22Q1 + 120
Total Cost Function for firm 2: 0.82(Q2)2 + 18Q2 + 160

Each firm has a minimum capacity of 0 but no maximum capacity.

The inverse demand curve for the market is: P = 475 - 0.6Q

1. What is the inverse supply curve for the entire market? When calculating this curve, make sure you account for the minimum capacity of the firms. If the price is too low, firms produce nothing, not a negative quantity. (note that you may have a non-smooth curve). Draw it.
2. What is the market clearing price for this market? What is the market quantity?
3. Calculate the Consumer Surplus (CS), the Producer Surplus (PS), and the Social Welfare (SW).

3 Elasticity

Vertically integrated utilities often offer two-part tariffs to encourage their consumers to shift demand from on-peak load periods to off-peak periods. Consumption of electrical energy during on-peak and off-peak periods can be viewed as substitute products. The table below summarizes the results of experiments that the Southern Antarctica Power and Light Company has conducted with its two-part tariff. Use these results to estimate the elasticities and cross-elasticities of the demand for electrical energy during peak and off-peak periods.

	On-peak price	Off-peak price	Average on-peak demand	Average off-peak demand
	π1	π2	D1	D2
	($/MWh)	($/MWh)	($/MWh)	($/MWh)
Base Case	0.08	0.06	1000	500
Experiment 1	0.08	0.05	992	509
Experiment 2	0.09	0.06	985	510

4 Supply Function Equilibria

The operator of a centralized market for electrical energy has received the bids shown in the table below for the supply of electrical energy during a given period.

Company	Amount (MWh)	Price ($/MWh)
Red	100	12.5
Red	100	14
Red	50	18
Blue	200	10.5
Blue	200	13
Blue	100	15
Green	50	13.5
Green	50	14.5
Green	50	15.5

1.     Build the supply curve

1. Assume that this market operates unilaterally, that is, that the demand does not bid and is represented by a forecast. Calculate the market price, the quantity produced by each company and the revenue of each company for each of the following loads: 400 MW, 600 MW, 875 MW.
2. Suppose that instead of being treated as constant, the load is represented by its inverse demand curve, which is assumed to have the following form:

D = L - 4.0π

where D is the demand, L is the forecasted load and π is the price. Calculate the effect that this price sensitivity of demand has on the market price and the quantity traded.

5 Strategic Behavior

Consider a market for electrical energy that is supplied by two generating companies whose cost functions are

CA  = 36PA$/h (1)

CB  = 31PB$/h (2)

The inverse demand curve for this market is estimated to be

π = 120 - D$/MWh (3)

a. Write the problem for the two generating companies

b. Solve the optimality conditions
c. Illustrate the pure strategy Nash Equilibrium for the two companies in a diagram (Reaction curves)

6 Scarcity Rents

Generator 1 has 140 MW capacity and its marginal cost is $80/MWh. Generator 2 has 220 MW capacity and its marginal cost is $130/MWh.
The inverse demand curve is: P = 465 - 0.7Q.

1. Draw the supply curve and the inverse demand curve.
2. At what price does supply = demand?
3. Identify on the graph the Consumer Surplus (CS), the Producer Surplus (PS), and the Scarcity Rent (SR) (based on the second definition given in class on scarcity rent). What is the total scarcity rent?
4. Some people argue that we should not allow for scarcity rents (a market clearing price that is higher than the largest supplier bid), that instead the price should never exceed the largest supplier bid. What do you think, should we allow scarcity rents? Explain.