Question

In an electricity market, there is only one provider who calls itself '' Electricity-to-All. The company's total cost function can be written as

TC(Q)=10.000.000+200Q

where Q is the amount of electricity produced. The demand curve can be written as

Q=200.000-250P

where the price is for a unit of electricity

1- How much output should the company produce to maximize profit? What will the price be?

2- How much profit and how much '' consumer surplus '' does the company generate

3- Discuss briefly whether it can pay for Electricity for everyone to charge a two-part tariff '' two-part price '' for electricity

4- Calculate the welfare benefits of this regulation

5- What is the lowest maximum price that the authorities can impose if Electricity-to-All is to remain in the market

The authorities consider that the price of the monopoly is too high and are therefore considering setting a maximum price of EL P^L=400

4- Calculate the welfare benefits of this regulation

5- What is the lowest maximum price that the authorities can impose if Electricity-to-All is to remain in the market

Answer 1

The total cost is and the demand is , and the inverse demand is or .

1. The marginal cost is or or . The marginal revenue would be as or or .

The profit would be maximum where or or or untis. The price would be or or or .

2. The profit would be or or or , and for the given quantity, we have or or .

The graph is as below.

The CS would be the area of triangle ABF, which would be as or or or .

3. Under two part tariff, the firm would charge product at the perfectly competitive level and charge a lump sum fee of an amount of the CS. Hence, it would definitely pay the firm to charge a two part tariff as the firm would cover the entire CS (equivalent to the area of triangle ACE).

4. The welfare benefit here would be that the dead-weight loss (DWL) is also included in two part tariff. The DWL would be equal to the area of tringle FDE, which would be as or or or .

Hence, the welfare benefit after two part tariff is implemented would be .

Note that welfare benefit is not equal to the total surplus (area of triangle ACE=45000000), but is the increase in total surplus than before (which is equal to the DWL, ie the surplus not allocated to producer or seller).

5. The lowest price would be the perfectly competetive price, which would be where or or or , and the price would be or or . This is the lowest price that can be charged.

Note that the lowest price charged is basically the price charged per output under two part tariff. Also note that since the MC is constant at 200 for all quantity, the lowest competitive price would would equal to the P=MC or P=200, however it is true only if the MC is constant.