Answer to Question #193391 in Accounting for mahlet berhanu

Question

Suppose Ethiopian Electric Light and Power Corporation (EELPC) is a multi plant

monopolist having two plants, Tekeze plant (plant1) and Fincha plant (Plant2). The

operating costs of the two plants are given as follows:

Tekeze Plant: TC1 = 10 Q1

2 and where Q1 - Amount of electric power produced in

Tekeze

Fincha plant: TC2 = 20 Q2

2 Q2 – amount of electric power produced in Fincha

EELPC estimates the demand for electric power by the following function

P= 700 – 5Q where P - is price (total in million birr) per Giga watt and

Q – is the total amount of Giga watt sold and Q = Q1 + Q2

Note that a Giga watt of electric power, whether it comes from Fincha or Tekeze plant worth

equal price

a) What level of output (electric power) should EELPC produce and what price per Kilowatt

should it charge to maximize its profit?

b) How much of the total output should be produced in each plant?

Answer 1

a. The equilibrium condition is:

MR = MC1 and MR = MC2.

$TR = P×Q = (700 – 5Q)×Q = 700Q - 5Q2,$

MR = TR'(Q) = 700- 10Q, where Q = Q1 + Q2.

Thus, MR = 700 – 10Q1 – 10Q2,

MC1 = dTC/dQ1 = 20Q1 and MC2 = dTC/dQ2 = 40Q2.

Now the equilibrium occurs when:

700 – 10Q1 - 10Q2 = 20Q1 and

700 – 10Q1 – 10Q2 = 40Q2.

Rearranging the above equations we get the following simultaneous equation.

30Q1 + 10Q2 = 700 and

10Q1 + 50Q2 = 700.

Solving the above equations simultaneously, we get:

Q1 = 20 giga watts and

Q2 = 10 giga watts.

The profit maximizing level of output is, thus, Q1 + Q2 = 30 giga watt.

To determine the equilibrium price we substitute the total output (30) in the demand function:

Accordingly, P = 700 – 5×30 = 550 mill birr.

b) The Tekeze plant should produce 20 giga watts and Fincha plant should produce 10 giga watts.