Answer to Question #264337 in Economics of Enterprise for dom

Question

Lomar Corp. produces two types of generators – diesel and gas turbine. The revenue and cost functions are given as follows: 𝑅(𝑥,𝑦)=2𝑥+3𝑦 𝐶(𝑥,𝑦)=𝑥2−2𝑥𝑦+2𝑦2+6𝑥−9𝑦+5

where x is the quantity of diesel generators and y is the quantity of gas turbine generators. Both revenue and cost are measured in millions of ringgits.

(a) Determine the profit-maximising output level. How many of each type of generators should Lomar Corp. produce to maximise profit?

(10 marks)

(b) Determine the total profit generated by the optimal output level as in (a) above. What is the maximum profit?

(2 marks)

(c) Determine whether Lomar Corp. is operating in the short run or long run. Explain.

(3 marks)

Answer 1

Solution:

a.). Profit (π) = R – C

π = (2x + 3y) – (x² – 2xy + 2y² + 6x – 9y + 5)

π_x = $\frac{\partial \pi } {\partial x}$ = 2 – 2x – 2y + 6 = 0

π_y = $\frac{\partial \pi } {\partial y}$ = 3 – 2x + 4y – 9 = 0

First function (x): simplify

2 – 2x – 2y + 6 = 0

x = 4 – y

Second function (y): simplify

3 – 2x + 4y – 9 = 0

x = 2y – 3

Set: X = X

4 – y = 2y – 3

4 + 3 = 2y + y

7 = 3y

y = 2.3

Quantity of gas turbine generators (y) = 2.3

Substitute to derive x:

x = 4 – y = 4 = 2.3 = 1.7

x = 1.7

Quantity of diesel generators (x) = 1.7

 

b.). Profit = R – C

Profit = (2x + 3y) – (x² – 2xy + 2y² + 6x – 9y + 5)

Profit = (2(1.7) + 3(2.3)) – (1.7² – 2(1.7) (2.3) +2(2.3²) + 6(1.7) – 9(2.3) + 5

Profit = 10.3 – 0.15 = 10.15

Profit = 10.15

 

c.). Lomar Corp. is operating in the short-run since there are fixed costs in the cost function. There are no fixed costs in the long run since all inputs are varied.