Question

You are the manager of a firm that produces output in two plants. The demand for your firm's product is P = 78 − 15Q, where Q = Q1 + Q2. The marginal costs associated with producing in the two plants are MC1 = 3Q1 and MC2 = 2Q2. What price should be charged to maximize profits?
A 20,5
B. 40.5
C. 60.5
D. 80.5

Answer 1

Answer:

correct option is B. 40.5

Explanation:

given data

P = 78 - 15 Q

Q = Q1 + Q2

MC1 = 3Q1

MC2 = 2Q2

to find out

What price should be charged to maximize profits

solution

we get here first total revenue and marginal revenue that is

total revenue TR = P × Q   .......1

total revenue TR = 78Q - 15Q²

and

marginal revenue MR = $\frac{change\ in\ TR}{change\ in\ Q}$

marginal revenue MR = 78 - 30Q

now we get here

marginal revenue MR = MC1 = MC2

put here value

78 - 30Q1 - 30Q2 = 3 Q1 or 33 Q1 = 78 - 30Q2   ......................................a

78 - 30 Q1 - 30 Q2 = 2 Q2 or Q2 = 78 - 30Q1/32   ................................b

by equation a and b we get here

33 Q1 = 78 - 30 (78 - $\frac{30Q1}{32}$ )

so here Q1 = 1 and

Q2 = 78 -  $\frac{30*1}{32}$

Q2 = 1.5

so that Q will be

Q = Q1 + Q2

Q = 1 + 1.5

Q = 2.5

now we get value of P that is

P = 78 - 15 Q

P = 78 - 15 (2.5)  

P = 40.5

so charged to maximize profits is 40.5

so correct option is B. 40.5