Question

Rexburg Technologies operates two plants. The demand equation for Rexburg's product is P = 38 – 2.5Q, where Q is in thousands of units. The marginal cost of production in the two plants are MC1 = 2Q1 and MC2 = 4Q2, respectively. To maximize profits, Rexburg should charge a price of:

• 23.00.
  
  

• $32.50.
  
  

• $8.00.
  
  

• $10.75.
  
  

• None of the options

Answer 1

At first we will find total marginal cost or summation of marginal cost curves which is horizontal summaton of each marginal cost curve

MC1 = 2Q1

Q1 = MC1/2

MC2 = 4Q2

Q2 = MC2/4

Q1 + Q2 = MC1/2 + MC2/4

Q = MCT/2 + MCT/4 (sinceMCT = MC1 = MC2)

= 3MCT/4

MCT = 4Q/3

Thus  ​​​MC = 4Q/3

P = 38 - 2.5Q

MR = 38 - 5Q

MR = MC (Profit maximizing condition)

38 - 5Q = 4Q/3

38 = 4Q/3 + 5Q

38 = (4Q + 15Q)/3

38 = 19Q/3

19Q = 38×3

Q = 38×3/19

Q = 6

P = 38 - 2.5(6)

= 38 - 15

= 23