Question

1) Company XYZ has a monopoly on a new product. The product can be manufactured in elther of two factories. The costs of production for the two factories are C = 5Q and C2 = 10Q2. The firm's demand for the product is P =500-4Q. a. (10) Find the quantity produced by factory 1, the quantity produced by factory 2, the total quantity produced, and the price that maximize profit. b. (10) There is an increase in the cost of labor in Factory 1 but the cost of labor in Factory 2 remains the same. How will this increase in labor cost affect the quantity produced in Factory 1the quantity produced in Factory 2? Total output? Price? HTML Editora Β Ι Ο Α Α IX E 31 1 x x V CDTi 12pt Paragraph

Answer 1

(a)

Demand: P = 500 - 4Q

TR = P x Q = 500Q - 4Q²

MR = dTR/dQ = 500 - 8Q

For factory 1, C1 = 5Q1²

MC1 = dC1/dQ1 = 10Q1, hence Q1 = MC1 / 10 = 0.1MC1

For factory 2, C2 = 10Q2²

MC2 = dC2/dQ2 = 20Q2, hence Q2 = MC2 / 20 = 0.05MC2

Aggregate output: Q = Q1 + Q2, hence

Q = 0.1MC1 + 0.05MC2

Substituting MC1 = MC2 = MC,

Q = 0.1MC + 0.05MC = 0.15MC

MC = Q / 0.15

Profit is maximized when MR = MC, so

500 - 8Q = Q / 0.15

75 - 1.2Q = Q

2.2Q = 75

Q = 34 [accepting only integer value for output]

MC = 34 / 0.15 = 226.67

Q1 = 0.1 x 226.67 = 22.67

Q2 = 0.05 x 226.67 = 11.33

P = 500 - 4 x 34 = 500 - 136 = 364

(b)

Increase in cost of labor in factory 1 increases MC1, leaving MC2 unchanged. Hence, in the equation

Q = 0.1MC1 + 0.05MC2,

The first part will increase, and the second is unchanged.

As a result, aggregate output (Q) will increase. Output at factory 1 (Q1) will decrease and output at factory 2 (Q2) will remain unchanged. Because Q will increase, price will decrease.