Question

Question 1 20 pts 1) Company XYZ has a monopoly on a new product. The product can be manufactured in either of two factories. The costs of production for the two factories are Cį = 5Qị 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 1? the quantity produced in Factory 2? Total output? Price?

Answer 1

(a)

P = 500 - 4Q

TR = P x Q = 500Q - 4Q²

MR = dTR/dQ = 500 - 8Q

C1 = 5Q1²

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

C2 = 10Q2²

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

As Q = Q1 + Q2,

Q = 0.1MC1 + 0.05MC2

Setting MC1 = MC2 = MC,

Q = 0.1MC + 0.05MC = 0.15MC

MC = Q / 0.15

Setting MR = MC,

500 - 8Q = Q / 0.15

75 - 1.2Q = Q

2.2Q = 75

Q = 34 [considering 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)

If labor cost in plant 1 increases, MC1 will increase but MC2 will stay the same. So, in the relationship

Q = 0.1MC1 + 0.05MC2,

The first component will increase, and the second stays the same.

Therefore, total output (Q) will increase. Output at plant 1 (Q1) will decrease and output at plant 2 (Q2) will stay the same. Since Q will increase, price (P) will decrease.