QUESTION 1 Bates Corporation is composed of a marketing division and a product division The marketing division packages and sells the fabric produced by the product division

QUESTION 1

Bates Corporation is composed of a marketing division and a product division The marketing division packages and sells the fabric produced by the product division. The demand for the finished product sold by the marketing division is

Pm = 100 – 1.5Qm

where Pm is the price of the finished product, and Qm is the quantity sold. Excluding the production cost of the basic fabric item, the marketing division’s total cost function is

TCm = 50 + 7.5Qm

where TCm is the marketing division’s total cost. The production division’s total cost function is TCp = 2.5 - 1.5Qp + 0.2Qp²

Where TCP is total production cost, and Qp is the total quantity produced of the basic fabric item.

(a) If Qm = QP (i.e. the production division only sells its fabric to the marketing division), what is the optimal output for both divisions and what is the optimal price for the finished product?

(b) If there is a perfectly competitive market for the basic fabric item, the price being CFAF10 per unit, what will be the optimal output for each division, and what is the optimal price for the finished product?

QUESTION 2

Company Z is selling product A for $4/unit. The average variable cost is $2, and the total fixed costs are $300,000.

a) How much should the company produce in order to break even?

b) Company Z decides to add a new product to its production line. They decide to produce the same quantity of product B. This would usually cost 500,000. However, the Total cost of producing both products together is 1,000,000. Calculate the degree of economies of scope.

QUESTION 3

The Smith Corporation and the Jones Company are the only two producers of a certain type of escalator part. The demand for this particular part has the following equation: P = 1000-5Q

Each of the companies has a different total cost function.

TCSmith = 600 + 100Q +50Q2 TCJones = 100 + 200Q + 100Q2

The companies want to collude. a. How many escalator parts should the Smith Company produce? b. How many parts should Jones produce?

c. What price should the companies charge?