Below are two answers to the questions, can you explained which one is the correct one and why?

Dell assembles personal computers and sells them in the retail marketplace. The company is organized into two profit centers: the assembly division and the distribution division. The demand curve facing the company (and the distribution division) is P=3,500 - 10Q. The marginal cost for assembly (which includes purchasing the parts) is constant at $450. The distribution division faces constant marginal distribution costs of $50 per unit. A. What is the profit-maximizing retail price and output for the firm as a whole? B. If the assembly division has monopoly power to set the transfer price, what transfer price will it select (assuming it knows all the information above)? Calculate the profits for the two divisions in this case.

The profit maximizing output will be at the point where price is equal to the marginal cost.

P=MC

P=3500-10Q

MC=450+50=500

3500-10Q=500

10Q=3000

Output Q=300

P=3500-10(300)

=3500-3000

Retail price P=500

With Monopoly power optimal production(output) is at the point where Marginal Cost=Marginal Revenue

Total Revenue=P*Q

=(3500-10Q) * Q

= 3500Q-10Q2

Marginal revenue=dTR/dQ=3500-20Q

3500-20Q=500

20Q=3000

Q=150

P=3500-10(150)

=3500-1500

=2000

Profits= 150*2000-500*150

=225,000

From the calculation then the profit for each division will be775*150 = 116250 and the Market price = $2000

(A) :-

When MR= MC , then a firms maximize it's price.

MC = 450 + 50

[ MC = 500 ]

MC = $500

MR = (d/dQ) Q x ( 3500 - 10Q)

[ MR = 3500 - 20Q ]

Now ,

MR = MC

3500 - 20Q = 500

3500 - 500 = 20Q

3000 = 20Q

Q = 3000/20

[ Q = 150 ]

Now,

P = 3500 - 10Q

= 3500 - 10 x 150

= 3500 - 1500

= 2000

[ P = $2000 ]

(B) :-

The Marginal cost for assembly = $450

Market price = $2000

Therefore optimum transfer price should be

= 450 + [ 2000 - 450]/2

= 450 + 1550/2

= 450 + 775

= $1225

Optimum transfer price = $1225

Profit for each division will be = 775 x 150

= 116250