# Economics

• Oct 6th 2010, 03:31 PM
Kellychu977
Economics
Hi Everyone,

I recently got this question as a homework exercise, and I tried to do it but am having a lot of trouble and would love any help you can give.

Thanks guys, here's the question:

The market for luxury female shoes consists of two firms: Milono Shoes and Blanc Shoes. Milono Shoes has a patented technology that permits it to produce its stiletto shoes in a manner that is more efficient than its rival, Blanc Shoes. As a result, Milono Shoes is the first to choose its profit-maximising output level in the market. Milono Shoes is considering whether or not it should undertake a merger with Blanc Shoes as an external consultant has suggested that a merger would be profitable. The inverse demand function for luxury female shoes is given by P = 800 – 4Q, Milono Shoes costs are CM(QM) = 40QM and the costs for Blanc Shoes are given by CB(QB) = 40QB.
Would it be profitable for Milono Shoes to merge with Blanc Shoes? If not, explain why not.

Kind regards,

Kelly
• Oct 6th 2010, 08:02 PM
raphw
Simple answer: Merges are (almost) always good for the producers in IO-models. In this simple model you face a Stackelberg game to be solved by backward induction. For BS the output of MS is given. Thus:

$\pi_{BS} = (800 - 4(Q_{MS}+Q_{BS}) Q_{BS} - 40Q_{BS}$

If you optimize this profitfunction for the output of BS you have this company's optimal outputlevel ( $Q^*_{BS}$) with respect to what MS has chosen. Using this outputlevel (MS will antizipate this level, too.) you can now optimize the MS profits:

$\pi_{MS} = (800 - 4(Q_{MS}+Q^*_{BS}) Q_{MS} - 40Q_{MS}$

Now you know what both Q will be and therefore what the total Q will be. This will yield both companies profits. You will see that the sum of both profits is lower then the profit in a monopoly and therefore a merge would be profitable.
• Oct 13th 2010, 02:19 AM
knightly
Hi,
If the sum of both profits are lower than the monopoly. Would it be more profitable for the MS to not merge?
Sorry, Im just curious
• Oct 13th 2010, 07:57 AM
raphw
No, because if they merged they could split the profits in a way that both sides earn more.
• Oct 14th 2010, 12:52 AM
knightly
Correct me if im wrong,

But I decided to work it out and found out that total profits for MS was $18,050 whilst total profits for BS was$7,125. I also worked out that if MS wasnt to merge their profit would be \$39,900.

Could someone give me a working out of how to get to the correct answer?
• Oct 14th 2010, 08:34 AM
raphw
$\frac{\partial \pi_{BS}}{\partial Q_{BS}} = 800 - 4Q_{MS} - 8 Q_{BS} - 40 = 0 \Rightarrow Q_{BS} = 95 - \frac{1}{2}Q_{MS}$

Then:

$\frac{\partial\pi_{MS}}{\partial Q_{MS}} = 800 - 8Q_{MS} - 95 + \frac{2}{2}Q_{MS} - 40 = 0 \Rightarrow Q_{MS} = 95$

Thus: $Q_{BS} = 47.5$

If I now fill in, the market price will be 230 so BS earns: 9025 and MS: 18050, Total: 27075

In a monopoly, the maximization problem will be:

$\frac{\partial\pi}{\partial Q} = 800 - 8 Q_{BS} - 40 = 0 \Rightarrow Q_{BS} = 95$

Thus $\pi = 39900 > 27075$