Posted by klynn on Tuesday, September 25, 2007 at 10:53am.
This is an MBAlevel Managerial Economics course. I am working on a homework assignment and have a couple problems that I don't really know how to get started. Here is the first:
Altmann, Inc. is a U.S. manufacturer of edible econimics texts. The firm has been exporting its least expensive model (the cherry flavored introductory microeconomics text), which sells for U.S. $1,500 to Mexico, where the demand has proven to be:
Q = 3500  2P
Where Q = quantity demanded and P = price. Altmann wants to break into the South American markets in Brazil, Argentina, and Chile. If the demand in each of these countries is the same as Mexico,
a.) How many texts can Altmann expect to sell in all three countries at a price of $1500?
b.) What will the total revenue, TR, be from sales in all three countries at $1500?
c.) What is the point price elasticity of demand in each country when the price is $1500? Would a price increase of 10% be advisable? (Assume that elasticity remains constant for the price increase.)
d.) What is the MR at a price of $1500 in each country?
e.) How many units should ALtmann sell in each country to maximize revenue? What price should he charge?
f.) Show that price elasticity equals 1.0 when total revenue is maximum.
If someone could at least tell me where to get started (i.e. which formulas I should be using, etc.) I would greatly appreciate it. Thanks!

Managerial Economics/Math  economyst, Tuesday, September 25, 2007 at 5:39pm
a) Demand is Q=35002P. If P=1500, Q becomes 500. Since there are 3 countries, Total Q=1500.
b) Total revenue is P*Q = 1500*1500=
c) Price elasticity is (%change in Q)/(%change in P). So, if P rises by, say 1% to 1515, then Q (in a country) drops to 470, a drop of 30. And 30/500 is 6%. So, the elasticity is 6%/1% = 6.0
For d,e, and e, may I use simple calculas?. Otherwise, we can approximate the results using the results from a,b, and c)
d) total revenue (per country) is P*Q=3500P  2P^2
MR is the first derivitive of TR. SO (for each country) MR=35004P. At 1500, MR=2500 (7500 for all three countries).
e) To maximize a function, set MR=0. So, 35004P = 0 when P=875.
f) repeat the steps in c) above. 
Managerial Economics/Math  klynn, Tuesday, September 25, 2007 at 9:58pm
economyst 
Thank you so much for all of your help. Your answers really help me, and I've been able to apply them to other parts of the HW that are similar.
I just have some questions on one of your answers; I just need a little clarification. On question e, after setting MR = 0 and solving, P = 875. Since P is price in the equation, does the 875 represent the price that the units should be sold at? If so, how do I go about finding the number of units that should be sold in order to maximize revenue? Or, if the 875 represents the number of units that should be sold in order to maximize revenue, how do I find the price that the units should be sold at? Any help is appreciated. Thanks!
klynn 
Managerial Economics/Math  economyst, Wednesday, September 26, 2007 at 9:41am
P=875 is the price that maximized total revenue. Plug this P into the original demand Q=35002P to get the quantity.

Managerial Economics/Math  klynn, Wednesday, September 26, 2007 at 12:08pm
Oh, okay. That was obvious...I should have seen that. I worked on the other parts using the info you provided. On question C, the second part of the question asked, "Would a price increase of 10% be advisable? (Assume that elasticity remains constant for the price increase.)" So, a 10% price increase would cause P to go from $1500 to $1650. After plugging the $1650 back into the original Q=35002P, Q = 200. To find TR, P x Q, so $1650 x 200 = $330,000. The original TR w/a price of $1500 was $750,000. So, since the TR w/the 10% price increase is lower than the original TR, the 10% increase would not be advisable, right?

Managerial Economics/Math  klynn, Wednesday, September 26, 2007 at 12:12pm
Also, I worked out question F to show that price elasticity equals 1.0 when TR is at its maximum. When TR is maximized, P = $875 and Q = 1750. So, if $875 was increased by 1%, Q would drop to 1732.50, which is a drop of 17.5. So, 17.5/1750 = .01. So, .01/.01 = elasticity of 1.0.
I just wanted to post this to make sure I worked it out right. Thanks again for all of your help! :) 
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