This is an MBA-level 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!

a) Demand is Q=3500-2P. 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=3500-4P. At 1500, MR=-2500 (-7500 for all three countries).

e) To maximize a function, set MR=0. So, 3500-4P = 0 when P=875.

f) repeat the steps in c) above.

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

P=875 is the price that maximized total revenue. Plug this P into the original demand Q=3500-2P to get the quantity.

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=3500-2P, 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?

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! :)

Which of the following cost functions exhibits cost complementarity?

A. -4Q1Q2 + 8Q1
B. -4Q2 + 8Q1
C. 6Q1Q2 - Q1
D. 4Q2Q1 + 8Q1

Find 1-the marginal and 2-the average cost functions for the following total cost function calculate them at Q=4 A Q=6 Tc=3Q*Q+7Q+12.

with the aid of the diagram discuss the importance of managerial economics

To start solving these problems, you will need to use some basic concepts and formulas from managerial economics. Here is a step-by-step guide to help you get started:

Step 1: Understanding the demand function
The demand function given is Q = 3500 - 2P, where Q is the quantity demanded and P is the price. This equation represents a linear demand curve, where quantity demanded decreases as price increases.

Step 2: Determining the quantity sold in all three countries at a price of $1500 (part a)
To calculate the quantity sold in all three countries, substitute P = $1500 into the demand function and solve for Q. Repeat the process for each country (Mexico, Brazil, Argentina, and Chile) and sum up the quantities.

Step 3: Calculating total revenue (part b)
Total revenue (TR) can be calculated by multiplying the quantity sold (Q) with the price (P). For each country, multiply the quantity sold at $1500 by $1500 to get the total revenue. Sum up the total revenues from all three countries.

Step 4: Finding the point price elasticity of demand (part c)
The price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. The formula for point price elasticity of demand is:

E = (% change in quantity demanded) / (% change in price)

To calculate the price elasticity at $1500, differentiate the demand function with respect to price (dQ/dP), multiply it by P/Q, and substitute P = $1500 and Q from part a. The resulting value will give you the elasticity for each country.

To determine if a 10% price increase is advisable, compare the absolute value of elasticity (ignore the negative sign) with 1. If the absolute value is greater than 1, demand is elastic, and a price increase would decrease total revenue.

Step 5: Calculating marginal revenue (part d)
Marginal revenue (MR) represents the additional revenue gained from selling one more unit. The formula for MR is:

MR = dTR/dQ

To find MR at a price of $1500, take the derivative of total revenue (TR) with respect to quantity (Q). The resulting value will give you the marginal revenue in each country.

Step 6: Maximizing revenue (part e)
To maximize revenue, find the quantity (Q) that corresponds to the maximum value of MR (where MR = 0), and then calculate the price (P) at that quantity. Use the formulas from step 5 to find the values that will maximize the revenue in each country.

Step 7: Showing that price elasticity equals -1.0 when total revenue is maximum (part f)
To prove that price elasticity equals -1.0 at maximum total revenue, differentiate the total revenue function with respect to price (dTR/dP), multiply it by P/TR, and substitute P and TR from part b. The resulting value should be -1.0.

Remember to use your calculator or spreadsheet software to perform the necessary calculations to get the numerical values for each step.

By following these steps, you should be able to solve the problems in your assignment. Good luck!