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.
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!
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