For B) First, if the firm faces a downward sloping demand curve, then the firm has some monopoly power -- Use the general monopoly model to figure your solutions. While true that you don't know what costs are, you can be certain, at least, that marginal costs are positive. So, the firm can certainly do better if it raises price such that MR=MC=0. BTW, at MC=0 with the given demand curve, you would find the price elasticity to be -1.0.
For C) I see you have made a math error, which has gotten you off track.
For these kinds of problem, I (personally) like to see demand equations of the form P=f(Q) (Like the equation for Jimbo cigars above. This way, I don't get confused about what the demand equation would look like in a graph). So, do some simple algebra and re-arrange terms.
You start with Q=100/(P^2). So, P^2 = 100/Q. So P=sqrt(100/Q) = 10/(Q^.5)
Now then TR=P*Q = 10*Q^.5.
MR is the first derivative. MR=5/(Q^.5)
Take it from here.
I wanted to post this as a new question to make sure you saw it. Thanks! :)
Posted by klynn on Wednesday, October 3, 2007 at 11:29am.
This is an MBA-level Managerial Economics Course. I'm working on some HW and just want to double-check my answers.
1. Jimbo's is a new company producing exploding cigars. Jimbo's company has the following demand curve for the cigars:
P = 10 - 2Q
Jimbo is currently charging $2 per cigar.
A. A marketing official cliams that the price elasticity of demand at $2 is -2.0. Do you agree? If you disagree, what is the correct price elasticity?
On A, I found the price elasticity to be -.25. In the problem, P=2 and Q=4 (as a result of P=2). With a 1% increase in P, the new P is $2.02. The new Q as a result of the price increase is 3.99. So, a $.02 increase in price led to a .01 decrease in Q demanded. Price elasticity is the % change in Q/% change in P, so:
-.01/4 divided by .02/2 =
-.0025/.01 =
-.25
Can someone tell me if this is correct? If not, can you tell me how to get the correct answer? Thanks! :)
For Further Reading
Managerial Economics/Math - economyst, Wednesday, October 3, 2007 at 2:33pm
I agree with your methodology and answer.
Managerial Economics/Math - klynn, Wednesday, October 3, 2007 at 4:11pm
Ok, great! Thanks! If you don't mind, the question does have a couple other steps that I need a little bit of help on.
B. Evaluate the wisdom of the pricing policy. If a price change is advisable, what price would you recommend that, with certainty, would improve profits the most and why? Given that you do not know marginal costs, state the necessary conditions for further price changes, up or down, from the price that you feel is certain to improve profits the most. Hint: think of the changing price elasticities as you slide down a linear demand curve.
For this one, I know that the top part of the demand curve is elastic, the middle is unit elasticity, and the bottom part is inelastic. Given that the elasticity is -.25, this (i think?) should fall into inelasticity. In the inelastic part of the demand curve, prices will rise. But, I'm not sure how to figure out exactly what price to charg since we don't have costs.
C. If, in fact, Jimbo's company has a demand curve equal to Q = 100P^-2 and constant marginal costs of $4 per cigar, what would be the profit maximizing price for the cigars?
On this one, I know I need to set MC = MR to find the profit maximizing point. MR = 200P^-3 and MC =4. So, this is 4 = 200P^-3, which then goes down to -50 = P^-3 (i think?). But, I'm not sure how to get P by itself b/c the -3 exponent is throwing me off.
Any help is much appreciated. Thanks so much for all your help! Without you, I'm not sure how well I'd be making it through this class! :)
1 answer