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! :)
I agree with your methodology and answer.
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! :)
a copy company expand production. Is 20 workers sharp copiers. Two months ago, firm added copiers, output increases 100,000 pages day. One month ago, added worker, productivity increased 50,000 pages da
To calculate the price elasticity of demand, you need to find the percentage change in quantity demanded relative to the percentage change in price. The formula for price elasticity of demand is:
E = (% change in quantity demanded) / (% change in price)
Let's go through the steps to calculate the price elasticity of demand at a price of $2:
1. Start by finding the quantity demanded at the initial price of $2. Using the demand curve equation, plug in P = $2:
Q = 10 - 2(2)
Q = 10 - 4
Q = 6
2. Calculate the total revenue at $2 per cigar. Total revenue (TR) is the product of price and quantity demanded:
TR = $2 * 6
TR = $12
Now, we will consider a small increase in price to find the new quantity demanded:
3. Increase the price by a small percentage. Let's assume a 1% increase in price. Multiply $2 by 1.01 to get the new price:
New price = $2 * 1.01 = $2.02
4. Find the new quantity demanded corresponding to the new price. Substitute the new price into the demand curve equation:
Q = 10 - 2(2.02)
Q ≈ 10 - 4.04
Q ≈ 5.96
To calculate the percentage change in quantity demanded and the percentage change in price, use the following formulas:
% change in quantity demanded = [(new quantity demanded - original quantity demanded) / original quantity demanded] * 100
% change in price = [(new price - original price) / original price] * 100
5. Calculate the percentage change in quantity demanded:
% change in quantity demanded = [(5.96 - 6) / 6] * 100
% change in quantity demanded ≈ -0.67%
6. Calculate the percentage change in price:
% change in price = [(2.02 - 2) / 2] * 100
% change in price ≈ 1%
Now, we can calculate the price elasticity of demand:
E = (% change in quantity demanded) / (% change in price)
E ≈ (-0.67% / 1%)
E ≈ -0.67
The price elasticity of demand at a price of $2 is approximately -0.67, not -2.0 as claimed by the marketing official. Therefore, your calculation of -0.25 appears to be incorrect.
Note: To calculate the price elasticity of demand with greater precision, you may consider using smaller percentage changes in price and quantity demanded.