Demand Estimation and Elasticity 7 Questions of long algebra formulas

Please complete these 7 questions and make sure to show all steps taken to get to the answer as demonstrated at the bottom of this page. This is VERY IMPORTANT and if it is not done correctly (as shown below after question 7), I will demand a FULL Refund.

If you only put down a numeric answer alone That means nothing to me. Where did you get that? Random? I have no way to know. To arrive at that answer, you would have had to work through a bunch of steps so include those!

1) Suppose equilibrium price in the market is $30, and the marginal revenue is $20. What is the price elasticity of demand?

2) You are a manager at Hancock Tires. If the marketing department estimate of the demand for its high-end tire is Q = 150-15P, what price should it charge to 15.3 maximize its revenue?

3) The David Company's demand curve for the company's product is P = 2,000 – 20Q, where P = price and Q = the number sold per month.

A. Derive the marginal revenue curve for the firm.

B. At what output is the demand for the firm's product price elastic?

C. If the firm wants to maximize its dollar sales volume, what price should it charge?

4) Rebel Sole is a rapidly expanding shoe company. The following is the demand estimate for its popular shoes. The estimate was done using 40 observations. Q = 10 – 10 P + 4 A + 0.42 I + 0.25 Py

       (3)   (1.8)    (0.7)   (0.1)     (0.1)

F = 93, s = 6, R2 = 93%

Q is quantity sold (in thousands), P is shoe price, A is advertising expenditure (in thousands), the numbers in parentheses are standard errors, I is disposable income per capita (thousands of dollars), and Py is the price of related goods.

a. Evaluate the model based on F, R2.

b. Test the significance of Py.

c. If P = $5, A = $30,000, I = 50,000, and Py = $6, calculate advertising elasticity.

d. Given the information in c. above, calculate the 95% confidence interval for Q.

5) Mr. Douglas's marginal rate of substitution is six slices of bread for two Pepsis at the present combination of Pepsi and bread he is consuming. If the price of each Pepsi is $2.00 and the price of a slice of bread is $3.00, is Mr. Douglas maximizing his utility? If not, how should he change his consumption? Briefly explain your response.

6) Airlines give away millions of tickets each year through their frequent flyer programs, with the typical airline awarding a free ticket for each 25,000 miles flown on the airline. The average airline ticket costs $500 and is for a 2,500-mile round trip. Given this information, evaluate the following statement: Airlines could have the same effect on demand by eliminating their frequent flyer programs and simply lowering the average ticket price by 10 percent.

7) Please identify a heuristic (quick rule of thumb) that you have employed when making a decision, whether in business or as a consumer. Were you better off by making the heuristic decision, or would it have been better to follow a longer decision process? Explain briefly.

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EXAMPLE EXAMPLE EXAMPLE EXAMPLE

Solve for equilibrium and quantity.

Given: Monthly quantity demand function for a product is Qd = 10,000-80P and monthly quantity supply function for a product is Qs=20P.

(If you put down: 2000 as the answer. That means nothing to me. Where did you get that? Random? I have no way to know. To arrive at that answer, you would have had to work through a bunch of steps so include those!)

Here is an example of how to present you work on this problem which would allow me to follow your steps:

1)    Qd=Qs   which is also equal to:

2)    10,000 – 80P = 20P

Next add 80P to both sides and divide by 100 to get:

10,000 =100p

Divide by 100 to get P by itself:

 100 = P

This is equilibrium price. 

Next, you need equilibrium quantity.

Plug the equilibrium price (100) into either  demand or supply function. 

 If we plug it into the demand function you get:

 Qd= 10,000 – 80*100 = 2,000

(80*100 is 8,000 and 10,000 minus 8,000 is 2,000)

If you plug it into the supply function you get:

Qs = 20*100 = 2,000

Here, the quantity supplied is equal to the quantity demanded.