Economics tutor help

Ashford 5: – Week 4 – Instructor Guidance

Class, I’m going to start with helping you with problem 2. This is the most difficult problem and if I can get you through this one hopefully Problem 1 won’t be so bad.

 

 Problem 2 NOTE: “constant” just means the number you calculate from given values.

1.     To derive the demand curve for Western states, substitute the values for advertising, income and prices and derive function for the price. Add up the constant terms to get
Qe=(coefficient)P + constants
or if this looks more familiar Q=a+bP, (Q/b)-(a/b) = P, a/b reduces to a constant and Q/b= 1/b*(Q) where 1/b is a number

2.     Solve for P to get the inverse demand curve, i.e. rearrange the equation above to get

Qe/coefficient – constants/coefficient = P
Just divide the constants by the coefficient to get a new constant. You can express the first term as 1/coefficient * Q where 1/coefficient will divide out to be a number.
3.     Similar for the Eastern states.

Qe = [coefficient] Pge + [constant] – [constant] +[constant]
Pge=[constant] -Qe/ [constant]  is the derived demand curve

b) Let us start with the Western market:
TRw=(Pw)*Qw
Note that because P= a+b(Q) when you multiply times Q you’ll get TR=aQ+b(Q)^2
MR is the first derivative of that equation. The book shows you some ways to get it without calculus but lets just say the rate of change of aQ is just a and the rate of change of Q^2 is 2Q so:
MRw=[constant] – 2*Qw/[constant]

For the Eastern market, we have:

TRe=(Pe)*Qe                  from the total revenue equation TR = PQ

MRe=[constant] -2*Qe/ [constant]

The cost information is the same for both markets:
TVC=755.363Q+0.005*Q^2
MC=755.363+2*0.005*Q

We create some values for Q and derive the respective values for MC, and for P and MR in each market. Then we plot the functions for each market:

 

Q

Pgw

MRw

MC

Pge

MRe

0

3498.725

3498.725

755.363

2179.875

2179.875

3000

 

 

 

 

 

6000

2510.524

1522.323

815.363

1984.874

1789.874

9000

 

534.1226

 

 

 

12000

 

 

875.363

 

 

15000

1692.374

18000

1009.874

21000

40.02214

-3418.68

965.363

1497.374

814.8733

 

Western Market

It is clear from the graph that the optimal solution is where MR and MC intersect, which from the graph seems to be for quantity between _____?  and _____? units.

[you can also just set MC = MR and solve for Q as below in c.] 

 
Eastern Market

For the Eastern states, the price is lower and quantity is just under _____?

 

c) We can calculate quantity exactly by setting MR=MC and solving for Q and then using that Q value to find P from the demand curve:

 
 
 

For the Western market:

Qw*=_____?
 Pgw*=$_____?

For the Eastern market:

 Qe*= ________?

 Pge*=$______?

d)The price elasticity of demand in the western states is:

Elasticity (Western) = (dQw/dPw)*(Pw/Qw) =  [Note: eQw/dQw is just the coefficient of Pw given above, and you just solved for Pw/Qw so just plug in the numbers]

Elasticity (Eastern) = (dQe/dPe)*(Pe/Qe) =  
[Remember: if the absolute value (forget the – sign) is less than one it is inelastic, if >1 it is elastic. So recall how revenue changes depending on the price elasticity of demand]

With _______? demand, it makes sense for price to be _________ so as to _________ sales. This indicates that the GGC strategy to ?_____ prices for the Eastern states is ?__________.

e) As the competitor is charging $2100 in both markets, it appears that GGC’s pricing strategy is ?______ in the Eastern markets as it will ?______ its sales and allow it to more than double its sales there. The pricing in the Western markets is very similar to its competitor’s pricing.

 

Market Structures and Pricing Decisions Applied Problems.
Please, complete the following 2 applied problems in a Word or Excel document. Show all your calculations and explain your results. Submit your assignment in the drop box by using the Assignment Submission button.

Week 4 Assignment Study Guide

1. A small business which produces plastic vacuum-suction covers for round household dishes has a monopoly that is protected by a utility patent. The market demand curve for this product is estimated to be:  Q = 6009 – 25P where Q is the number of plate covers per year and P is in dollars.  Cost estimation processes have determined that the firm’s cost function is represented by TC = 120 + 2500Q -0.25*Q2. 

(i)                 What is the profit-maximizing price and output level? Solve this algebraically for equilibrium P and Q and also plot the MC, D and MR curves and illustrate the equilibrium point.

(ii)               What profit do you expect that the firm will make in the first year?

(iii)             Do you expect this profit level to continue in subsequent years? Why or why not?

 

2. Greener Grass Company (GGC) competes with its main rival, Better Lawns and Gardens (BLG), in the supply and installation of in-ground lawn watering systems in the wealthy western suburbs of a major east-coast city. Last year, GGC’s price for the typical lawn system was $1,995 compared with BLG’s price of $2,100. GGC installed 9,130 systems, or about 55% of total sales and BLG installed the rest. (No doubt many additional systems were installed by do-it-yourself homeowners since the parts are readily available at hardware stores.) GGC has substantial excess capacity—it could easily install 25,000 systems annually, as it has all the necessary equipment and can easily hire and train installers. Accordingly, GGC is considering expansion into the eastern suburbs, where the homeowners are less wealthy. In past years, both GGC and BLG have installed several hundred systems in the eastern suburbs but generally their sales efforts are met with the response that the systems are too expensive. GGC has hired you to recommend a pricing strategy for both the western and east¬ern suburb markets for this coming season. You have estimated two distinct demand functions, as follows:

Qw = 1,035.548 – 6.07164Pgw  + 2.83Pbw + 2,100Ag – 1,500Ab + 0.2348Yw

for the western market and

Qe  = 49,714.29 – 30.7692Pge  + 6.984Pbe + 1,180Ag – 950Ab + 0.0825Ye

for the eastern market, where Q refers to the number of units sold; P refers to price level; A refers to advertising budgets of the firms (in millions); Y refers to average disposable income levels of the potential customers; the subscripts w and e refer to the western and eastern markets, respectively; and the subscripts g and b refer to GGC and BLG, respectively. GGC expects to spend $1.5 million on advertising this coming year and expects BLG to spend $1.2 million on advertising. The average household disposable income is $55,000 in the western suburbs and $25,000 in the eastern suburbs. GGC does not expect BLG to change its price from last year, since it has already distributed its glossy brochures (with the $2,100 price stated) in both suburbs, and its TV commercial has already been produced. GGC’s cost structure has been estimated as TVC = 755.363Q + 0.005Q2 where Q represents single lawn watering systems.

a.       Derive the demand curves for GGC’s product in each market.

b.      Plot graphically the demand and MR curves for each market, and also show GGC’s combined marginal revenue curve (MR) and its MC curve. Show graphically the quantities that should be produced and sold, and the prices that should be charged, in each market.

c.       Confirm your quantity and price results algebraically.

d.      Calculate the price elasticities of demand in each market and discuss these in relation to the prices to be charged in each market.

e.       Add a short note to GGC management outlining any reservations and qualifications you may have concerning your price recommendations