economics case study and need the explanation and answer to help me learn.
Directions: I will provide all 6 Module 2 documents to support the Problem Set. Prior to accepting bid, I believe I limited to additional attachments.
Please follow the instructions on the syllabus indicating how to complete and turn in this assignment. Graphs are essential when asked for – write them clearly and label everything!
(2 points) Is the following statement true or false? Why? “If MC is positive and demand is downward sloping, then it is always true that the revenue maximizing output level is greater than the profit maximizing output level.”
Suppose I estimate the following demand function for a watch I produce and sell:
(2 points) What is the conceptual difference between an increase in demand and demand becoming more inelastic? Provide an example of a factor that could cause and increase in demand, and then provide a different example of a factor that caused demand to become more inelastic.
Q = 10000 – 4P +200PR
Where:
Q = quantity demanded in units
P = price in dollars
PR = number of YouTubers who positively review my watch
We are currently operating at the following values:
P = $400
PR = 10
In addition, suppose MC is $300.
Given all this, please answer the following questions:
(1 point) Derive the firm’s current demand curve and calculate and interpret the firm’s current price elasticity of demand. Be as precise as you can with your elasticity interpretation.
(1 point) Given you answer in b, should the firm increase or decrease output in order to maximize profits (NOT revenues)? Explain and show your work on a well labeled graph. Hint: your graph should indicate the current output level as well as the profit maximizing output level.
(2 points) What is the profit maximizing output and price? Show and explain all your work and match up your answer to your work in part b.
(2 points) Suppose I want to also incorporate YouTubers who give a negative review. How would I go about doing so and what do you think the impact of this would be relative to positive reviews? Note: there isn’t just one clear answer – there are lots of ways to do this.
Requirements: Thorough explanation
ECON 509 Module 2 Pre Problem Set
Student’s Name
Institutional Affiliation
Course
Date
Discussion Question
From Module 2:
One of the products I buy are movie tickets. The average price per ticket is $8.00 (adults), $7.50 (seniors), $7.00 (child), and +$3.00 (3D movie). This means that some of the non-price demand variables that are likely to shift the demand curve for movie tickets are tastes and preferences (T), consumers’ income (I), advertising (A), and age which is a demographic (Ad). Therefore, the demand function in Module 2: Part 5 would have the following results:
Qd = 50 – 0.5P + 0.01T + 0.12I + 0.32A + 0.20Ad
Assume the following are the values for the independent variables:
P = 70
T = 3
I = 50
A = 15
Ad = 20
When the non-price demand determinant values are inserted into the demand function, the demand curve would look as follows:
Qd = 50 – 0.5P + 0.01(3) + 0.12(50) + 0.32(15) + 0.20(20)
= 50 – 0.5P + 0.01(3) + 0.12(50) + 0.32(15) + 0.20(20)
= 50 – 0.5P + 0.03 + 6 + 4.8 + 4
= 50 – 0.5P + 14.83
Therefore, Qd = 64.83 – 0.5P
Question:
Given the non-price supply variables that can cause a shift on the supply curve, such as price of related goods (Pr), input costs (C), number of suppliers (S), and government policy (G) how would the supply function look like? If the values of these variables were the same as the ones inserted in the demand function, would the equation look like this: Qs = 64.83 – 0.5P?
Person 1:
Hi Everyone,
I found this section very interesting and am anxious to see how we apply finding this shift in demand to our datasets for the project. I would like to figure out how to get the relevant data points to try this at my current firm.
For most of this module I was able to keep up… then we got to Part 5.
In Part 5, when we discuss elastic demand points, are we primarily focusing on the extent of fluctuations in the demand curve? In other words, does finding the value of “E” in our example allow us to gauge the degree to which specific variables influence the significance of changes in the demand curve?
Hopefully I didn’t just make that more confusing for anyone. Thanks for any insights!
Person 2:
Similar to my question from module 1 I am still trying to wrap my head around whether these economic principles apply in situations where the price is either not relevant or strictly dictated to those who provide the product/service. when comparing price and quantity of demand we need to assume that the ONLY thing changing is one variable like price. If the price changes, what happens to demand? To the customer (i.e patient) the incidence of acute stroke is what it is regardless of price and considering that it is a life-threatening emergency patients will go and get treated with no regard to cost, assuming they even have an idea of what actual costs are. Because prices are set by the government it does not matter if demand is 1 or 1,000, the price is the same. For most products we are talking about price deltas of 15% would impact demand. I guess I am not sure there is data to suggest that a 15% price change to treat acute stroke would impact the demand (i.e. patients seeking treatment). whereas our material covers demand curves with a slope over a wide range of price and demand points starting at zero demand.
Person 3:
As I progressed through the modules, I initially felt like I had a decent grasp of the concept of the demand curve when it was introduced in Module 1. One specific area that’s been on my mind is how to apply the theoretical understanding of demand curves to real-world situations. It’s one thing to draw a demand curve on paper, but it’s quite another to translate that into practical scenarios. I’ve been working on this and attempting to put the real-world examples into context. It’s an ongoing process, and I know that I’ll likely have more specific questions as I continue to study and try to integrate these concepts.Currently, I’m going through the course materials step by step. I start by reading the notes to get a solid foundation, and then I go back to watch the video lectures. This approach helps me consolidate my understanding and connect the theoretical concepts to practical applications. While I’m making progress, I also realize that the learning process can be iterative, and sometimes it takes time to fully grasp certain concepts.
Module 2: Part 1
When you think of demand “increasing” or “decreasing” what, precisely, do you mean? How do we measure that? what causes it? This lecture works through these issues. Pay close attention to the difference between a shift in demand and a movement along demand.
This part will cover the following Module Learning Objectives:
Define the factors that shift a demand curve
Demonstrate shifts in demand mathematically, graphically, and in words
Here is the notes file:
Introduction:
So let’s start focusing on demand. Pause for a moment and think about a produce you sell or buy. What has happened to demand for that product? Why? What will happen? How do you think about “demand?” What does it mean? How do you measure changes in it?
We need a set of concepts around demand to specify and answer all these questions…
There are two types of demand changes:
A shift in demand (a change in the intercept of the demand curve):
A change in the slope of the demand curve:
This Module will work through both changes to the demand environment of firms.
To keep the module “alive” to you please keep that product you thought of in mind and apply each section to it.
Introductory Analysis of Shifts in Demand:
This section will help us begin to delve deeper into demand – the key relationship for a firm.
First, what is “demand?” It is a term that we all use, but we need to be precise about terminology.
Demand shows the relationship between price and Quantity demanded.
That is, “demand” refers to an equation or a graph – NOT to a particular value.
So, saying that my demand is 2,000 units is completely wrong: 2,000 units is NOT an equation!
To be more accurate, you would replace “demand” with “quantity demanded.” And then specify a particular price:
“my quantity demanded is 2,000 units when price equals $5” is much better…
As we have seen, relationships can be represented graphically, verbally, in a table, or by an equation.
Below is an example of an equation form with its graph:
P = 10 – Q
Economists write and graph this equation with P on the y-axis (left hand side of the equation) and Q on the x-axis (right hand side) because in economics (rather than business) we are interested in how markets work and the key variable that does this is price, not quantity.
However, in business we like to think about how price changes impact quantity – so we want an equation with Q on the left hand side.
We will make this conversion in the next module, but let’s lay some math groundwork now in preparation:
Suppose we have P = 10-Q
How do we rearrange to get Q by itself?
P = 10-Q
P+Q = 10
Q = 10-Q
Let’s try another:
P = 20-2Q
P+2Q = 20
2Q = 20-P
Q = 10-.5P
First question: are demand curves always downward sloping? Is there always a negative relationship between price and how much people would like to buy?
Answer: there is a theoretical case in which this is not true, but in practice I have not seen one.
The reason is that, when you examine a relationship between two variables (price and quantity demanded in this case) you must hold all other factors constant (ceteris paribus assumption).
That is, we are saying: if the only thing that changes is price, will customers as a result decide to increase or decrease their quantity demanded?
We will work with what we most commonly see – a demand curve with a negative slope.
Now, here is the catch…demand curves move over time. Demand can increase or decrease
Reasons demand curves shift:
Factors controlled by the firm:
Advertising
Quality changes
Customer service
Tie-in sales
Factors controlled by other decision-makers
Price of substitutes
Price of complements
Regulatory shifts and other government action
Other (demographic factors)
Increase in number of consumers
Income
Tastes and preferences
Seasonality/weather
So let’s work through some of these demand dynamics:
Example 1: Suppose that I am selling wine, and real GDP rises:
Example 2: Suppose I sell tennis balls and the price of tennis rackets falls:
Example 3: Pickleball…. Demand has increased tremendously over the past two years – why? Tastes and preferences? Demographics? Will demand keep shifting out? To what degree?
Note: it would be helpful if you worked through more on your own – good practice…
In summary, when we think of a demand increase or decrease – a shift in demand – we are dealing with a change in the intercept, not the slope. However, the slope of a demand curve can also change, but its interpretation is very different.
Module 2: Part 2
In part 1 we examined how to capture shifts in demand. This lecture focuses on changes in the slope of the demand curve: The key point to remember is that we measure the price sensitivity of consumers through the price elasticity of demand.
This part will cover the following Module Learning Objectives:
Define and calculate the price elasticity of demand
categorize price sensitivity into elastic and inelastic
link elasticity to the slope of a demand curve
Here is the notes file:
Last time we modeled shifts in demand: a change in the intercept of the demand curve.
This time we will discuss changes in the slope of the demand curve: what does it mean when your demand curve gets flatter or steeper?
These notes explore this change more carefully – what does it mean, why does it happen, and what should we do in response?
The slope of demand (sort of…):
Consider the following two demand curves which differ in their slope:
Demand curve 1 is “steep” and demand curve 2 is “flat:”
What is the implication of this?
To see, consider an increase in price. We know that, because demand is downward sloping, using either demand curve will result in a drop in quantity demanded.
The slope of the demand curve will tell us exactly how much quantity demanded will fall.
Using demand curve 1, the increase in price from $10 to $11 results in a “small” decrease in quantity demanded from 100 to 95 . For some reason, the consumers decided to drop their consumption only a little in response to the higher price.
In contrast, demand curve 2 shows a much larger decrease in quantity demanded (from 100 to 80) as a result of the price increase. These consumers are very price sensitive.
Overall, we have:
Flat demand curves generally correspond to price sensitive consumers whereas steep demand curves reflect price insensitive consumers.
Consider the following demand curve:
P = 50 – 1/2Q
As written it is difficult to gauge the effect a change in price will have on Q. To make this easier (and for other reasons), we can rewrite the demand curve as follows:
Q = 100 – 2P – this is called the “inverse demand curve”
(we worked through the math steps last time)
Question: what is the slope of the inverse demand curve?
Answer: -2.
Question: what does this mean?
Answer: if price increases (decreases) by $1, then quantity will decrease (increase) by 2 units.
The slope of demand is nice – it tells us how responsive consumers are to changes in price.
The key (as indicated by the bold parts above) is that the slope of demand is measured in units. This can have advantages, but redefining the slope will prove beneficial.
The Price Elasticity of Demand:
The price elasticity of demand is just the slope of the inverse demand curve redefined in terms of percentages rather than units.
Definitions:
Slope: change in Q/change in P = dQ/dP = derivative of inverse demand curve
Elasticity = E = percentage change in Q/percentage change in P
Example: if E = -2 then a 1% increase in the price will lead to a 2% decrease in quantity demanded all else equal.
Calculation:
Calculating the price elasticity of demand is quite easy:
E = (dQ/dP)(P/Q)
Example:
Go back to our previous inverse demand curve: Q = 100 – 2P
E = -2(P/Q).
Thus, elasticity depends upon where we are on the demand curve, not just its slope!
Consider the following points:
A: a point with a high price: P = 40 and Q = 20.
At this point the price elasticity of demand is: E = -2(40/20) = -4
Thus, at this point a 1% increase in price will lead to a 4% decrease in Qd – consumers are very price sensitive!
B: a point with a low price: P = 10, Q = 80.
At this point E = -2(10/80) = -.25.
Thus, at this point a 1% increase in price will lead to a .25% decrease in Qd – consumers are not very price sensitive.
Does this variation in E across the demand curve make sense? Sure – when prices are high to begin with consumers will be more sensitive to a price increase then when price is low.
What are the determinants of elasticity?
The current P/Q position on the demand curve
Factors that affect the slope of the demand curve
Number of substitutes
Type of good – necessity vs. luxury
Time horizon
Scope of market (gas generally vs a particular brand of gas)
So like the last notes – think of some products where consumers are very price sensitive and are not price sensitive. Which of the factors above are the drivers of this?
Now that we understand the concept of elasticity, let’s incorporate it into our general framework.
Module 2: Part 3
Part 3 incorporates the elasticity work of part 2 into the profit maximizing framework developed in Module 1. We do so on the revenue side – so these notes link up E with TR and MR. The derivations are not important, but the conclusions are!
This part will cover the following Module Learning Objectives:
determine when price increases lead to higher or lower total revenue and explain how this depends on price elasticity of demand
use the MR = P(1+1/E) equation to determine if profits are being maximized based on a calculated elasticity
The notes are here:
Last time we defined, calculated, and interpreted the price elasticity of demand. What we now want to do is connect this work with the profit maximizing problem we developed in Module 1.
To do so, we start by realizing that elasticity is a demand feature, and demand drives revenues. So let’s connect up elasticity and TR and MR.
WHAT’S THE POINT OF ALL THIS THEORY???
Good question… As you know, firms collect data on consumers all the time, and then analyze that data to uncover patterns in demand. If we had some fundamental understanding of how demand conditions impact pricing and output strategies we could quickly form data driven decisions. That is our aim…
Elasticity and Total Revenues:
This section can be summarized as answering the following:
“Should I raise or lower my price in order to increase TR?”
The answer is “if your consumers are price sensitive then you should lower your price because the negative impact of a lower price will be outweighed by the positive increase in Q. However, if your consumers are not very price sensitive then raise your price, because the benefit of higher prices will outweigh the drop in sales.”
In fact, we can be more precise than this:
If |E| > 1 then demand is termed “elastic” and you should lower your price to increase revenues.
If |E | < 1 then demand is termed “inelastic” and you should raise your price to increase TR.
Question: suppose |E| = 1?
Well, then the percent change in price is exactly equal to the percent change in Q so TR will remain the same!
Elasticity and MR:
We know that Q* is where MR = MC, so it is natural to try to draw a link between MR and E.
Let’s start with definitions:
MR = dTR/dQ
E = (dQ/dP)(P/Q).
Let’s work with MR a bit…
TR = P*Q where P = f(Q).
When we take a derivative of two terms multiplied together we have to use what’s called the “product rule.” Some of you may remember this (first times derivative of second plus second times the derivative of the first….)
Using the product rule, we have: MR = P(1) +Q(dP/dQ) = P + (dP/dQ)Q
Look at the last term – it looks a bit like elasticity…
We can play around with this and get the following:
MR = P(1+1/E)
That was a lot – and I do not expect you to always have this in your head so…. What use is it?
Well, for starters, suppose that E = -1 – in this case MR = 0 and TR is maximized!
Suppose that E = - .5 (we are producing on the inelastic portion of demand), then MR = -P which means our last unit produced yielded negative MR – we obviously are NOT maximizing profits.
So, to maximize profits you MUST be producing on the elastic portion of demand!
Question: Suppose P = 10, E = -2, and MC = 7. Am I currently maximizing profits? If not, should I raise or lower my price to do so? Explain.
Module 2: Part 4
Part 4 lays out the basic organizational structure of how to make decisions directly using results from data analysis. We essentially are going to take the profit maximization problem developed in Module 1 and re-organize the structure so that we can incorporate demand data analysis directly into it.
This part will cover the following Module Learning Objectives:
compare and contrast and demand curve and a demand function
explain the benefits of a demand function
The notes are here:
Now we have finished with ideas and measurement related to demand and revenue changes, we can now recast the profit maximization framework developed in Module 1 in two important ways:
Let’s bring in all the other demand determinants so we can examine how they impact decision-making
Let’s set up the problem in a way that could come directly from empirical work rather than theory in isolation.
A Demand Function:
Ok…everything above would be great to do in practice, but it assumes that we know our demand curve.
How does a firm derive its demand curve?
The only way to do so is to look at the past and try to infer from it steady relationships that are likely to apply today.
Put differently, we need to collect data and analyze it properly!
Suppose I looked at the past 4 quarters and found the following:
P Qd
10 100
11 120
13 145
17 155
What does this imply?
Does this imply that my demand curve for this period is positively sloped?
No, not at all. Remember that demand curves are drawn assuming all other demand determinants are held constant!
It is likely that during this year incomes changed, my rival’s prices changed, tastes changed, and these factors all influenced Qd.
The main point is this: To get a good estimate of a demand curve, we must control for all other determinants of demand. This will not only ensure an accurate measure of demand, but will also yield important information on other demand factors we are interested in!
Thus, we want to estimate a demand function: a function showing the relationship between Qd and all its determinants.
It will take the following form: Qd = f(P, Psub, Pcom, Tastes, Income, ect….)
A demand curve can easily be derived from a demand function.
Before moving forward, write out a demand function like the one above but for a product you are familiar with – try to be specific!
Estimating a Demand Function:
Step 1: What variables should be included?
Use your knowledge of economics together with your experience
Step 2: How should each variable be included?
I.e., what should the specific functional form of the demand function be – linear, nonlinear?
Again, use economic theory.
Step 3: How should each variable be measured?
Use statistical knowledge and data limitations
Step 4: How should the effects of each variable be estimated?
Use statistical/econometric tools – this is tough!
Step 5: How should the statistical results be interpreted?
Use statistical/econometric tools
Step 6: How should the results be used?
Use economic theory
Example:
Step 1. Suppose for our firm we believe that the following variables may be important in determining Qd:
Own price: P
Consumers’ income: I
Tastes and preferences: T
Price of substitute: Py
Price of Complement: Pc
Advertising: A
Step 2: Now we need to determine the exact functional form of the equation.
For now, we will assume a linear relationship (note that we will vary this later…)
So, the equation we will want to estimate is:
Q = Bo + B1P + B2I + B3T + B4Py + B5Pc + B6A + “other stuff we cannot measure including random noise”
So, we collect data on the variables of interest and use these data to estimate the B’s which tell us the impact of each variable on Q.
A note on terms and definitions:
Q – the variable we are attempting to explain, is called the dependant variable.
The variables on the right hand side are called independent variables.
Step 3: Now we have to figure out how to measure each variable – some will be easy, others so difficult that they end up in the “others…”
Steps 4 & 5: This is the econometric work we will be doing – essentially we will be doing what is termed “regression analysis” to estimate the B’s. More later…
