This is the first part of the question in microeconomics graduate level. I would really appreciate your help

Demand Estimation

At Canvas, the problem set 6 folder included PS6_demo.R and FoodDiary.csv. You dont need to do anything with those if you dont want to, but if you are interested you can go ahead and follow the directions to replicate the work shown here. In PS6_demo.R, if you edit the read.csv line of command (line 5) so that it finds the food diary data and replicate the results you will see here.

FoodData.csv contains the monthly food diary data from a random sample of 2,500 Danish households during 1997 to 2001. Specifically, these households tracked their quantity of milk (by conventional/organic and 3-tiers of fat content) purchased and the price of each type of milk those households faced at the time of their purchases. A copy of the original study saved as Org Milk Study.pdf is available at Canvas as an FYI but is not necessary. If you click on the spreadsheet icon next to the data, you can see the data itself. Here is a description of the variable names:

CMilk1	Quantity of Conventional Milk, 3-5% Fat
CMilk2	Quantity of Conventional Milk, 1-3% Fat
CMilk3	Quantity of Conventional Milk, 0-1% Fat
OMilk1	Quantity of Organic Milk, 3-5% Fat
OMilk2	Quantity of Organic Milk, 1-3% Fat
OMilk3	Quantity of Organic Milk, 0-1% Fat
CMP1	Price of Conventional Milk, 3-5% Fat
CMP2	Price of Conventional Milk, 1-3% Fat
CMP3	Price of Conventional Milk, 0-1% Fat
OMP1	Price of Organic Milk, 3-5% Fat
OMP2	Price of Organic Milk, 1-3% Fat
OMP3	Price of Organic Milk, 0-1% Fat
Y1998 Y1999	=1 if year is 1998, else =0 =1 if year is 1999, else =0
Y2000 Y2001	=1 if year is 2000, else =0 =1 if year is 2001, else =0

The next area of code runs a regression to create a linear demand curve of the following function:

OMilk2= 0+1CMP1+2OMP2+3Y1999+4Y2000

This is done by calling the lm function (the linear regression model). The results can be viewed by running the summary function, and will appear in your console:

R has estimated the parameter estimates, so that your linear demand function can be read as:

OMilk2= 5.77485-0.14271*CMP1-0.59448*OMP2+0.11623*Y1999+0.08374*Y2000

In the above equation, OMilk2 is the variable name used to represent the quantity of Organic Milk (1-3% fat content) purchased in a given month. The s represent parameter estimates different variables, mostly prices of milk. We can see that if the price of high conventional milk (CMP1) increases by $1, the quantity demand for medium fat organic milk (OMilk2) declines by 0.14271 units, indicating that they are complement goods. If medium fat organic milks own price (OMP2) increases by $1, the quantity demanded falls by 0.59448 units. In other words, this is just like every other demand curve you have worked with all semester. Suppose CMP1=$1 and we are in 1999 (Y1999=1, Y2000=0). The demand function then can be written as:

OMilk2= 5.74837-0.59448*OMP2

You have seen a demand function just like this numerous times in homeworks and class, so you can do all the same things youve done in previous problem sets (e.g., calculate marginal benefit of a given unit of OMilk2, total benefits, consumer surplus, etc.). For example, if the price of this kind of milk is $3, the quantity demanded will be 3.96493 units (i.e., if OMP2=3, then OMilk2=3.96493). Note: Since this regression is over household data, the models predict the monthly quantity demanded by a household.

Now lets represent the demand function for low fat conventional milk as a function of prices of its own price and all other alternative milk prices:

CMilk3= 0+1CMP3+2CMP2+3CMP1+4OMP1+5OMP2+6OMP3+7Y1999+8Y2000

Here are the results of estimating that function:

If CMP1=6.15, CMP2=5.36, CMP3=5.14; OMP1=7.39; OMP2=6.56; OMP3=6.33, Y1999=0, and Y2000=1, then your quantity demanded should be 1.85 units. We will henceforth refer to these values as the default variable input values.

Using the linear demand models point estimates to answer the questions. Tip: Use a program like R or Excel to calculate values, youll get answers much more quickly. 7. What is the point price elasticity of demand at the default variable input values (i.e. where the price of lowfat milk is $5.14 and quantity demanded is 1.895)?

What is the point price elasticity at the default variable input values?

Calculate the point price elasticity of demand for conventional lowfat milk when its price is $2 (CMP3=2), holding constant all the other variable inputs at their default values? (Note: You will need to calculate a new quantity demanded for the case when price is $2. Study Tip: based on your notes, do you expect the elasticity to become larger or smaller in absolute value terms now that the price is lower and quantity demanded is larger?)

Calculate the households consumer surplus for conventional lowfat milk at the default values (including CMP3=5.14). Review notes from lectures 2 and 3 if you need refresher on calculating this.

Based on the demand equation, is organic lowfat milk a substitute or complement to conventional lowfat milk?

What is the point cross-price elasticity with organic milk with 0-1% fat (OMP3) at the default variable input values?

Assuming the default variable input values for every variable except CMP3, what would be the marginal benefit of the second unit of lowfat conventional milk?