Statistic Problem Solution

Suppose there are two types of food: Slow and Fast. Slow food is food that takes a lot of time and energy to prepare, and is possibly more “authentic.” Consider it a high-end luxury good. All other food we’ll call Fast. It’s a staple needed to live, is quick to acquire and cheap. The slow food costs $20 per unit, while the fast food costs $5 per unit. The price elasticity of demand for slow food is -2.8. The price elasticity of demand for fast food is -.20. The government is considering a tax on food. The tax on slow food is denoted ts, and the tax on fast food is denoted tf.
a. Comment on the significance of the different elasticities of demand?
b. What is the equation for the optimal (Ramsey) value of ts in terms of tf.
c. In a clearly written paragraph, comment on the relative size of ts compared to tf, and why we are seeing this result.
d. Suppose the government has selected tax levels ts and tf using the Ramsey rule. Furthermore, at those taxes, the market sells 3 million units of slow food and 300 million units of fast food., the government collects $1 billion in revenue from these taxes. What are the values of th and tp?

Answer:

The different price elasticities of the two goods help in explaining the behavior of the two goods in the market. That is the responses of the quantity demanded with change in prices. Slow food shows that 1% change in price results to decline in quantity demanded by 2.8 units while fast foods shows that 1% change in price will results to decline in quantity by 2 units.

Optimal value of fast food VF= $5 – t f
       Optimal value for slow food VS=$20 – t s

The t s in fast moving foods is low because of the low price elasticity of demand of -2.0 while the t f in slow food is high due to high price elasticity of demand of -2.8.


300 units of fast foods
3 million units of slow foods
Rev 1 billion, therefore TS= 3/303 *1Billion=9900990
T f=300/303 * 1Billion=990099010

Assignment

1. For a distribution of scores, X = 40 corresponds to a zscore of z = +1.00, and X = 28 corresponds to a zscore of z = -0.50. What are the values for the mean and standard deviation for the distribution? (Hint: Sketch a distribution and locate each of the zscore positions.) Solution: we know Z=(x-µ)/𝞼  then we get x=µ+𝞼Z…..(1) For X=40 and Z=1 we get from (1) ,  40=µ+𝞼…………(2) For X=28 and Z=-0.50 we get from (1), 28=µ-0.50*𝞼…………(3) Subtracting (3) from (2)  we get 40-28=µ+𝞼- µ+0.50*𝞼=1.50𝞼 ð  12=1.50𝞼 ð  𝞼=8. ð  Putting 𝞼=8 in equation (2) we get µ=40-8=32 ð  Hence the mean µ=32 and standard deviation 𝞼=8 3. For a normal distribution,           a.  What z-score separates the highest 10% from the rest of the scores? Solution:Z-scores separates the highest 10% from the rest of the scores is 1.282           b.  What z-score separates the highest 30% from the rest of the scores? Solution: Z-scores separates the highest 30% from the rest of the scores is 0.5244.           c.  What z-score separates the lowest 40% from the rest of the scores? Solution: Z-scores separates the highest 40% from the rest of the scores is -0.253           d.  What z-score separates the lowest 20% from the rest of the scores? Solution: Z-scores separates the highest 20% from the rest of the scores is -0.8416 4. A population consists of the following N = 10 scores: 0, 6, 4, 3, 12, 6, 7, 5, 1, 11 Your task is to enter the data for this variable into SPSS, use the descriptives command to do a z-transformation of the whole distribution into a standardized distribution, and then get the frequencies with mean and standard deviation for both the original raw scores distribution and the standardized distribution. Attach the printout with the frequencies to this homework. Statistics esteem Zscore(esteem) N Valid 10 10 Missing 0 0 Mean 5.5000 .0000000 Std. Error of Mean 1.22247 .31622777 Median 5.5000 .0000000 Mode 6.00 .12934 Std. Deviation 3.86580 1.00000000 Variance 14.944 1.000 Skewness .404 .404 Std. Error of Skewness .687 .687 Kurtosis -.357 -.357 Std. Error of Kurtosis 1.334 1.334 Range 12.00 3.10414 Minimum .00 -1.42273 Maximum 12.00 1.68141 Sum 55.00 .00000 esteem Frequency Percent Valid Percent Cumulative Percent Valid .00 1 10.0 10.0 10.0 1.00 1 10.0 10.0 20.0 3.00 1 10.0 10.0 30.0 4.00 1 10.0 10.0 40.0 5.00 1 10.0 10.0 50.0 6.00 2 20.0 20.0 70.0 7.00 1 10.0 10.0 80.0 11.00 1 10.0 10.0 90.0 12.00 1 10.0 10.0 100.0 Total 10 100.0 100.0 Zscore(esteem) Frequency Percent Valid Percent Cumulative Percent Valid -1.42273 1 10.0 10.0 10.0 -1.16405 1 10.0 10.0 20.0 -.64670 1 10.0 10.0 30.0 -.38802 1 10.0 10.0 40.0 -.12934 1 10.0 10.0 50.0 .12934 2 20.0 20.0 70.0 .38802 1 10.0 10.0 80.0 1.42273 1 10.0 10.0 90.0 1.68141 1 10.0 10.0 100.0 Total 10 100.0 100.0     For any kind of stats related problem please contact.We are here for easy and quick solution.