How much will soda consumption decrease after the tax is

Question

Assignment:

1. In homework 1 we solved the equilibrium in the beer market represented by the following supply and demand functions:

Q_d = 20 - 4p +2p_w + 3Y + 15HOLIDAY
Q_s = -4 + 26p - 2p_g - 1p_t

Q = pints of beer (in thousands)
p = price of beer ($ per pint)
p_w = price of wine ($ per bottle)
Y = Average income (000's of $)
HOLIDAY = variable which takes a value of 0 when there is no holiday and takes a value of 1 if there is a holiday
p_g = price of grains ($ per bushel)
p_t = price of transportation ($ per ton-mile)

When the price of wine is $7 per bottle, average income is $30,000 (Y = 30), the price of grains is
$3 per bushel and the price of transportation is $3 per ton-mile. The equilibrium price and quantity was $4.57 per pint and 106 thousand pints.

a. Calculate the Price Elasticity of Demand at the equilibrium.

b. Calculate the Price Elasticity of Supply at the equilibrium.

c. Calculate the Income Elasticity of Demand.

d. Calculated the Cross-Price Elasticity of Demand between wine and beer.

2. Higher Education Analysis

a. What do you think is a reasonable estimate for the price elasticity of demand for higher education in the State of Kansas? Give an economic justification for your answer. Post your answer to this question on the following Discussion Board on D2L: https://d2l.washburn.edu/d2l/le/62327/discussions/topics/42523/View (Try to complete this part by Sunday night)

b. The price of higher education is the Net Tuition students pay (Published tuition minus institutional grants and scholarships) measured in thousands of dollars and the Quantity of Higher Education is the number of full-time equivalent students measured in thousands of students. Suppose the Net Tuition is the state of Kansas is $5,000 (P = 5) and the full- time equivalent enrollment is 100,000 students (Q = 100). Using this information and your elasticity estimate from question 1, derive the demand function for higher education in Kansas.

c. The Supply and for higher education in Kansas can be given by the following equation:

Q_s = -28 + 16STATE + 16P

Q = Student FTE Enrollment
P = Tuition (000's of $)
STATE = Per Student State Aid to Universities (000's of $)

Suppose per student state aid to universities is $3,000 (?????????? = 3) Using your demand function from part b. verify that the equilibrium occurs at a Net Tuition of $5,000 and Enrollment of 100,000.

d. If the state increased it's per student state aid from $3,000 to $4,000, what would happen to Net Tuition and Student Enrollment? How much better off is the individual student as a result of the $1,000 per student increase in state aid?

3. Berkley, CA recently passed a soda tax of $0.20 per bottle. Suppose the price of a bottle of soda was $1.25 and the average person consumed 320 bottles of soda per year.

Suppose the price elasticity of demand for soda is -0.2 and the price elasticity of supply of soda is 0.6.

a. How much would we expect the price of a bottle of soda to increase if the $0.20 tax is imposed on the market?

b. How much will soda consumption decrease after the tax is imposed on the market? (HINT: For this problem you do not have to calculate the full supply and demand functions. You can find the answer by using only the Elasticity of Demand formula.)

Suppose the price elasticity of demand for soda is -5.0 and the price elasticity of supply of soda is 10.0.

c. How much would we expect the price of a bottle of soda to increase if the $0.20 tax is imposed on the market?

d. How much will soda consumption decrease after the tax is imposed on the market?