Homework 4-

1. Excise Taxes:

Hipsteria is a town made up of only hipsters. The people of Hipsteria consume many vinyl records according to the demand curve: P = 190 - (1/4)Q_d. Records are supplied by Hipster-Phonics, the local record label, according to: P = 10 + Q_s.

a. What are the equilibrium price and quantity of records in Hipsteria?

b. Calculate the value of consumer surplus (CS) and producer surplus (PS) in the market for vinyl records in Hipsteria.

Now, suppose that the government of Hipsteria decides that Hipsters are listening to too much music, and thus decide to impose an excise tax of $30 per record.

c. Graph the market for records in Hipsteria with the excise tax and solve for the new equilibrium price and quantity, P_e^T and Q^T.

d. What is the price that buyers pay once the excise tax is implemented? What is the price that sellers receive once the excise tax is implemented?

e. Draw a new graph of the market with the excise tax. On that graph, label each of the following and calculate the corresponding values.

(i) Consumer surplus with the tax (CS^Tax)

(ii) Producer surplus with the tax (PS^Tax)

(iii) Consumer tax incidence (CTI)

(iv) Producer tax incidence (PTI)

(v) Deadweight loss from the tax (DWL)

f. Calculate the government revenue from the tax.

g. Who pays more of the tax? Why is this true?

2. Elasticity:

Suppose that the city of Hewletton consumes only two goods, computers and pumpkins. Demand for computers is given by: Q_C = 205 - 2P_C + P_P - (1/4)M, where P_C and P_P are the prices of computers and pumpkins, respectively, and M is income.

Currently, citizens of Hewletton are purchasing computers and pumpkins at P_C = $10 and P_P = $15. Income in Hewletton is equal to $400.

a. What is the quantity of computers currently being consumed?

b. At the current amount of computers being purchased, use the point elasticity formula to calculate the price elasticity of demand for computers, ε_D, at the quantity you determined in part (a). (Hint: plug in all the information given EXCEPT for the price of computers. After doing so, the problem should look more familiar since you will now have an equation with two variables, Q_c and P_c.)

c. Given the above price elasticity of demand, are suppliers maximizing their revenue? If not, should they increase or decrease the price to increase their revenue?

d. At what price and quantity is total revenue maximized? (Hint: to find where total revenue is maximized, use the same method of plugging in information as in part (b).)

e. At the current prices and income, it can be shown that the income elasticity of demand will be equal to ε_M = (-1/4)*(400/100) = -1. What does ε_M = -1 say about computers?

f. At the current prices and income, it can be shown that the cross-price elasticity of demand will be equal to ε_CP = (1)*(15/100) = 3/20 = 0.15. What does ε_CP = 0.15 say about computers and pumpkins?

3. Real vs. Nominal:

Your elderly neighbor, Lou, tends to be a bit long-winded when it comes to stories of what things were like when he was a child. Lou's favorite story to tell is that of how much going to the movies cost him. Back in 1940, a movie was only $0.50, and popcorn and two drinks were only $0.50. Lou could take a girl out for $1.00! His sweetheart, Betty, lived pretty far away, he tells you. Lou would have to drive his dad's car 10 miles to pick Betty up for a date. Lou's dad demanded that he replace any gas that he used, which meant that the 10 gallons of gas he had to use between driving to pick Betty up, going to the movie, and then dropping her off came out of his own pocket. Gas was cheap in 1940 at just $0.50/gallon.

You are taking economics 101 and you get a little bit curious about how the prices back in 1940 really compare to today. Lou seems caught up on the nominal price differences in the past 70 years, but you know better than to ignore the real price changes.

After doing a little research, you create the following table of information:

You make some calculations in order to compare the prices:

a. Calculate the overall inflation from 1940 and 2011.

b. What was the average annual inflation over the time window?

c. Calculate the real price of each of the following in 1940 and 2011 using 1984 as the base year.

(i) A movie ticket

(ii) Popcorn and drinks

(iii) Gasoline

d. Calculate the overall percentage change in the real price of each of the following, using the values you calculated in part (c).

(i) Movie tickets

(ii) Popcorn and drinks

(iii) Gasoline

e. What would the nominal price of popcorn and drinks have to have been in 1940 for the real price of popcorn and drinks to be unchanged between 1940 and today?

f. What would the nominal price of gasoline have to have been in 1940 for the price of gasoline in 1940 and the price of gasoline today to have the same real value?

4. Indifference Curves:

a. Jerry is 6 years old. He likes to spend his allowance on action figures and toy trucks, but that's about it. His utility from consuming action figures (A) and trucks (T) is given by U(A,T)=AT. Fill in the tables showing all the combinations of action figures and trucks that will give him the listed utilities:

U(A,T) = 12

U(A,T)=8

b. Plot the indifference curves for U=8 and U=12 using the data you found in part a, with T on the vertical axis. Connect the points with smooth lines.

c. Estimate the marginal rate of substitution of toy trucks for action figures when going from 3 to 4 action figures on the U=12 indifference curve, using the data you found in part a. Be sure to include units.

d. Using calculus, we could find the exact formulas for the marginal utility of toy trucks and the marginal utility of action figures at a given point. (Note: you will not have to do this yourself in 101!) For this example and using calculus we would find that the marginal utilities are given by: MU_T = A and MU_A = T. Using this information, what is the marginal rate of substitution when A=3 and U=12? Was your estimate in part c close?

e. Suppose your budget line goes through the point on the U=12 indifference curve where A=3, and that this is your optimal consumption point. Use the marginal rate of substitution you found in part d to find the price of action figures if the price of toy trucks is $1. (Round your answer to the nearest cent.)

5. Deriving a Demand Curve:

Jimmy has a $60 junk food budget for the month. He can use it to buy candy at $1 a piece, or salty snacks (price to be discussed in a moment). The graph below shows Jimmy's indifference curves for candy and salty snacks, with pieces of candy on the y-axis and bags of salty snacks on the x-axis. (Remember, utility increases from left to right, so each indifference curve represents a higher level of utility than the curves to the left of it.)

a. Using a ruler or straight-edge, carefully draw Jimmy's budget lines on the indifference curve graph for each the following cases:

1. Salty Snacks cost $1

2. Salty Snacks cost $2

3. Salty Snacks cost $4

b. Using your graph, fill in the following table with the optimum consumption levels of salty snacks and candy: (Remember, the price of candy has been fixed at $1 in all cases!)

c. Using the table in part b, plot your data for your demand curve. (To make things easier, just connect the data points with straight lines. Note that this is an approximation of the actual demand curve, which would be a smooth curve.)

d. How could you theoretically improve the approximation of the demand curve you found in part c?

e. (This is unrelated to finding your demand curve, but it's good practice for you anyway!) Use your table in part b to find the cross-price elasticity of demand for candy as the price of salty snacks goes from $1 to $2. (Hint: use the standard percentage change formula to calculate the percentage change in the quantity demanded of candy and the percentage change in the price of salty snacks.) Are these goods complements or substitutes?