QAs

Assignment 2: ECON 2101-001 S. Dodds, Fall Term, 2014

Please write up your answers in groups of 1, 2 or 3 students and submit your assignment in class on Tuesday, November 4, 2014. The whole assignment is out of 100 marks. A 10% penalty is assessed to assignments 1 day late. Assignments will not be accepted more than one day late. Answers will be posted at 4pm on November 5. (Since this is the last class before the second midterm, you may wish to make a copy of the assignment for reference before you hand it in).

1. [18 marks] Think about a society which has only three people: Jun, Kevin and Lara. Each person cares about a good (car trips per month) and a bad (pollution). Let c be the number of car trips a person consumes and P be the the amount of pollution in the air (in tonnes). If the total level of pollution in the air is P , then each person consumes a third of this amount (i.e. p = P/3). Each person’s preferences over (c, p) bundles are defined in the following way: they always prefer a bundle where c−p is larger, and they are indifferent between two bundles if c−p is the same in each.

There are three social states — A, B and C — where cJ is Jun’s consumption of car trips, cK is Kevin’s and cL is Lara’s:

P cJ cK cL State A 60 25 35 40

State B 15 15 12 5

State C 45 20 20 20

a. [6 marks] Write out each person’s preference ordering over the three states.

b. [6 marks] Which states are Pareto-efficient? Explain your answer carefully.

c. [6 marks] Suppose the government adopts the following rule for choosing between states: a state is socially preferred to another if (cJ + cK + cL)−P is larger. (This means total consumption - total pollution). Which state would be chosen in this case? Is there a different state that would make everyone better off? Explain.

2. [16 marks] Sonya spends her money, m = 36, on chocolate bars (x1) and all other goods (x2). Her demand function for chocolate bars is x

∗ 1 = 2m/3p1.

a. [4 marks] Use the budget constraint to find Sonya’s demand function for x2.

b. [6 marks] Calculate the income and substitution effects from a decrease in p1 from $2 to $1, and show these effects on a diagram. (Be sure to show x2 at each point.)

c. [6 marks] Calculate the income and substitution effects from an increase in p1 from $1 to $2, and show these effects on a different diagram. (Be sure to show x2 at each point.)

3. [30 marks] Pocassi is an artist with preferences over paintings (x1) and sculptures (x2) given by:

u(x1, x2) = min{2x1, 3x2}

where “min” means “the minimum of”. Every month, Pocassi produces 5 paintings and 10 sculptures. This is his endowment. If he wants, Pocassi can sell some or all of these items at the local market for p1 and p2 respectively. Or, he can choose to keep some or all of his artwork for himself.

a. [8 marks] Suppose Pocassi had income m. Find his ordinary demand functions for paintings and sculptures: x1(p1, p2, M) and x2(p1, p2, M).

b. [6 marks] Now suppose that instead of having income, Pocassi has his endowment (which he can trade in the market, if he likes). If p1 = 300 and p2 = 300, draw his budget line and show his endowment on this line.

c. [5 marks] Given the prices in (b.), how many paintings and sculptures will he consume? What, if anything, will he buy and sell at the market? Show on a diagram that includes his indifference curves.

d. [6 marks] Suppose the price of paintings, p1, rises to $1800. Carefully redraw the budget line for Pocassi and show his new consumption of paintings and sculptures.

e. [5 marks] Explain why Pocassi is worse off than he was before, even though the value of his endowment has risen.

4. [16 marks] Cindy’s demand curve for plays at the theatre per year (x) is given by:

x = 80 − 2p

where p is the price of a play. Show your reasoning for each of the following questions:

a. [4 marks] What value, in dollar terms, would Cindy place on a drop in price from $35 to $30?

b. [4 marks] What value, in dollar terms, would Cindy place on an increase in price from $25 to $30?

c. [4 marks] Suppose the price of a play is currently $30. Cindy is then given the option to buy a ‘package’ deal which allows her to attend 40 plays for a lump sum of $ z. What is the maximum z she would pay for this package?

d [4 marks] Suppose the price of a play is currently $20, and the government puts a $10 tax on all plays. What is the total cost to Cindy of this tax? Explain.

5. [20 marks] A firm has production technology given by y = √ z1z2, where z1 and z2

are inputs. The marginal product of input 1 is

MP1 = 1

2

√ z2 z1

a. [4 marks] Draw the firm’s isoquant for y = 4.

b. [4 marks] Pick any two input bundles on this isoquant. Show that a half-half mixture of these two bundles would produce more total output.

c. [2 marks] Suppose z2 is fixed at 4. What amount of z1 would be needed to produce 12 units of output?

d. [4 marks] Suppose z2 is fixed at 4. Accurately draw the firm’s MP1 and AP1 functions.

e. [6 marks] Repeat parts (c) and (d) for z2 = 9. Comment briefly on how your answers change when z2 rises.