Homework 2 Intermediate Micro

1. Camp Caspar is an amusement park that charges $3 per ride. Jane has $30 to spend at Camp Caspar on rides and the only other good at the park which is cotton candy. A bag of cotton candy costs $2.

a) Putting rides on the x-axis and bags of cotton candy on the y-axis illustrate Jane's budget set. What is the opportunity cost of a ride? Show (algebraically) that Jane can afford 8 rides and 3 bags of cotton candy.

b) Suppose that Jane's MRS at (8,3) is 1. Is (8,3) Jane's best bundle? Why or why not?

Briefly explain your answer. If not will she choose more or fewer rides?

Suppose Camp Caspar introduces a "discount" ticket. If Jane purchases a bracelet for $10 then she can pay a reduced price of $1 per ride.

c) In your diagram for part (a) illustrate Jane's budget set if she purchases the bracelet. What is the new opportunity cost of a ride?

d) If when the price of a ride was $3 Jane purchased 6 rides would she necessarily want to buy the bracelet? Briefly explain your answer.

2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences over these two goods can be represented by the utility function U(x,y) =0.5x + 5ln y where x represents the number of cans of soda and y represents the number of juice boxes.

a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y).

b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda and juice. Write Ping's demand curve for juice (y). Illustrate his demand curve.

c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and $30, resp.). Use your demand functions to find his best bundle. In an indifference curve diagram illustrate his best bundle at these prices.

For the remainder of the question assume that Ping's allowance (income) rises to $36 per week and the prices of the two goods are unchanged at Px = $1.5 and Py = $1.

d) Use your demand functions to find his new best bundle.

e) Illustrate the new budget line and the new best bundle that you found above in your diagram for part (c). Be sure to indicate the slopes of both budget lines.

f) What is the income elasticity of soda (as a function of prices and income)?

3. A family has the following utility over childcare, c, and food, f,: U ( c, f) = c^1/5 f^4/5

The price of childcare Pc = 2 , the price of food Pf = 4 and income I = 20.

a) What is the family's demand for childcare and food?

b) Suppose the government gives the family an income subsidy of S = 10. How will the family allocate the subsidy in the consumption of the goods c and f (in other words by how much does the consumption of each of these goods rise)? What is the level of utility attained by the family after the subsidy?

c) Suppose now that the government decides to give an in-kind transfer to the family. The in-kind transfer takes the form of 4 hours of childcare and 0.5 units of food. Assume that the transfer cannot be re-sold. Draw a carefully labeled graph where you show that the pre- and post transfer budget constraint.

d) What are the new consumption levels after the in-kind transfer is given? What is the level of utility attained by the family at this consumption level?