There are two goods, petrol g (in litres per year) and good y (in units of y per year), with prices pg and py respectively. Chun has income of M. Suppose Chun's preferences for goods g and y can be represented by the utility function

(, ) = 0.020.78

(In case it isn't clear, the exponents are 0.02 and 0.78).

1. Find Chun's demand functions for petrol and good y.
2. Is petrol a normal good or an inferior good or neither for Chun? (1)
3. Is petrol a substitute for y, complement to y, or neither for Chun? (1)
4. Suppose the price of petrol is $0.20 per litre, and the price of y is $1, and her income is $30,240. How much petrol and good y will Chun consume in a year? Call this her original bundle. (2)
5. Suppose the price of petrol increases to $0.60 per litre.

1)How much petrol will Chun consume in a year now, at the new prices?Call this her new bundle.

2) Find the change in Chun's consumer surplus from the increase in the price of petrol from $0.20 per to $0.60 per litre, ceteris paribus.

6.Government rebate plan. Suppose, in response to the price of petrol increasing to $0.60 per litre (and with an election coming up), the government gives Chun a petrol rebate of $m, that is just enough money (when added to her income) for her to be able to consume her original bundle at the new prices.

1) How much is the rebate to Chun?

2) How much petrol will Chun consume in a year at the new prices (with the rebate added to her income)?

7.Microeconomist's Plan. A microeconomist says to give her a petrol rebate that is just enough money (when added to her income) that she will be just as happy at the optimal bundle at the new prices and income with this rebate as she was at the original bundle. How much petrol will Chun consume in a year now? Note: there will be decimal amounts in the intermediate steps. It is okay to write the intermediate results to two decimal places (as I will in writing the solution), but do not round the intermediate results in your calculations in your calculator.

8. What is the substitution effect on petrol consumption from the increase in petrol price from $0.20 per litre to $0.60 per litre ...

1. ... using the Slutsky method?
2. ... using the Hicks method?