1. Set up a utility maximization model to think about the consumption of gasoline and other goods. Assume a utility function where is the consumption of gasoline and is a composite good, which includes all goods other than gasoline.

a) The budget constraint of a consumer with income and the price of gasoline can be written as + = . Note that the price of the composite good is $1 in the budget constraint. Draw the budget constraint on coordinates where y-axis is and x-axis is . What is the slope of the budget line?

b) Draw a diagram on coordinates where y-axis is and x-axis is to demonstrate the utility maximizing choice of the representative household as a tangency point of the budget constraint and an indifference curve.

c) On the same diagram, demonstrate the new utility maximizing choice when the price of gasoline ( ) decreases by 50%.

d) Use an auxiliary budget line to decompose the income effect and substitution effect on the same diagram. Do you think consumers will increase the consumption of the composite good C? Explain.

e) Assume Jacks utility function is given by = 0.50.5 So = 0.50.50.5 and = 0.50.50.5. If Jacks income is $2000, and the price of gasoline is $4 per gallon, and the price of the composite good is $1. What is Jacks utility-maximizing bundle of and ?