1. Set up a utility maximization model to think about the consumption of gasoline and other goods. Assume a utility function U=u(C,G) where G is the consumption of gasoline and C is a composite good, which includes all goods other than gasoline. a) The budget constraint of a consumer with income I and the price of gasoline PG can be written as C+PGG=I. Note that the price of the composite good C is $1 in the budget constraint. Draw the budget constraint on coordinates where y-axis is C and x-axis is G. What is the slope of the budget line? b) Draw a diagram on coordinates where y-axis is C and x-axis is G 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 (PG) 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 Jack's utility function is given by U=C0.5G0.5 So MUc=0.5C0.5G0.5 and MUG=0.5C0.5G0.5. If Jack's income is $2000, and the price of gasoline is $4 per gallon, and the price of the composite good C is $1. What is Jack's utility-maximizing bundle of G and C ? 1. Set up a utility maximization model to think about the consumption of gasoline and other goods. Assume a utility function U=u(C,G) where G is the consumption of gasoline and C is a composite good, which includes all goods other than gasoline. a) The budget constraint of a consumer with income I and the price of gasoline PG can be written as C+PGG=I. Note that the price of the composite good C is $1 in the budget constraint. Draw the budget constraint on coordinates where y-axis is C and x-axis is G. What is the slope of the budget line? b) Draw a diagram on coordinates where y-axis is C and x-axis is G 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 (PG) 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 Jack's utility function is given by U=C0.5G0.5 So MUc=0.5C0.5G0.5 and MUG=0.5C0.5G0.5. If Jack's income is $2000, and the price of gasoline is $4 per gallon, and the price of the composite good C is $1. What is Jack's utility-maximizing bundle of G and C
