Financial Economics

1. The article “High gas prices cut driving for 8th month: government” (Reuters, Aug. 13, 2008; http://www.reuters.com/article/idUSN1333749120080813 ) discusses changes in quantity of gasoline demanded by consumers in response to rapidly rising prices. Consider a representative individual who receives utility from units of food (F) and gasoline (G). The individual’s utility function is U(F,G) = F G. a. Graph the indifference curve associated with this utility function when U(F,G) = 4000. Specifically, for each of the following values of F: 20, 40, 60, 80, 100 and 200, solve for the corresponding value of G that would keep the consumer on the U=4000 indifference curve. (Results may include fractional amounts.) Plot these points and connect them with a smoothed line. Please label all axes clearly. (You may prefer to do this with a spreadsheet program). b. Explain “diminishing marginal rate of substitution.” Give an example which demonstrates that this utility function exhibits diminishing marginal rate of substitution. c. This consumer has a weekly budget of $1000. If food costs $1 per unit, and gasoline costs $3 per unit, how much F and G will she consume to maximize utility? d. Over the last six months, the price of gasoline has risen from $3 to $4 per unit. How much gasoline will the consumer purchase now? How much food? Are gasoline and food complements, substitutes or neither? e. Plot the consumer’s demand curve, given that her budget is $1000 and that food costs $1 per unit. (You may do this by deriving the demand curve algebraically, or by calculating the quantities of gasoline demanded at the following prices: $1, $2, $3, $4, $5, $6, finding the corresponding quantities demanded, plotting them, and connecting them with a smooth line).

Problem 1, continued. f. Calculate the approximate elasticity of demand at a price of $4. g. Show graphically how this demand curve changes if the consumer’s income increases, say from $1000 to $2000. (It is not necessary...