# consumer preferences and utility maximization

## Project Description:

homer’s utility function for donuts and… beverages is u= ½ ln(d) + ln(b), where d
is number of boxes of donuts and b is 40 oz. cans of… beverage. homer has \$300 to
spend this semester on these two items. each donut box(d) costs \$10, and each can
of beverage costs (b) \$5.
homer is currently consuming 20 donut boxes and 20 beverages this semester.
a) graph homer’s budget constraint, and show that this is a feasible bundle for
homer (on or inside his budget constraint). put donuts on the x-axis.
b) use the utility function to calculate homer’s marginal rate of substitution at the
current bundle. use the mrs and the slope of the budget constraint to show that
homer’s current consumption is not optimal. draw an indifference curve through
the current bundle that reflects the mrs you calculated and the suboptimality of
the bundle. you don’t need a precise graph of the indifference curve as long as
your graph captures the slope of the ic relative to the slope of the budget line.
lastly, based on the mrs and the slope of the budget constraint, propose a shift
in consumption that will increase homer’s utility.
c) now consider our “bang for the buck” measure mu/p. use this measure to prove
homer’s current consumption is suboptimal, and describe how the consumption
shift from 3b will change homer’s “bang for the buck.”
d) solve for homer’s optimal level of consumption. draw a new indifference curve
in your graph that shows that this new bundle is optimal. as in lecture, proceed in
two steps. first, use either criterion for the optimal bundle to derive an optimal
relationship between d and b, then plug that relationship into the budget
constraint to solve for specific values.
Skills Required:
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Price Type: Negotiable

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