Consumer Behavior, Individual and Market Demand

Consumer Behavior, Individual and Market Demand

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Three intermediate microeconomics problems that involves using MRS,marginal utility, and indifference curve.
the assignment there are only two math problems and one written question. combo order, 2 math problem and 1 page coursework

Assignment 2-D: Econ 2101

Consider the utility function U(x,y) = xy1/2. To answer this question, you will first need to derive
the marginal utility of each good (x and y) using calculus.
a) Is the assumption that more is better satisfied for both goods?
b) Does the marginal utility of x diminish, remain constant, or increase as the consumer buys
more x? Show this using calculus.
c) Derive an expression for the MRS (of x for y).
d) Is this MRS diminishing, constant, or increasing as the consumer substitutes x for y, i.e.,
moving down an indifference curve?
e) On graph paper (you can download and print out some from the web, just Google “graph
paper”) with numerical scales on each axis, with quantity of good x on the horizontal axis and
quantity of good y on the vertical axis, draw an indifference curve for this utility function, for
some value of utility of your choice. Also indicate on your graph whether the indifference curve
will intersect either or both axes. Label the curve U1 .
f ) On the same graph draw a second indifference curve U2, with U2 > U1.
At an optimal interior basket, why must the increase in utility from spending another dollar
on a good be the same for all goods?
Ram buys two goods: rice (R) and a composite of “all other goods” (O). The price of O (PO) is
$1 per unit. The price of rice (PR) is $5 per pound if 20 pounds or less are bought. For any
amount of rice over 20 pounds, the price is $4 per pound. Ram’s income is $200.
a) On a graph with O on the vertical axis and R on the horizontal axis, draw Ram’s budget
constraint. (Hint: This problem demonstrates that a budget constraint need not always be a
straight line.)
b) On the graph you drew in part (a), draw a set of indifference curves for which Ram’s optimal
market basket has him consuming more than 20 pounds of rice.
c) On a new graph, draw the same budget line you found in part (a). Now draw a set of
indifference curves for which Ram consumes less than 20 pounds of rice at his optimal market
How Should I Prepare My Answers?
Since two of the questions require diagrams to be drawn, I would suggest that you write out your
answers neatly by hand, scan them into an (Adobe) PDF file (see the syllabus for details), and
submit the file to me for grading via Blackboard (as you did for Assignment 1-E). Please make
sure that your scan is legible (handwriting isn’t too faint) and complete (no pages are missing).
Be sure to show all your work and to explain your answers.
Here are some pointers on this assignment:
1. When drawing diagrams be sure to use a ruler, and be sure that axes and curves
are clearly labeled, as are points or intersections of interest.
2. When drawing indifference curves representing preferences of a single individual,
make sure that: (i) the indifference curves don’t intersect and don’t look like they
might intersect (see Figure 3.4 on p. 73 of P&R for why); and (ii) indifference
curves are everywhere negatively sloped unless you are given information that
suggests otherwise, e.g., the good is a “bad”, or becomes one, or because
nonsatiation has set in.
3. Be sure to carefully label your answers so that I can easily determine which
question, or which part of a question, you are answering.
This assignment will take some time to do, so be sure to get an early start on it.

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