Consumer Behavior, Individual and Market Demand

Order Description

Three intermediate microeconomics problems that involves using MRS,marginal utility, and indifference curve.

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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

1.

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.

2.

At an optimal interior basket, why must the increase in utility from spending another dollar

on a good be the same for all goods?

3.

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

basket.

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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