Reference no: EM132314811

Case Study: Consumer Theory

Please address the following case study relating to consumer theory in a fictitious home market. This case study relates to Chapter 5 of the textbook and the lecture on Consumer Theory.

Note: The lecture is decomposed into four sections that correspond to a section of the case study and related pages of the book. The lecture section and book pages are indicated with each section of the case study.

Please submit your work as a single Word document. When I request calculations, you can write them by hand and incorporate a photograph into the document or you can type up the calculations in the document. Similarly, you can create any tables by hand, in Word, or other ways, but your tables should be clear. The document should be approximately 2-4 pages (counting each side of the paper as a page) in length. Please indicate in some way which part of the document responds to each question. The assignment will be graded based on correctness, effort, and presentation.

This table contains 6 houses (A, B, C, D, E, and F) with different combinations of amenities and size.

House	Amenities	Size (100's sq ft)
A	5	10
B	3	25
C	2	20
D	6	13
E	6	30
F	7	20

Section 1. Preferences and Utility (pages 159 - 163)

Suppose that we know the following about consumer preferences for the 6 houses in the table:

A < D, D ∼ B, F ? D, F ∼ E, C ? A

Make a table containing utility values for each house (bundle) that are consistent with these preferences. (There are multiple correct answers.)

Section 2. Indifference Curves (pages 163 - 169)

a) Create a graph with Size on the x-axis and Amenities on the y-axis. Plot a point on the graph for each of the houses in the table above. Draw 4 indifference curves that are consistent with the preferences (and utilities) identified in Section 1. . (Note that this may be exceptionally difficult in Excel, so you should probably draw it. And when you draw it, give yourself plenty of room because we will be adding to the graph later.)

b) In general, do we expect the marginal utility of size to be higher for house D or for house E? Explain.

c) Is the marginal rate of substitution higher for house B or for house D? Is the marginal rate of substitution higher for house E or for house F? Explain.

Section 3. Consumer Maximization (pages 169 - 180)

a) Create a graph with Size on the x-axis and Amenities on the y-axis. Amenities cost $25,000 and Size costs $10,000. Draw the budget curve for a consumer with a budget of $200,000. Also draw the budget curves for a consumer with a budget of $400,000 and a consumer with a budget of $600,000. When drawing the curves be sure to indicate a couple points on each curve. (The x-intercept and the y-intercept are usually good choices.)

b) Now take the graph with your indifference curves from section 2 and add in a couple budget curves. You can put the budget curves in any of several places, but they should meet a couple constraints. The budget curves should be parallel because they are for constant prices. Each budget curve should be tangent to a single indifference curve. The resulting optimal combination of features (amenities and size) should be marked. This point need not correspond to one of the 6 houses in the original table.

Section 4. Indifference Curves and Demand (pages 180 - 185)
We will now stay in the same setting but change the scale and units so they are easier to work with. Suppose a consumer has utility that is a function of Size (S) and Amenities (A). The utility function is:

U(S, A) = S1⁄2A1⁄2
a) Take the derivative with respect to Size (S) to find the general form of the consumer's marginal utility of Size (S).
b) Take the derivative with respect to Amenities (A) to find the general form of the consumer's marginal utility of Amenities (A).
c) Use the marginal utilities to find the marginal rate of substitution (MRS).
d) Suppose the consumer has an income (M) of 10. Assume the price of Amenities (pA) is 2.5 and the price of Size (pS) is 1. Write the consumer's budget equation by substituting the prices and income into the general budget equation:

M = pSS + pAA

e) What amounts of size and amenities will the consumer choose? (Hint: You need to solve a system of two equations with two unknowns. The first equation will come from setting the general form of the MRS equal to the price ratio. The other equation will come from the budget equation.)

f) Now, construct a demand curve for Size for this consumer by finding the optimal amount of Size when the price of Size is 1, then 2, then 3, and then 4.

g) Now suppose that we have a second consumer with the same utility function but a budget of 20. Construct his demand curve for prices of 1, 2, 3, and 4.

h) Finally, find the aggregate demand curve for the two consumers for prices of 1, 2, 3, and 4.

Attachment:- Transcript - Consumer Theory.zip