Answer to Question #263889 in Microeconomics for lilu

Question

Question 2

Table 1 below shows Troy’s consumption choices of three goods. Each observation consists of a set of prices and quantity consumed of the three goods. [25%]

Table 1

Observation 𝑝1 𝑝2 𝑝3 𝑥1 𝑥2 𝑥3 1332844 2212486 3414248

Note: The prices are in dollars and the quantities are in units.

a. Write a table containing the total expenditure of each bundle under each set of prices. List all the affordable bundles at each set of prices.

b. Refer to the table in (a). List all the direct and indirect revealed preferences and explain whether the data satisfies the WARP and SARP.

c. Usethetablein(a)toexplainwhatyouunderstandaboutthetwoproperties of strict order.

d. Suppose that Troy now consumes only good 1 and good 2. The prices and quantities consumed of the two goods remain unchanged for the three observations in Table 1. Sketch a diagram to explain whether WARP and SARP is violated.

Answer 1

a.

Each cell has been calculated by using the formula

Expenditure = $p_1x_1 + p_2x_2 + p_3x_3$

For example, the value in cell 1 (corresponding to first set of prices and first bundle)$= 3×8 + 3×4 + 2×4 = 24 +12+8 = 44$

b.

 Actual amount spent by the person on each bundle is given by the diagonal values as those represent the bundle brought at those prices. Bundle 1 is purchased at the first set of prices, bundle 2 at second set of prices and bundle 3 at third set of prices.

Now, along any row, if the expenditure on any other bundle is less than on the actual bundle brought at those prices (represented in bold), then we put a star sign on them. The bold bundles were brought even when there were cheaper options (star) available. Like in row 1, at first set of prices, bundle 1 is brought even when bundle 3 could've been brought at a lower price i.e., 34.

Now, for WARP to hold, if bundle x is revealed preffered to bundle y, then bundle y cannot be revealed preferred to x.

Thus, bundle 1 is directly revealed preferred to bundle 3. Similarly, bundle 2 is directly revealed preffered to bundle 3.

WARP is not violated.

For SARP, we need to check the indirectly revealed preffered bundles as well. Here, there aren't any chains of observations that indirectly link two bundles. Thus, SARP is not violated.

c.

WARP- Weak Axiom of Revealed Preference - It says that if a bundle (x1, x2, x3) is directly revealed preferred to a different bundle (y1, y2, y3), then it is not possible for bundle (y1, y2, y3) to be directly revealed preffered to bundle (x1, x2, x3).

SARP - Strong Axiom of Revealed Preference - This is a stronger version of the WARP. This states that if a bundle (x1, x2, x3) is directly or indirectly revealed preferred to a different bundle (y1, y2, y3), then it is not possible for bundle (y1, y2, y3) to be directly or indirectly revealed preffered to bundle (x1, x2, x3) under any conditions.

d.

Again here, bold numbers represent expenditure on chosen bundles. Star values denote bundles which have lesser cost but weren't chosen.

So, bundle 1 is revealed preffered to bundle 3 and bundle 2 is revealed preferred to bundle 3.

Neither WARP nor SARP is violated.