How much of each variety will this consumer purchase use a

Question

Intermediate Microeconomics

Assignment

Question 1: On April 24, 2013 a factory collapse in Sam, Bangladesh killed more than 1,100 workers. Most of these workers were employed by factories producing garments for Western markets, including Australia. Such tragic incidents have led to a concerted effort by some retailers to sell ethically-produced clothing.'

These retailers are essentially betting (hoping?) that consumers will appropriately value such clothing. Is there any evidence to support this? A study conducted by the research firm McCrindle found that eight out of 10 Australian consumers are willing to buy a product that has a charitable component over one that does not as long as the price between the two are similar.' This need for prices to be similar highlights the challenge faced by many socially conscious retailers. As long as a garment produced in a safe workplace costs more than a similar garment produced in an unsafe workplace, the retail price for the former will always be higher.

This may explain why, when it comes to buying ethical clothing, Australian consumers "do not put their money where their mouth is" .

Motivated by the behaviour of Australian consumers referred to above, consider a model where a consumer must decide how much of a garment to buy. Suppose that this garment comes in two varieties: (a) a low quality variety that is produced in an unsafe factory overseas and (b) a high quality variety that is produced in a safe factory overseas. Let us suppose that this consumer's preference for the two varieties can be represented by the following utility function:

U = X_L + X_H (1)

where X_L > 0 is the number of units of the low-quality variety that she purchases and X_H > 0 is the number of units of the high-quality variety that she purchases. Let the price of these varieties be Pi, and PH respectively and let this consumer's income be I.

(a) Suppose that P_H > P_L. How much of each variety will this consumer purchase? Use a diagram with XH on the horizontal axis to explain.

To see whether we can induce this consumer to buy more of the high-quality variety, now suppose that the consumer's utility not only depends on her purchase of each variety, but also on her reputation in society. This means that we can now write her utility function as follows:

U = X_LR + X_H (2)

where

R = D + vX_H (3)

represents her reputation in society. This reputation is an increasing function of the amount of the high-quality variety that she purchases. In other words, in this model, the consumer's decision to purchase the high-quality variety is motivated by both the utility that this decision will provide as well as the enhancement to her reputation. This means that purchasing XH allows this consumer to engage in "virtue signaling". That is, it allows her to signal to the rest of society that she is a socially conscious consumer that buys ethical garments. We will assume that buying the low-quality variety does not affect her reputation.

In this model, D represents this consumer's baseline reputation. It is her reputation if she chooses to not purchase the high-quality variety at all. In contrast, v represents the increase in her reputation from a one unit increase in the her purchase of X_H.

(b) Suppose that P_H = 2 and I = 20. Using this information as well as (2) and (3), find this consumer's optimal consumption of each variety. The optimal consumption levels should be a function of P_L, D, and v.

Now suppose that a group of socially conscious retailers develop a campaign to induce more consumers to purchase ethical garments. The key element of their campaign will be to attach a label to their garments that will certify that the garment has been produced in a safe workplace overseas. The advantage of this symbol is that it will allow a consumer to signal to society that she is socially conscious. That is, the symbol will allow the consumer to enhance her reputation by purchasing the high-quality variety.

(c) Let us assume that the use of this symbol increases this consumer's v from 0.5 to 1. You can also assume that D = 3, P_L, = 0.5, P_H = 2, and I = 20. Use a diagram with X_H on the horizontal axis to illustrate this consumer's indifference curve for both values of v. Can you infer from this diagram alone whether the higher v makes this consumer better off or not? Explain. [Hint: when drawing the diagrams for this part you can assume a fixed value of u = 130.13.]

(d) One way to measure the magnitude of the effect of a change in v on X_H is to calculate an elasticity. Specifically, define the elasticity of X_H with respect to v, ε^v, as

ε^v = Percentage change in X_H/Percentage change in v

Calculate this elasticity when v changes from 0.5 to 1. You can continue to assume that D = 3, P_L = 0.5, P_H = 2, and I = 20.

Another way to increase the consumption of X_H is to tax X_L. This tax will raise the price of X_L, h. We can measure the impact of such a tax using the elasticity of XH with respect to P_L. Let this be defined as

ε^P_L = Percentage change in X_H/Percentage change in P_L

(e) Calculate this elasticity when PL changes from 0.5 to 1. Here you can assume that D = 3, v = 0.5, PH = 2, and I = 20. Compare this elasticity with the one you calculated in part (d). What does this imply about the effectiveness of a tax on X_L relative to exploiting a consumer's desire to engage in virtue signaling?

(f) State and explain two limitations of this model that might lead you to be unconvinced that virtue signaling is more effective than the tax.