Suppose a business offers a 10% discount on the good x1 that it sells.

a. Illustrate a consumer's before and after-discount budget constraint by modeling x2 as a composite good.
b. Suppose you observe only the after-discount consumption decision of the consumer. Can you tell from this information how much revenue the firm is giving up (from this consumer) by offering the discount? If so, illustrate this in your graph.
c. Suppose that, instead of the firm offering the 10% discount, the government subsidized consumption of x1 sufficiently to reduce p1 by 10%. Suppose again that you only observe the after-subsidy decision of the consumer. Can you tell how much of a subsidy payment is made to this consumer by the government? If so, illustrate it in your graph.
d. Why are your answers to (b) and (c) different?

What will be an ideal response?

a. The graph should contain two budget lines with the same vertical intercept but different slopes --- with the shallower constraint representing the after-discount budget constraint.


b. No, you cannot. The reason for this is that we do not know what decision the consumer would have made in the absence of the discount --- and so we can't tell whether (or how much) revenue was lost.


c. Yes, you can. The subsidy payment by the government is the vertical difference between the before and after-subsidy constraints measured at the after-subsidy consumption bundle.


d. If you are a firm and you want to assess the impact on revenues of a discount policy, you need to know what consumers do both before and after the discount --- because you need to calculate the difference in revenues. If you are a government subsidizing a good, you don't have to know what consumers do before the subsidy in order to calculate how much the subsidy will cost --- because all that matters is how much consumers will buy under the subsidy.