Instructions: Work with this file as a template, perhaps by File: Download: Microsoft Word. Other options are fine as long as they are legible. Name and SID at the top. Did you work with other    students? Identify them below. Type your name to sign the Honor Code. Profit.

Problems based on Bhattacharya, Hyde, and Tu (2013):

Topic                                                 Question        Points

Cost-effectiveness                            14.15               17   .

17

Did you work with other students? List them below:

Please type your name as an affirmation of the Honor Code at the University of California, Berkeley.

“As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others.”

Type your name:

14.15 [17 points total] If you have back pain, ICER it? Suppose Jay has been experiencing back pain, and has four options for treatment shown in Table 14.6:

a) [5 points] Plot these four treatments on axes showing pain reduction (y-axis) versus cost (x- axis). Create a cost-effectiveness frontier by connecting potentially cost-effective treatments.

See the answer key spreadsheet. The best definition of the CEF is the blue lines shown below.  Students could also draw the red line connecting chair cushions directly to acupuncture, skipping cortisone injections. But the formal definition of the CEF in the textbook implies that the blue line is a better answer. (And it’s probably a better choice here since in part (f) we are finding a curved indifference curve that selects cortisone as optimal.)

b) [2 points] Calculate the ICER between cortisone injections and a chair cushion, and between acupuncture and cortisone injections.

(Recall that the ICER is the difference in cost, the y-variable, divided by the difference in effectiveness, the x-variable.)

ICER(injections, cushion) =  =  =             $120 per pain reduction unit

ICER(acupuncture, injections) =  =  = $12 per pain reduction unit

Just for kicks, here are the 4 other possible ICER’s. There is no need to calculate them too .

ICER(cushion, nothing) =            =          =

$1000−$100        $900

50−20                30

ICER(acupuncture, nothing) =  =  =

$700−$0         $700

25−0              25

$50 per pain reduction unit

$30 per pain reduction unit

$200 per pain reduction unit

$28 per pain reduction unit

[Note the renumbering from this point forward, compared to the textbook version.]

c) [3 points] Use your answers to part b) to explain why there is no possible range of Jay’s     valuations for a pain reduction unit that would lead him to pick cortisone injections as the cost effective treatment.

(Note: You can also reference your answer to part a). The valuation for a pain reduction unit is the inverse of the slope of the linear indifference curve. The ICER between a pair of treatments is the inverse of the slope of a line segment that connects them.)

Our answers to part b) imply that there are no possible valuations for a PRU that would induce Jay to pick cortisone injections, but it might not be easy to see that, per se.

It is much easier to see in the graph we drew in part a), and our answers to part b) basically      make what we see numerical. But the problem is that our eyes are used to seeing slopes, while the ICERs are the inverses of slopes.

Students can say that injections are inside the cost-effectiveness frontier (CEF) in part a) and therefore never cost effective, and therefore there is no valuation of pain reduction that    would lead Jay to pick injections.

Formally, it’s also possible to remark about the ICER thresholds that we found in part b).

Suppose Jay values a PRU at less than $120, then he would prefer a chair cushion to injections, because the ICER between those two is $120 per PRU. If Jay values a PRU at more than $120, that same ICER says he would choose injections. But the other ICER = $12 says     that he would also prefer acupuncture to cortisone at any value of pain reduction over $12.       What if his value of pain reduction is less than $12? That second ICER says he would prefer cortisone to acupuncture, but the first ICER says he would prefer a chair cushion to injections.

There are a lot of words in the preceding paragraph, but the bottom line is that there are no valuations of pain reduction that would lead Jay to choose cortisone injections. (Isn’t it much easier just to examine the CEF!)

d) [2 points] Assume that indifference curves in this space are linear. (Note that they actually  slope upward here, because pain reduction (y) is good but cost (x) is bad.) Briefly interpret this assumption in terms of its implications for how Jay values incremental units of pain reduction.

This assumption means that we value all pain reduction units at a constant rate. For example, we value 2 pain reduction units exactly twice as much as we value 1 pain reduction unit, across all levels of pain reduction. This seems reasonable for small changes in pain, but it probably     isn’t so reasonable when we’re thinking about the full spectrum of pain from zero to maximum.

e) [2 points] Under this assumption of linear indifference curves, is it possible to draw indifference curves such that cortisone injections will be cost-effective?

No, this is impossible because of the geometry of the CEF. Any indifference curves that would  indicate a preference for cortisone injections over the chair cushion would have to be relatively  shallow, and would imply that acupuncture in turn was even more desirable than cortisone        injections. Likewise, any indifference curves that would indicate a preference for acupuncture    over cortisone injections would have to be relatively steep, and would imply that a chair cushion is even more desirable than cortisone.

f) [3 points] Relaxing this assumption, redraw the graph with a curving indifference curve such   that cortisone injections are preferred to all other treatments. Describe the preferences that your indifference curves imply, in terms of willingness-to-pay for additional pain reduction at different levels of pain reduction.

(Hint: Do your best; this is possible but not easy. Remember that cost is bad, so the indifference curve needs to look like a “J” rather than like an “L,” or opening toward the upper left rather than the upper right as we are more accustomed to seeing in economics.)