Assignment:
1. Assume demand for medical services is expressed by the following equation: 3Qd =1800 - 9PP, where PP is the out-of-pocket price. Further, assume this medical service has a list price of PL = $40.
a. Draw the demand curve (i.e., straight line) expressed by the quantity demanded (Qd) equation given above on a graph with price on the vertical axis and Qd on the horizontal axis. Show the y- and x-intercepts.
b. What is Pp under no insurance? Calculate the Qd under no insurance. Show/mark Qd and Pp under no insurance on the graph drawn in part a.
c. Is there any welfare loss under no insurance? Why or Why not? If any welfare loss, calculate the welfare loss and show the area that represents welfare loss on the graph drawn in part a.
d. What is Pp under full insurance? Calculate the Qd under full insurance. Draw the demand curve that represents Qd under full insurance on a graph with price on the vertical axis and Qd on the horizontal axis. Help/Tip: It may help to see the answer for this part, and more importantly for the next part (part e), if you re-draw the demand curve from part a on the same graph you are asked to draw in this part, with price on the vertical and Qd on the horizontal axis as usual.
e. Is there any welfare loss under full insurance? Why or why not? If any welfare loss, calculate the welfare loss and show the area that represents welfare loss on the graph drawn in part d.
f. What is Pp under an insurance plan with a 50% co-insurance? Calculate the Qd under an insurance plan with a 50% co-insurance. Derive an equation for Qd as a function of PL (list price) under an insurance plan with a 50% co-insurance. Do/does the slope, x-intercept, and/or y-intercept of this Qd equation you just derived differ from those/that of the Qd equation above that is given in the question? Help/Tip: Although you are not asked to draw a graph of any Qd equation in this part, it may help to see the answer for this part, and more importantly for the next part (part g), if you re-draw the demand curve from part a and also draw the demand curve represented by the Qd equation you are asked to derive in this part on the same graph, with price on the vertical and Qd on the horizontal axis as usual.
g. Is there any welfare loss under the insurance plan with a 50% co-insurance? Why or why not? If any welfare loss, calculate the welfare loss and show the area that represents welfare loss on a graph with price on the vertical and Qd on the horizontal axis as usual.
h. What is Pp under an insurance plan with a co-pay of $30? Calculate the Qd under an insurance plan with a $30 co-pay. Draw the demand curve that represents Qd under an insurance plan with a $30 co-pay on a graph with price on the vertical axis and Qd on the horizontal axis. Do/does the slope, x-intercept, and/or y-intercept of this demand curve differ from those/that of the demand curve drawn in part a? Help/Tip: It may help to see the answer for this part, and for the next part (part i), if you re-draw the demand curve from part a on the same graph you are asked to draw in this part, with price on the vertical and Qd on the horizontal axis as usual.
i. Is there any welfare loss under the insurance plan with a $30 co-pay? Why or why not? If any welfare loss, calculate the welfare loss and show the area that represents welfare loss on the graph drawn in part h.
j. Would the insurance plan with a 50% co-insurance or the insurance plan with a $30 co-pay be better at mitigating moral hazard? Why?