# Find the equilibrium Q under the observed supply and demand

MG.1. Consider the market for a course of antibiotics. Suppose the supply of antibiotics follows P = 5 + 2QS and the demand follows P = 20 – 2QD. Here, Q represents antibiotics, denominated in millions of units. The use of antibiotics generates an external harm of $2 per Q, due to the risk of increased antimicrobial resistance. Also assume that the supply curve for antibiotics is currently higher than the marginal cost curve. Specifically, prices (as described by the equation P = 5 + 2QS ) are $3 higher than the marginal costs of producing the drugs (for any level of quantity, Q). You can assume for the purposes of this problem that the reason for higher-than-marginal costs supply curve is producer market power.

Find the equilibrium Q under the observed supply and demand

Find the efficient Q

Find the equilibrium Q if the government imposed a $2 tax on antibiotics to force consumers to internalize the externality they generate

Find the equilibrium Q if several new producers entered the market, and thereby forced the supply curve down to just equal the marginal cost curve.

How do the findings in parts a-d relate to the Theorem of the Second Best? (Two sentences)

MG.2. Consider the three alternative allocations of money (m) in an economy composed of three people, with people labeled A, B, C, and alternative allocations labeled X, Y, Z. The values in the 9 cells are the moneys accruing to each person under each alternative allocation (You may wish to look back at Chapter 18):

Person A B C

Allocation X 5 5 5

Allocation Y 7 5 4

Allocation Z 11 6 0

Which distribution is preferred by a Rawlsian Social Welfare Function? Assume that utility is defined as ui = mi and recall that Rawlsian Social Welfare function would be equal to the minimum utility experienced by any person under the allocation.

Which distribution is preferred by a Utilitarian Social Welfare Function that is defined as Σ(ui), where ui = mi ?

Which distribution is preferred by a different Utilitarian Social Welfare Function that is defined as Σ (ui), where ui = mi1/2 ?

MG.3

The production function for primary care visits is Q = 100 D0.5N0.5, where Q indicates total visits produced in a year. D and N stand for doctors and nurse practitioners, respectively. The cost of employing a doctor is $100,000 and the cost of employing a nurse practitioner is $50,000.

a) Draw a production isoquant. Put D on the vertical axis. Put N on the horizontal axis.

b) Draw an isocost line. Put D on the vertical axis. Put N on the horizontal axis. Find the slope of that line (dD/dN).

c) Find an expression for the slope of the production isoquant if Q=1000. (hint: get D alone on the left hand side before taking the derivative dD/dN.

d) Describe in words how the cost minimizing mix of input relates to the curve from (a) and the line from (b).

e) Find the cost-minimizing mix of inputs needed to produce 1000 primary care visits per year in the office. (For our purposes here, it is ok if you find “fractional” amounts of doctors and nurse practitioners—e.g. 3.7 doctors.)

f) How do the results in this exercise contrast with the view that only doctors should be able to sell primary care visits, as opposed to these being sold by other kinds of healthcare workers?

MG.4. If you have multiple pages in your solution, staple them together. The TA is not responsible for any lost pages on assignments that are not stapled.