Round all values for the number of workers to the nearest (so, round up or down) whole number, but report wages to two decimal places. To avoid rounding e
ors ca
y through a sufficient number of significant digits until your final answer, where you may round.
Part 1: Perfect competition
Perfect competition is the supply and demand model that is often used to (inaccurately) represent all of economics. Supply is simply the aggregation of individual firms’ supply curves, which in turn, are nothing more than their marginal cost curves. Demand tells us how much consumers will purchase at different prices. Note: supply curves assume that producers have no control over prices and demand curves assume the same for consumers. This is what economists mean when they say ‘the price is set in the market.’ For other market structures, the price is often set in someone’s office
Suppose the market for nurses can be modeled using supply and demand (the market is perfectly competitive). There are a large number of hospitals, doctors’ offices, clinics, etc., so that no individual employer has an impact on the market wage. The nurses are not unionized so they individually have no impact on the wage.
Demand is given as Qd = 24,000 – 320W, where Qd is the quantity demanded (in full-time equivalents) and W is the hourly wage rate.
Supply is given as Qs = -18,000 + 1250W, where Qs is the quantity supplied.
1. Find the equili
ium wage rate. This is done by setting the quantity demanded equal to the
quantity supplied and alge
aically solving for W. That is, solve the following equation for W:
24,000 – 320W = XXXXXXXXXX1250W
2. Find the equili
ium quantity. Plug your answer from (1) into either the supply or demand function to get Q. Or better yet, plug it into both to make sure you get the same answer. If you don’t, you have the wrong answer for 1.
If, at this point, you have a negative wage or negative quantity, you have made an e
or and should start over.
Another way to solve the above problems would be to derive the ‘inverse demand curve’ and the ‘inverse supply curve.’ The inverse supply curve gives the wage as a function of the quantity supplied. Given the supply function above, the inverse supply function is:
W = XXXXXXXXXX0008Qs
Be sure you can duplicate the above answer before moving on to 3.
3 And 4. Derive the inverse demand function. It should take the form W = a + bQd, where a and b are derived from the demand function’s parameters. You will report a as the answer to (3) and b as the answer to (4). b should be reported to 6 decimal places.
If you set the inverse demand function equal to the inverse supply function you can solve for the equili
ium quantity (while you have Qd and Qs in the equations, you can make use of the fact that, in equili
ium, Qd = Qs, so that you are simply solving for Q).
XXXXXXXXXXWhat is the wage rate using the above approach?
Part 2: Monopsony
A market for labor can fail to be perfectly competitive if there is a single large employer, as might be the case when all medical services are provided by a single provider. Suppose that is the case with the nurses. The following use the equations used in the prior set of questions, though they may take on different meanings.
Solving for the equili
ium wage and quantity is a multi-step procedure. First you will need the marginal resource cost (MRC) curve. This curve gives the marginal cost of hiring an additional nurse (in cost per hour). Since attracting an additional nurse requires raising the wage rate for all nurses, this cost is above the wage rate required for that additional nurse. If the inverse supply curve is given as:
W = a + bQs,
the marginal resource cost is:
MRC = a + 2bQs
Essentially, it has the same y-axis intercept as the supply curve, but twice the slope.
With a single buyer there isn’t a demand curve, but what we would think of the demand curve is the marginal value curve. In this case, it gives the marginal value product (in dollars per hour) of nurses. Hence, you can replace W in the inverse demand function with MVP.
To find the quantity of nurses hired, set MRC = MVP and solve for Q.
XXXXXXXXXXWith a monopsony, how many nurses are hired?
XXXXXXXXXXWhat is the wage rate? (hint: use the inverse supply curve – not the MRC or demand curve – for this purpose).
XXXXXXXXXXIf the hospital could hire as many nurses as it wanted with the wage rate you found in (7), how many nurses would be hired? (hint: use the demand curve to answer this – plug in the wage from (7)).
XXXXXXXXXXWhat is the ‘shortage’ of nurses? (This is the difference between your answers to (8) and your answers to (6)).
Part 3: Monopsony with 3rd party supplie
With the nursing shortage found above, the hospital is interested in finding a solution whereby it can get more nurses, but not raise the wage to its existing nurses. A nursing ‘temp’ agency has moved into the region and can supply as many nurses as are needed, at a wage of $35/hour.
10. How many nurses does the hospital hire via the temp agency?
Part 4: Monopoly
Your pharmaceutical company has developed a therapy that can cure peanut allergies. The inverse demand function for this therapy is given as:
P=$150,000 – 62.5Qd, where Qd is the annual quantity demanded.
While development costs were substantial, your marginal costs for a full treatment are ‘just’ $800 per treatment.
11. If you set single price to maximize profits, what quantity will you supply ear year?
(Guidance: The marginal revenue (MR) function has the same y-axis intercept as the inverse demand function, but twice the slope. Set MR equal to MC and solve for Q.)
12. What is the price for treatment? (Hint: plug your quantity from 11 into the inverse demand function.)
13. If the treatment was priced at the marginal cost to your company, how many treatments would be provided per year?
14. What is the deadweight loss due to monopoly power in this market?