Question

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 equilibrium wage rate. This is done by setting the quantity demanded equal to the quantity supplied and algebraically solving for W. That is, solve the following equation for W:

24,000 – 320W = -18,000 + 1250W

2. Find the equilibrium 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’ve made an error 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 = 14.4 + 0.0008Qs

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 equilibrium quantity (while you have Qd and Qs in the equations, you can make use of the fact that, in equilibrium, Qd = Qs, so that you are simply solving for Q).

5. What is the wage rate using the above approach?

Answer 1

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