Question

CS AND PS Price Controls for Medical Care. Consider a town where the equilibrium price of a doctor's visit is $60 and the equilibrium quantity supplied is 90 patient visits per hour. For suppliers (doctors), each $1 increase in price increases the quantity supplied by two visits. For consumers, each $1 increase in price decreases the quantity demanded by one visit. Suppose that in an attempt to control the rising costs of medical care the government imposes price controls, setting a maximum price of $50 per visit. a. Use a completely labeled graph to show the effects of the maximum price on (a) the quantity of visits to doctors and (b) the total surplus of the market.

Answer 1

First, we need to derive the equations of the demand and supply curves.

Given, Equilibrium price = $60 and equilibrium quantity = 90 units.

Suppose a-bQ= P is the equation of the demand curve.

Now, with each unit increase in price, quantity demanded decreases by one unit. This means the slope of the demand curve is -1 (i.e, b=1).

Putting values of P and Q in the demand equation,

a-(1*90)= 60

or, a=150 is the vertical intercept of the demand curve.

Thus, P=150-Q is the equation of the demand curve.

Similarly, suppose c+dQ=P is the equation of the supply curve.

Now, with each unit increase in price, quantity supplied increases by two units. This means the slope of the supply curve is 1/2 (i.e, d=1/2).

Putting values of P and Q in the supply equation,

c+(1/2*90)= 60

or, c=60-45=15 is the vertical intercept of the supply curve.

Thus, P=15+1/2Q is the equation of the supply curve.

We have shown the curves on the diagram below:

Price in dollars per hour 150 Supply Demand Quantity in patient visits per hour 150 70 90 100

With the imposition of price control of $50 per visit, quantity supplied falls to 70 patient visits per hour whereas quantity demanded rises to 100 patient visits per hour.

Thus, here, the total surplus falls from area (A+B+C+D+E+F) to area (A+B+C+D) and area (E+F) is the dead weight loss.

Now, new total surplus = area of the trapezium (A+B+C+D) = 1/2*height*(sum of parallel sides) = 1/2*70*(135+30) = $5,775.