Health economics?

Question

Government provides Dental care for low income seniors at rate of $50. Also, dentist have patients who pay out of pocket. The demand curve is shown below. Dentist are individual monopolist.

i) If each dentist works on profit-maximizing basis, how many treatments will be provided to the paying patient and to the funded patients.

ii)What will the # of paying patients and federally funded patients be if federal agency raises rate to $60 per treatment.

Out of pocket price is shown in 2nd column.

Qnty dmd Price TR MR TC MC

0 $80 $50

1 70 $70 $70 70 $20

2 60 $120 $50 110 40

3 50 $150 $30 170 60

4 40 $160 $10 250 80

5 30 $150 $-10 350 100

6 20 $120 $-30 470 120

Answer 1

Q... P.... TR... MR... TC... MC... Profit

0... 80..... 0..... X..... 50..... X..... -50

1... 70.... 70.... 70.... 70..... 20..... 0

2... 60... 120... 50... 110.... 40.... 10

3... 50... 150... 30... 170.... 60... -20

4... 40... 160... 10... 250.... 80... -90

5... 30... 150.. -10... 350... 100.. -200

6... 20... 120.. -30... 470... 120.. -350

i)

Profit-maximizing P=60 Q=2 (MR≥MC) but for dental-care rate at P=50; Q=3 so we don't know if these patients not already included in gov dental-care funded program.

If we assume that they are even proportion then

Funded: Q=3; P=50

Paying: Q=2; P=60

ii)

Funded: Q=2; P=60

Paying: Q=2; P=60

P.S. Actually all there is messed up in initial task - we don't know if both markets follow the same demand and cost patterns, thus some elements of total cost may be double-counted and marginal cost may follow different pattern.

So just give more assumption for this task to solve it right. Provide more details how these patients are differentiated (at least by costs if they follow the same demand).