Your inverse demand curve for medical care is given byP = 18 -

1) The inverse demand function is given as P = 18-0.5Q........(1)

to get the x itercept, we set P=0 which gives Q = 36

and to get the y intercept we set Q=0 which gives P = 18

Now, at a market price of P=10,

we get Q= 16 from (1)

The deductible is worth 200.

Therefore, to get the quantity at the deductible, we have to divide the deductible by the per unit market price.

Hence, the quantity demanded when the deductible is met = 200/10 = 20.

2) For Q>20, the deductible limit is crossed and the coinsurance kicks in which changes the demand curve entirely.

New Demand curve DD2:

0.5Q = 18 - (coinsurance rate).P

=> 0.5Q = 18-0.1P

Now at a market Price of 10,

from DD2, we get,

Q= 34.

Therefore the consumer has two options.

If he wishes to stay within the deductible limit then buy Q = 16 units

and if he wishes to coss it, then buy Q = 34 units.

Calculation of Consumer surplus:

In case of DD1,

CS1 = 0.5 * (18-10) * 16 = 64.

In case of DD2,

y intercept of DD2 is where, Q=0

=> 0.5(0) = 18-0.1P => P = 180.

therefore, CS2 = 0.5 * (180-10) * 34 = 2890.

Calculation of net gain of the consumer:

In case of DD1,

Net gain = CS1 - total cost = 64 - 16*10 = 64 -160 = -96.

In case of DD2,

Net gain = CS2 - total cost = 2890 - [200 + 0.1*(34*10 - 200)] = 2676.

Since net gain in case of DD2 > DD1, the consumer will choose the option to cross his deductible amount and buy

Q=34 units.

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