Question

Suppose a company has invented and patented a new drug to reduce the flu symptoms. The marginal cost of producing the drug is constant: MC = $3. Sup??pose this drug is not covered by any insurance plan and the market demand is as follows: What is the equilibrium quantity? ?d =60−4?

a) How much should the firm charge per unit to maximise its profit?

b) Suppose the drug is now covered by a government insurance plan with a co-insurance rate of 50% and everyone is eligible. What price should the company charge and what is the equilibrium quantity?

c) Suppose the drug is still covered by the same insurance plan as in b) but the firm’s marginal cost of producing the drug is reduced from $3 to $2: that is, ?C = $2. Will the firm charge a higher or lower price compared to the price it charges in b)

Answer 1

Ans.

Given that marginal cost MC = 3 (Assuming no fixed cost)

Market demand is given by Q = 60 - 4P

Where Q is quantity demanded at Price P.

1) profit of a firm = Total revenue - total cost

Total revenue = P(Q) = (15 - (Q/4)).Q

Total cost = integral of marginal cost with quantity = 3Q

Profit = (15 -(Q/4)).Q - 3Q = (12 - (Q/4)).Q

For profit maximisation:

Differentiate profit function with respect to quantity and equal it to zero to get the optimum quantity value for maximum profit

So, we get 12 - (Q/2) = 0 => Q = 24.

So price P = 15 - (Q/4) = 15 - (24/4) = 9.

Price per unit quantity = 9 for the maximum profit.

2) Given that co-insurance rate is 50%

That implies people can now only pay 50% of the price.

So, now the demand increases.

It changes as following :

Q = 60 - 4(P - (50P/100)) = 60 - 2P.

Now considering profit maximisation:

Profit of firm = P(Q) - TC = (30 - (Q/2))Q - 3Q

Applying the same condition as in answer 1

We get 30 - 3 - Q = 0 =>Q = 27

Price paid = ( 60 -27)/2 = 16.5 ( only 50% of this will be paid by the consumer per unit quantity)

3) If MC = $2 Then we get

Then price P = $16 ( only 50% of this will be paid by the consumer per unit quantity)

( We can get to this step by using the same technique we used in 1st and 2nd part)

So we can see that price of the drug is decreased. And this is also true because decrease in MC is decrease in cost for the firm to produce one more unit. Since the total cost decreased price also goes down.