Question

Demand curve is given as D = 100 – 2P. If a monopoly company, whose cost function is C = 2Q, can do 1st degree price discrimination, what will be the market quantity and profit of the firm?

Answer 1

Under first degree price discrimination Firm charges each consumer price equal to there maximum willingness to pay.

Maximum willingness to pay is given by the demand curve D = 100 – 2P

Monopolist will sell its output to those only whose maximum willingness to pay is greater than or equal to additional cost required to produce it i.e. Marginal Cost.

Thus He will produce that quantity at which Price = Marginal Cost

Q = 100 - 2P => P = (1/2)(100 - Q)

Total Cost : C = 2Q => Marginal cost(MC) = dC/dQ = 2

So, P = MC => (1/2)(100 - Q) = 2

=> Q = 96

Thus Market quantity = 96 firms

As, Q= 96 => C = 96*2 = 192

As it is charging consumers maximum willingness to pay, Thus Total revenue will be area under demand curve till Q = 96

When Q = 0, P = 50 and When Q = 96 , P = 2

Thus Area under demand curve till Q = 96 = (1/2)h(Sum of parallel sides)

= (1/2)*96*(50 + 2)

= 2496

=> Total revenue = 2496

Hence Profit = Total Revenue - Total cost

= 2496 - 192   

= 2304

Thus, Profit of the firm = 2304