Question

Suppose the demand for a price maker’s product is estimated to be Q = 12 – 2P and its total cost function is C(Q) = 0.5Q. Under first-degree price discrimination, what will be the firm’s profits?

Answer 1

Ans. In first degree price discrimination, the profit of the producer is the whole consumer surplus. So, the equilibrium quantity when.
Price = Marginal cost

and Marginal cost = dC/dQ = 0.5 and demand function gives the inverse demand function,

=> 6.0 - 5Q = 0.5

=> Q = 11 units

=> P = $0.5

And. y-intercept of demand function, P' = $6

So, after using the price discrimination, entire consumer surplus (because MC is constant, so, consumer surplus equal to total surplus) is the profut of the firm,

So, Profit = ConsumerSurplus = 0.5*(P' - P)*Q = 0.5*(6-0.5)*11 = $30.25

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