Question

A monopolist faces a downward sloping demand curve, P = 911.0 - 16.5*Q. It has a marginal cost curve described by the equation MC = 17 + 13*Q. The competitive market price is estimated to be ____ and the monopoly price will be ____.

A) $410.97 ; $590.33

B) $455.5 ; $606.8

C) $590.33 ; $455.5

D) $455.5 ; $606.8

A monopolist faces a downward sloping demand curve, P = 369.0 - 12.5*Q. Total revenue will be maximized at a price of ____.
A) $162.99
B) $184.5

C) $249.67 D) $2306.3

A monopolist faces a downward sloping demand curve, P = 913.0 - 29.0*Q. It has a marginal cost curve described by the equation MC = 13 + 7*Q. The profit-maximizing price will be ____ and the monopoly quantity will be ____.

A) $511.46 ;13.85

B) $540.5 ;13.85

C) $456.5 ;13238.5

D) $511.46 ;13238.5

Answer 1

Answer : 1) The answer is option A.

For competitive market :

At equilibrium condition, P = MC.

=> 911.0 - 16.5*Q = 17 + 13*Q

=> 911 - 17 = 13Q + 16.5Q

=> 894 = 29.5Q

=> Q = 894 / 29.5

=> Q = 30.305

Now, P = 911 - (16.5 * 30.305)

=> P = 410.97

Therefore, in competitive market the price level is $410.97.

For monopoly market :

TR (Total Revenue) = P * Q

=> TR = (911.0 - 16.5*Q) * Q

=> TR = 911Q - 16.5Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 911 - 33Q

At equilibrium condition, MR = MC.

=> 911 - 33Q = 17 + 13*Q

=> 911 - 17 = 13Q + 33Q

=> 894 = 46Q

=> Q = 894 / 46

=> Q = 19.434

Now, P = 911 - (16.5 * 19.434)

=> P = 590.33

Therefore, in monopoly market the price level is $590.33.

2) The answer is option B.

When P = $184.5,

184.5 = 369 - 12.5Q

=> 12.5Q = 369 - 184.5

=> 12.5Q = 184.5

=> Q = 184.5 / 12.5

=> Q = 14.76

Now, TR (Total Revenue) = P * Q

=> TR = 184.5 * 14.76

=> TR = $2,723.22

As when P = $184.5 then we get higher total revenue of $2,723.22, hence the option B is correct.

3) The answer is option A.

TR = P*Q

=> TR = ( 913.0 - 29.0*Q ) * Q

=> TR = 913Q - 29Q^2

MR = TR / Q

=> MR = 913 - 58Q

At equilibrium condition, MR = MC.

=> 913 - 58Q = 13 + 7*Q

=> 913 - 13 = 7Q + 58Q

=> 900 = 65Q

=> Q = 900 / 65

=> Q = 13.846 = 13.85

Now, P = 913 - (29 * 13.846)

=> P = $511.46

Therefore, the profit maximizing monopoly price is $511.46 and quantity is 13.85 .