1- Professor Stoian writes a book. The demand for the book is P=20-Q. The margin

Question

1- Professor Stoian writes a book. The demand for the book is P=20-Q. The marginal cost to make it and sell it is $2 per book. The total fixed cost is $10. If a unique price is charged, how many books will he sell?

2- Professor Nolan writes a book. The demand for the book is P=20-Q. The marginal cost to make it and sell it is $2 per book. The total fixed cost is $10. If a unique price is charged, what will be the optimal price?

3- Professor Nolan writes a book. The demand for the book is P=20-Q. The marginal cost to make it and sell it is $2 per book. The total fixed cost is $10. If a unique price is charged, what will be the profit?

4- At the profit maximizing level of output for the monopolist?

5-If a firm knows that the elasticity of demand is -5 and its marginal cost is $20, what would be the optimal price?

Explanation / Answer

1) no of books he will sell when MR =MC

so MR =d/dQ(P*Q)

=d/dQ((20-Q.)*Q)

= 20-2Q

so 20-2Q= 2 (As MC=2)

=> Q=9 units

so he must sell 9 books

2)Unique price = 20-Q

=20-9 (Q=9 , As optimum quantity =9)

=$11

3)profit =P*Q-Total cost

=> total cost = fixed cost+MC*quantity

=10+2*9

=28

so profit =9*11-28

=$71

4)So profit level of monopolist =$71 with selling 9 books

5) if elasticity of demand is -5 and its marginal cost is $20 then for optimal price,

=>P*(1-1/e) = MC

=> P*(1-1/(-5))=20

=>P*(1+1/5) =20

=>P=16.6666

=> optimum Price =$16.67 (apprx)

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