Question

Q1) Suppose that American Borax is a monopolist and that the worldwide demand for borax is Q= 100-P where Q is tons of borax and P is the price per ton. The total cost function for American Borax is TC= 10Q+ 0.5Q^2.

.a. Write out the firm's total revenue as a function of Q.

b. Over what range of output is the revenue increasing?

c. What is the profit function for American Borax?

d. Find the firm's profit-maximizing quantity by applying calculus to the profit function.

e. Over what range of output is the monopolist's profit increasing.

f. Find American Borax's profit-maximizing price and profit.

g. Find the consumer surplus, producer surplus, and deadweight loss from the monopoly.

Answer Question G Please.

Answer 1

inAccording to question

a)

• First solve for the inverse demand curve to obtain price as a function of quantity

Q= 100 –P

P= 100 –Q

Now,find total revenue as price times quantity

TR= PQ

= (100 –Q)Q= 100Q–Q2

b)

Total revenue function is as follows - TR = P * Q = (100 - Q) * Q = 100Q - Q​​​​​​2

​​​​C)

Profit is total revenue minus total cost.

π= TR–TC= 100Q–Q2–(10Q+ 0.5 Q​​​​​​2)

= 100Q–Q2–10Q–0.5Q2

= 90Q–1.5Q2.

d)

Solve the profit-maximization problem

maxQπ

= 90Q–1.5Q2

Takethe first-order condition and solve for Q*

dπ/dQ= 90 –3Q = 0

3Q = 90

Q* = 30tons

F)

Plug Q* into the inverse demand curve to get price

P* = 100 –Q*

100-30

=$70

Plug Q* into profit function

π= 90Q –1.5Q2= 90(30) –1.5(30)2= 2,700 –1,350 = $1,3504.

G)

P=100-Q

TR= P*Q= (100-Q)Q= 100Q-Q2

MR= dTR/dQ

MR= 100-2Q

MR= MC

100-Q2=10Q+0.5Q2

Q= 30

P=70

Locate the area of consumer Surplus and producer surplus,

Consumer Surplus(Triangle)

Producer surplus

Dead weight loss

Shown on finger below

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