You are the manager of a monopoly, and your demand and cost functions are given

Question

You are the manager of a monopoly, and your demand and cost functions are given by P = 300 – 3Q and C(Q) = 1,500 + 2Q2, respectively.

a. What price–quantity combination maximizes your firm’s profits?

Price: $ 210
Quantity: 30 units


b. Calculate the maximum profits.

$ 3000


c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price–quantity combination?

Inelastic

Unit elastic

x Elastic

d. What price–quantity combination maximizes revenue?

Price: $  
Quantity:  units


e. Calculate the maximum revenues.

$  


f. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price–quantity combination?

Inelastic

x Elastic

Unit elastic

Explanation / Answer

a)

When, MR = 300 – 6Q,

MC = 4Q,

Equating MR = MC, we get :-

300 –6Q = 4Q.

or, Q = 30 Units.

Now we obtain profit maximizing price by putting value of q in equation, P = 300 - 3(Q),

we get, P = 300 -3(30)

= $210.

b)

Now we calculate Revenue,

Revenues = 210 * 30

= $6300

Calculating costs, from equation C(Q) = 1500 + 2Q^2

Cost = 1500 +2(30)^2

= $ 3300

So, Total Profit = $6300 - $3300

= $3,000

c)

The demand is elastic in nature.

d)

Now, TR is maximum when MR = 0,

so, putting MR = 0, we get

300 – 6Q = 0.

Q = 50 Units.

Now by calculating price at this quantity we get,

P = 300 –3(50) = $ 150

e)

Maximum Revenue = 150 * 50

= $ 7500.

f)

The demand is Unit Elastic.

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