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# Pricing in Monopoly and Pure Competition

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Need help with this micro problem

Let's say the cost function and the demand function of a monopolistic firm are as follows.

C=10+q^2
p=20-q

A) what is the price and output this monopolistic firm will produce?
B) what will be the price and quantity of the government mandated that this monopolist behaves as a perfect competitor (charges price of a perfect competitor and sells quantity of a perfect competition)?
C)what is the PS,CS, and total welfare when in perfect competition? Compute the numerical value of PS, CS and TW.
D) What is the PS, CS, and total welfare is monopoly? Compute numerical values.
E) compute the deadweight loss when you move from perfect competition to monopoly?
F) if the government sets a price of p=10, what is the new price and quantity.

https://brainmass.com/economics/utility-demand/pricing-monopoly-pure-competition-607400

#### Solution Preview

Let's say the cost function and the demand function of a monopolistic firm are as follows.
C=10+q^2
p=20-q

A) what is the price and output this monopolistic firm will produce?
Total Revenue=TR=p*q=(20-q)*q=20q-q^2
Differentiate TR with respect to q to get MR
Marginal Revenue, MR=d(TR)/dq=20-2q

C=10+q^2
Differentiate C with respect to q to get MC
Marginal Cost, MC=2q

Set MR=MC to get optimal level of output
20-2q=2q
4q=20
q=5
p=20-5=20-5=\$15

B) what will be the price and quantity of the government mandated that this monopolist ...

#### Solution Summary

The solution depicts the steps to estimate the consumer and producer surplus in the given cases.

\$2.19