# Calculating deadweight loss in the given case

Brown guitar company hires you to consult and you estimate the demand for guitars to be Q=9000-6P. The supply of guitars is given by Q= -3000+9.

1 What is the equilibrium price and quantity of guitars?

2 What is the price elasticity of demand at the equilibrium price and quantity?

3 What is the price elasticity of supply at the equilibrium price and quantity?

If a per-unit excise tax of $ 90.00 per guitar is levied on the consumers, what price would consumers pay after the tax is levied ? What proportion of tax will be paid by the supplies of guitars? How many guitars will be sold after tax is imposed? How much consumer surplus do consumers get after the tax? What is the dead weight loss created by tax?

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#### Solution Preview

Please refer attached file for graph and tables.

1 What is the equilibrium price and quantity of guitars?

Qd=9000-6P

Qs=-3000+9P

In equilibrium Qs=Qd

-3000+9P=9000-6P

15P=12000

P=800

Qd=9000-6*800=4200

Qs=-3000+9*800=4200

Equilibrium quantity=4200

Equilibrium price=$800

2 What is the price elasticity of demand at the equilibrium price and quantity?

Equilibrium Price, P=800

Equilibrium Quantity, Q=4200

Qd=9000-6P

On differentiating with respect to P, we get

dQd/dP=-6

Price elasticity of ...

#### Solution Summary

Solution determines equilibrium parameters, price elasticity of demand and supply and dead weight loss created by tax.

Calculating dead weight loss (lost efficiency.)

Here's what I think I know about the answer: to get the $ value of DWL you have to take the area of the aggregate surplus under perfect competition and substract the area of the aggregate surplus under monopoly (helps to make a little graph.) The funny thing is, my main problem is I don't know the geometry necessary to do that. There may be another method, I'll leave it to you.

Here's the problem:

I am considering giving a patent for a new drug. The public demand is given by: P = 120 - 10Q, where Q is quantity of the drug and P is price. If the marginal cost of production is given by MC = 2Q, what will be the monetary value of the efficiency loss of granting the company monopoly power (meaning a patent)?

Remember that a marginal revenue function can be derived from a linear demand function by doubling the slope of that function.

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