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# Calculating deadweight loss in the given case

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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?

#### 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.

\$2.19