# Calculating equilibrium price and quantity

Given the following demand and supply equations:

Demand: Q=100 - 5P

Supply: Q=20P

1. What is the equilibrium price?

2. What is the equilibrium quantity?

3. Using Excel and prices in the range of $1 to $10, generate the demand and supply schedules for the initial equations.

4. Use Excel to plot a graph of your demand and supply curves that include the equilibrium point.

5. What are the new equilibrium price and quantity if supply remains constant and demand increases so that the new demand equation is: Q = 150 - 5P?

6. What are the new equilibrium price and quantity if demand remains contant and supply decreases so that the new supply equation is Q = 2P?

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#### Solution Preview

Please refer attached file for graph.

1. What is the equilibrium price?

For determining equilibrium price, put Q (demand)=Q(supply)

100-5P=20P

100=25P

P=4

Equilibrium price is $4.

2. What is the equilibrium quantity?

Quantity demanded at equilibrium price (i.e. P=$4)=100-5*4=80

Quantity supplied at equilibrium price (i.e. P=$4)=20*4=80

Equilibrium quantity is 80 units.

3.Using Excel and prices in the range of $1 to $10, ...

#### Solution Summary

Solution describes the steps to calculate equilibrium price and quantity in the given cases.

Calculating Equilibrium Prices and Quantity

Suppose the demand for guitars in State College is given by Qd = 9000 - 12P where Qd is the quantity demanded, and P is the price of guitars. Also, suppose the supply of guitars is given by Qs = 9P - 3852, where Qs is the quantity supplied of guitars.

a)Calculate the equilibrium price of guitars and the equilibrium quantity of guitars in State College. Show your work.

b)Suppose the actual price of guitars is $600. Determine if there is a shortage, a surplus, or if the market is in equilibrium at a price of $600. If there is a shortage or surplus, calculate how much the shortage or surplus is.

c)Given your answer to b), is the price of guitars likely to rise, fall, or stay the same?

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