Question

In: Economics

5. The supply curve for butter is QS = 100 + 3P Where QS   is the...

5. The supply curve for butter is QS = 100 + 3P
Where QS   is the quantity supplied of butter (in millions of kilos per year) and P is the price of butter ( in Kwacha per Kilo). If the demand curve for butter is a vertical line at QD = 106 millions of kilos per year.
( a ) If the government imposes a price floor of K1 per kilo on butter, will there be an excess supply or excess demand of butter, and how big will it be?
(b ) If the government’s price floor is set at K3 per kilo, will there be an excess supply or excess demand of butter, and how big will it be?
( c) Under the conditions described in part (a) , what is the price elasticity of demand for butter? Do you regard this as a realistic value for this price elasticity? Explain.

Solutions

Expert Solution

Given:

Supply function: Qs = 100+3P

Demand function: Qd = 106

Demand curve is vertical it means that the quantity demanded doesnt change with the change in price. And demand is perfectly price inelastic.

a.) Price floor of K1 per kilo on butter.

Price floor leads to only excess demand or excess supply when it is binding price floor.

First we have to find the equilibrium price, to find whether this price floor is binding or not. If it is not binding then it wouldn't lead to excess demand or excess supply and the market will remain in equilibrium.

At equilibrium, quantity demanded is equal to the quantity supplied.

that is,

Qs = Qd

100 + 3P = 106

3P = 106-100

P = 2

Therefore the equilibrium price of butter is K2 per kilo.

As price floors are binding only when they are set above the equilibrium price. As the price floor of K1 per kilo is below this equilibrium price, therefore it is not binding. So the market will remain in equilibrium and there will be neither excess demand nor excess supply.

Quantity demanded after non-binding price floor = 106 million kilos per year

Quantity supplied non binding price floor = 100+3P = 100+3(2) = 106 million kilo per year

The magnitude of excess demand or excess supply at price floor of K1 per kilo is zero, as the quantity demanded is equal to the quantity supplied. So the market has no excess conditions.

i.e. Quantity demanded - Quantity supplied = 0

Therefore, there is neither excess demand nor excess supply at price floor of K1 per kilo on butter.

b.) In order to determine whether there will be excess demand or excess supply at price floor of K3 per kilo, we have to find the demand and supply at a price floor of P = K3 per kilo on butter

At price floor = K3 per kilo on butter,

Quantity supplied is,

Putting P = 3

now as the demand function is a straight line and is not dependent on the price. therefore at every price the quantity demanded is same.

That is, at price = K3 per kilo butter

Quantity demanded is,

Qd = 106 kilo butter

As we can see the quantity supplied is more than the quantity demanded at a price floor of K3 per kilo on butter, therefore it means there is excess supply in the market at a price floor of K3 per kilo.

Now, the magnitude of excess supply is calculated by the difference between quantity supplied and quantity demanded at a price floor of K3 per kilo.

At the price floor of K3 per kilo

Excess supply = Quantity supplied - Quantity demanded

Excess supply = 109-106

Excess supply = 3 kilo butter per year

Therefore there is an excess supply of 3 million kilo butter per year.

c.) Under the conditions described in part (a), as the demand curve is vertical, it means that quantity demanded will remain same all over the price.

As we saw that with the change in price from equilibrium to the price floor of K1 per kilo, the quantity demanded didn't change. It means that the quantity demanded is not responsive to the change in price. That is demand is perfectly inelastic. Therefore the price elasticity of demand is zero.

Demand function: Qd = 106

If price floor is set of K1 per kilo on butter,

Quantity demanded = 106 million kilo butter per year

If price is in equilibrium, i.e. P = K2 per kilo on butter

Quantity demanded = 106 million kilo butter per year.

Therefore elasticity of demand is,

As the percentage change in price from K2 per kilo to K1 per kilo is:

And percentage change in quantity demanded is:

Therefore price elasticity of demand is,

I do regard this as a realistic value of price elasticity of demand. As demand for butter is price inelastic.

When butter is a pure necessity good. People would consume the fixed quantity of butter regardless of the price. It is realistic that with the change in the price of butter, people would still demand the same butter as what their necessity requires. And with the change in the price of butter, there is no change in quantity demanded of butter. As households will be consuming the same regardless of the price.

So price elasticity demand of butter zero is realistic as butter here is pure necessity good.


Related Solutions

A supply curve is given by QS = 4 + 3P. Draw the supply curve. You...
A supply curve is given by QS = 4 + 3P. Draw the supply curve. You don't have to draw to scale. Clearly show what happens on this supply curve when the price falls from $18 to $15. Label all appropriate points, as well as numerical values for prices and quantities. Include arrows to clarify.
Demand: QD = 100 - 2p Supply: QS = 3p If government imposes a 10% ad...
Demand: QD = 100 - 2p Supply: QS = 3p If government imposes a 10% ad valorem tax to be collected from sellers, what is the price consumers will pay? How much tax revenue is collected?
The demand and supply for a product is given by: Qd: 300-5P Qs: 3P-100 Suppose the...
The demand and supply for a product is given by: Qd: 300-5P Qs: 3P-100 Suppose the government imposes a tax T=$16 Calculate: A) Consumer surplus after tax B) Producer surplus after the tax C) Government Revenue D) Deadweight Loss
demand curve: QD=50-3P supply curve: QS=35+2P a)what is the equilibrium price and quantity? b) What is...
demand curve: QD=50-3P supply curve: QS=35+2P a)what is the equilibrium price and quantity? b) What is the price elasticity of supply at equilibrium? Is the price elasticity of supply elastic, inelastic or unit elastic? explain c) what is the price elasticity of demand at equilibrium Is the price elasticity of supply elastic, inelastic or unit elastic? explain d)If a 20 percent increase in income leads to a 5 percent decrease in the demand for a good, the income elasticity of...
Demand: Qd=90-4P, where Qd is quantity demanded and P is price Supply: Qs=-100+15P, where Qs is...
Demand: Qd=90-4P, where Qd is quantity demanded and P is price Supply: Qs=-100+15P, where Qs is quantity supplied and P is price Recall that equilibrium price was 19, while quantity was 50. At that price, the price elasticity of demand was -0.80. Now I want you to rearrange each equation, putting P on the left-hand side, and solve again for equilibrium P and Q (you ought to get the same answer). Now we want to figure the monopoly price. Take...
The supply and demand for organic peanut butter are QD = 70 – 5P and QS...
The supply and demand for organic peanut butter are QD = 70 – 5P and QS = 5P, where P is price per jar and Q is in hundreds of jars per day. The government has two pieces of legislation up for debate: a $1 supply subsidy or a price floor equal to $7.50. Defend your answers with math and economic logic! No defense means no credit. A) Which law would be more efficient (i.e. result in less deadweight loss)?...
Demand Equation: QD = 250 − 5P Supply Equation: QS = 10 + 3P
  Demand Equation: QD = 250 − 5P Supply Equation: QS = 10 + 3P 1. When P = 5, what is the elasticity of supply? 2. What is The equilibrium price? 3. At the equilibrium price (from Question 2), what is the Consumer Surplus equal to? 4. Suppose the government imposes a tax of of $8 per unit sold of the good. How much of the tax does the consumer pay (per unit)?
13-4) Demand is given by QD = 800 - 3P, and supply is given by QS...
13-4) Demand is given by QD = 800 - 3P, and supply is given by QS = -400 + 7P.             A) Find the equilibrium price and quantity.        (5 points)                                             B) Compute the price elasticity of demand and the price elasticity of supply at the equilibrium. (6 points)             C) In a diagram, show the consumer and producer surplus at the equilibrium. Explain these surpluses. (6 points)
Consider a perfectly competitive market with demand and supply Qd = 1550 – 3P and Qs...
Consider a perfectly competitive market with demand and supply Qd = 1550 – 3P and Qs = -50+5P The firm’s costs are described by the equations TC = 2500 – 5q +q2 and MC = -5 + 2q a. Find the equilibrium price and quantity in the market. b. Find the profit maximizing quantity for the firm. c. Find the firm’s profit. d. How many identical firms are in this market in the short run? Now consider the long-run where...
Market demand is given as Qd = 200 – 3P. Market supply is given as Qs...
Market demand is given as Qd = 200 – 3P. Market supply is given as Qs = 2P + 100. In a perfectly competitive equilibrium, what will be price and quantity? Price will be $20 and quantity will be 140. Price will be $50 and quantity will be 260. Price will be $100 and quantity will be 300. Price will be $140 and quantity will be 380.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT