Question

Question 4

Consider the market for potatoes. You can assume perfect competition.

It is known that the market equilibrium price is $3 per kg and the market equilibrium quantity is 100,000 kg. It is known that when the price is $3 price elasticity of demand is 0.4 and price elasticity of supply is 1.1.   Assume that initially the market for potatoes is in equilibrium.

1. Draw a diagram with (downward-sloping) demand and (upward-sloping) supply schedules. Indicate the market equilibrium, consumer surplus, producer surplus and the dead-weight loss. (Remember the relation between elasticity and the absolute slope of the demand and supply schedules. You do not have to be precise, just make sure it is clear which schedule is steeper).

You answer.

2. If the price increases by 5% what would be the percentage change of quantity demanded? What would be the new quantity demanded? If the price increases from $3 to $3.03 what would be the new quantity producers would be willing to supply?

You answer.

3. The government decides to introduce a 10% tax on the price of potatoes. How would such a decision affect the equilibrium price (paid by consumers) and the equilibrium quantity? Explain using a clearly labelled graph. (Note that you are not required to calculate anything in this question.)

You answer.

4. What would happen to consumer surplus, producer surplus, government revenue and the dead-weight loss when the 10% tax on the price of potatoes is implemented. Explain.   Show the new consumer surplus, producer surplus, government revenue and the dead-weight loss on the graph in part c). Who bears higher tax burden, consumers or producers? Explain.

You answer.

Answer 1

Sol :

a) Equilibrium Price is $3

    Equilibrium Quantity is 100000 kg

Equilibrium is the point where Quantity is equal to the supply of the commodity

and , there will be no deadweigh loss in the equilibrium point because there is no loss of trade .

So,

a2) If the price increases by 5% and Elasticty of demand is 0.4 then % change in quantity demanded will be as follows :

(i) ED = % change in Quantity Demanded / % change in prices

    0.4 = % change in Quantity Demanded / 5

0.4 x 5 = % change in Quantity Demanded

2% = change in Quantity Demanded

(ii) New Quantity demanded is = Old Quantity + change in Quantity demand

             Old quantity = 100000 kg

            Change = 100000 x 2% = 2000 (decreases )

New Quantity = 100000 - 2000 = 98000 kg

(iii) Price increases from $3 to $3.03

ES = Change in Quantity Supplied / Change in prices

     = (∆Q/∆P) x ( P/Q)

     = (∆Q/0.03) x (3/100000)

(1.1 x 100000) / 3 = (∆Q/0.03)

(110000/3) x 0.03 = ∆Q

1100 = ∆Q

∆Q = New Quantity - Old Quantity

1100 + 100000 = New Quamtity

101100 = New Quantity ( supplier wants to supply )

(a3) Tax by 10 % [ $3 x 10 % = 0.3] .

    New Price will be = $3.3

So, increase in taxes will increase the equilibrium prices and decreases the quantity sold or demanded

a4) Consumer Surplus will be decreases because of paying higher prices for the same amount of goods as consumer surplus is difference between (the price willing to pay - Price paid by him)

    Producer Surplus will also decreases than before because producer is recieving less prices for the goods than before.

Government Revenue will be increases by the amount of taxes (i.e by 10%)

Revenue = Taxes x Quantity sold

Deadweigh loss is the loss of trade because of taxes . it is also increases .

(ii) Burdern of taxes will fall heavily on that market side which is leass elastic .

So , elasticity of demand = 0.4

Elasticty of Supply = 1.1

So, consumer will have to bear the large burden of taxes.