Question

1. Use of a demand/supply diagram to analyze the market for energy - calculating the equilibrium quantities and prices - with taxes and with subsidies.

Answer 1

Equilibrium in case of  A Sales Tax:

A sales tax is a value based tax. It is imposed as a fixed percentage of the price of a commodity.

Lets assume the Amount of Tax be T.

Thus, we derive other equations as-

The Amount of Tax (t) = Demand price of the buyers ? Supply price of the sellers … (i)

the Demand price = Supply price + t … (ii)

And , the Supply price = Demand price -1 … (iii)

Here, t is a variable, Let it is assumed as 20 per cent.

At this point, at q = q0, the demand price and supply price are equal, and are equal to p0.

In order to impose the new post-tax equilibrium quantity, move from the point E downward to left along the SS curve. Consequently, the vertical gap between the demand price and the supply price will increase eventually, if we stop at a point C, where the vertical gap between the DD and SS curves has been 20% of the supply price (p2).

At Point C,q = q1, where the market would be in equilibrium after the tax imposition. Here the sellers would get the price p2, they would add the sales tax of 20% of p2 (lets say, which is = AC) to this price and would ask the buyer to pay the price p1. At the p1, the buyers would demand q1 of output and at the price of p2, the sellers would sell the same output (q1), and so the market would be in equilibrium.

The impact of the imposition of a sales tax upon the market equilibrium is explained on the basis of (ii), and with the help of Fig. 1.19(b). Here DD and SS are referred as the demand curves and supply curves for the goods.

Initially, we see that the equilibrium point is E (p0, q0). According to (ii), if a sales tax of 20 per cent is imposed, then at the post-tax equilibrium q, demand price would be = supply price + a tax of 20 per cent of the supply price.That is why, the S1S1 curve is drawn which gives us at any q, the supply price along the SS curve plus 20 per cent of the sales tax. Since, as q and the supply price increases, the amount of the tax will also increased,thus leading to the increase in the vertical gap between the S1S1 and SS curves.

Now, the post-tax equilibrium output, q1, would be obtained at the point of intersection, A, of the DD and S1S1 curves. At this output, as per (ii), the demand price would be equal to the supply price plus the sales tax. Here the buyer would pay a price of p1 (inclusion of the tax) and demand q1 of output and the sellers would obtain the price of p2 and supply the same output. So the market would again be in a demand-supply equilibrium.

The demand-supply analysis in a third way to explain the effects of the imposition of a sales tax is also applied on the basis of (iii) and with the help of Fig. 1.19(c). Here as before, the DD and SS curves are the demand and supply curves of the good, and the pre-tax equilibrium point is E (p0, q0).

According to diagram (iii), if the sales tax is imposed, then at the post-tax equilibrium q, the supply price would be the demand price MINUS the amount of tax. That is why, in Fig. 1.19(c), a D1D1 curve is drawn which gives, at any q, the demand price - the sales tax of the supply price. Since as q and the supply price increase, the amount of the tax also increases, and the vertical gap between the DD and D1D1 curves will increase.

Now, the post-tax equilibrium output, q1, would be obtained at the point of intersection, C, of the D1D1 and the SS curves. At this output, according to (iii), the supply price (p2) would be equal to the demand price (p1) less the amount of the tax. Since at the price of p1, the buyers would demand q, of output and at the price of p2, the sellers would supply the same output, the market would again be in equilibrium.

The demand-supply equilibrium analysis can be applied to obtain the impact of a sales tax upon the equilibrium quantity bought and sold of the commod­ity concerned. It is presented in three ways of explaining the effect of the tax.

As is expected, the effects have been the same in all the three cases. A comparison between the pre­tax and post-tax equilibrium situations would take us to the same conclusions as it is ob­tained in the case of a per unit excise tax.

Equilibrium of Quantity and Prices with regards to the Subsidy in Production.

In order to boost up the demand of a Commodity a subsidy is granted by the Government. It is collected by the producer of the commodity who charges the buyer a price which is lower than the supply price by the amount of subsidy.

Lets, Suppose, a per unit subsidy of a fixed amount, be as S.

Thus,

Subsidy (S) = Price of Supply– price of Demand … (i)

or, The price of Supply = price of Demand + S … (ii)

or, price Of Demand = price of Supply – S … (iii)

In diag. 1.20, DD and SS are the demand and supply curves for the commodity respectively, and the initial equilibrium point is E (p0, q0).

However, after the grant of the subsidy, the equilibrium quantity would be where demand price would be smaller than the supply price by the amount of subsidy(S)

i.e. Where demand price < supply price

That is why, in order to find this equilibrium quantity, we move along the DD curve from the point E downward towards right till the vertical gap between the SS and the DD curves becomes = S.

Therefore, the equilibrium quantity after subsidy would be one like (q1)at which the vertical gap is AC = S.

At q = q1, the sellers would get the price of p2 and the buyers would pay the price of p1, p2 – p1 being equal to S. At the price of p1, the buyers would demand the quantity q, and at the price of p2, the sellers would sell the same quantity. So the market would be in equilibrium at where (q = q1).

Comparing post subsidy effect by the Pre ssidy effect, We find that -

(a) After the grant of sub­sidy, equilibrium q has increased from (q0 to q1) whereas in the case of per unit excise tax, q has decreased from (q0 to q1).

(b) The equilibrium price for the buyers is p1 which is < the equilibrium price of the sellers by the per unit subsidy(S). But in the case of a per unit tax the buyers’ equilibrium price is > the sellers’ price.

(c) Although the buyers are getting a subsidy of S per unit, the post-subsidy equilibrium price for them is not less than the pre-subsidy equilibrium price by the amount of the subsidy, AC = S, but by a smaller amount, AB. On the other hand, the sellers are also getting a benefit of price rise—their price rises by BC. It may be noted that AB + BC = AC = S.

(d) In respect of quantity also, both the buyers are sellers are sharing the benefit of subsidy the buyers are buying more and the sellers are also selling more. In the case of the per unit tax or sales tax, the buyers buy less and the sellers also sell less.