Types of Subsidy on Monopoly (With Effects) | Microeconomics

A subsidy is a fiscal hand-out paid to certain sections of society at the cost of the tax pair. While a unit tax or an ad valorem (percentage) tax has the effect of raising the price of a commodity above the market clearing level a subsidy (being a negative tax) has exactly the opposite effect.

It reduces the price of a commodity below true cost. Now we may consider the effects of four different types of subsidy on monopoly price and output. The effects are exactly the opposite to those of a tax.

1. Subsidy of a Fixed Amount:

Let us first consider the effect of a lump-sum subsidy, i.e., subsidy which is of a fixed amount such as Rs. 1,000 irrespective of the level of output. This will increase the profit after subsidy of a profit-maximising monopolist, but will not effect his optimum price- quantity combination. In his case profit becomes;

π = R (Q) – C (Q) + S … … (1)

where S is the amount of the lump-sum subsidy and π is its profit after receiving subsidy Setting the derivative of (1) equal to zero, we get;

dπ/dQ = R’(Q) – C'(Q) = 0

or R’ (Q) = C’ (Q)

Since S is a constant, it disappears upon differentiation and the monopolist’s output level and price are determined by the equality of MR and MC as would be the case if no subsidy were given.

2. Unit Subsidy:

If a specific subsidy of 5 rupees per unit of output is paid the profit function becomes:

π = R (Q) – C (Q) + sQ

or = dπ/dQ = R’(Q) – C'(Q) + s = 0

or R’ (Q) = C’ (Q) – s .… (2)

The monopolist maximises profit after receiving the subsidy by equating MR with MC minus the per unit subsidy.

Taking total differential of (2) we get:

R” (Q) dQ = C” (Q) dQ – ds

or dQ/ds = – [1/R”(Q) – C”(Q)]

since R”(Q) – C”(Q) < 0 by the second-order condition dQ/ds > 0. So the optimum output level (Q) increases when a specific subsidy at the rate of s per unit reduced is provided to the monopolist. In order to sell more the monopolist has to reduce his price.

3. Subsidy as a Fixed Percentage (Constant Proportion) of the Price of Each Unit Produced:

Here the demand function is: 

P = D (Q)

and the total revenue function is;

R = QD (Q) = R (Q)

Let s be the rate of subsidy. Then the post-subsidy price = P + sP = (1 + s) D (Q)

Therefore post-subsidy revenue = P’Q = (1 + s) D (Q).Q

The profit function is;

π = (1 + s) D (Q). Q – C (Q)

= (1 + s). R (Q) – C (Q)

Dπ/dQ = (1 + S) R’ (Q) – C (Q) = 0

= (1 + s). MR = C’ (Q)

So MR rises because of subsidy. This means that the MR curve will become flatter. This is possible if and only if the demand curve becomes flatter. As a result equilibrium quantity and price will both rise.

4. Subsidy Per Unit Increasing with Increase in Output Level:

In this case subsidy per unit is a function of output or s = s (Q). So the profit function is;

π = [1 + s (q)]. D (Q). Q – C (Q)

Since the second term on the right hand side is positive MR after subsidy will be less than the original MC. This means that MR will fall due to subsidy. This happens in a monopoly situation when Q increases and P falls. So in this case, as in case (b), the effect of subsidy is to increase equilibrium quantity and reduce equilibrium price.