A firm in a perfectly competitive market has the long run marginal cost shown below. Its minimum LRAC is Rs 32. The government imposes a unit tax of Rs 4, and the market price stays at Rs 40.
| Output (units) | 40 | 50 | 60 | 70 |
|---|---|---|---|---|
| LRMC before the tax (Rs) | 30 | 36 | 40 | 46 |
How much does the firm produce in the long run before and after the tax?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 60 units before and 50 units after
In the long run the firm produces where price = LRMC, as long as price is not below the minimum LRAC. A unit tax of Rs t raises both LRMC and LRAC by Rs t at every output.
Given:
Price = Rs 40
Unit tax = Rs 4
Minimum LRAC before the tax = Rs 32
Before the tax: LRMC = 40 at 60 units, and 40 is above the minimum LRAC of 32.
After the tax:
\( LRMC + 4 = 40 \)
\( LRMC = 36 \)
The old LRMC is 36 at 50 units. The new minimum LRAC is 32 + 4 = 36, still below the price of 40, so the firm keeps producing.
The tax shifts the firm’s supply curve to the left: at the same price it supplies fewer units.
NCERT (2026-27): “4.5.2 Input Prices … Now, suppose the government puts in place a unit tax of Rs t. Since the firm must pay an extra Rs t for each unit of the good produced, the firm’s long run average cost and long run marginal cost at any level of output increases by Rs t. …” “… Recall that the long run supply curve of a firm is the rising part of the LRMC curve from and above the minimum LRAC together with zero output for all prices less than the minimum LRAC. Using this observation in Figure 4.12, it is immediate that S0 and S1 are, respectively, the long run supply curve of the firm before and after the imposition of the unit tax. Notice that the unit tax shifts the firm’s long run supply curve to the left: at any given market price, the firm now supplies fewer units of output.” |