Show that for a monopolist with a constant marginal cost and facing a

Show that for a monopolist with a constant marginal cost and facing a linear demand curve, if a specific tax is imposed on the monopolist, the tax burden is shared equally between the monopolist and the consumers.

What will be an ideal response?

ANSWER

A monopolist facing demand p = a – bQ and marginal cost c chooses a price and quantity:
p = (a + c)/2
With a tax of t, the monopolist’s costs are essentially c + t, making the price:
p = (a + c)/2 + t/2
The price will rise by half of the tax.