Answer to Question #214698 in Macroeconomics for Tivi

Question

Suppose a perfectly competitive industry can produce Roman candles at a constant marginal cost of R12 per unit. Once industry is monopolized, marginal costs rise to R16 per unit because R4 per unit must be paid to lobbyists to ensure that only this firm receives a Roman candle license. Suppose the market demand for Roman candles is given by

Q_d=1500-25P

And Marginal revenue curve by

MR= 20-Q/25

Calculate the monopoly price

Answer 1

The perfectly competitive output and price are:

Pd = MC,

P = 40 - 0.04Q,

$40 - 0.04Q = 12,$

Q = 700 units,

$P = 40 - 0.04*700 = 28.$

calculation for the price

Monopoly equilibrium is attained at a point where MR = MC

$P=40-0.04Q$

Multiply this equation for P by Q

$PQ=40Q-0.04^2$

then differentiate with respect to Q

$dPQ/dQ=40-0.08Q=16=TR^{'}(Q)$

In this case $MR = TR'(Q) = 40 - 0.08Q,$$40 - 0.08Q = 16,$

Q = 300 units,

$P = 40 - 0.04*300 = 28.$