(a) The profit-maximizing quantity of a monopolist facing a downward-sloping demand curve must be produced at a point where the demand is elastic (meaning the demand elasticity with respect to price e< -1)

(a) The profit-maximizing quantity of a monopolist facing a downward-sloping demand curve must be produced at a point where the demand is elastic meaning the demand elasticity with respect to price ( e< -1) - this statement is true because monopoly is only able to maximize profit by producing a quantity of output that falls in the elastic range of the demand curve. A monopoly cannot maximise profit in the inelastic range of demand because this involves negative marginal revenue and by virtue of the profit maximising equality between marginal revenue and marginal cost, it requires negative marginal cost which is just not a realistic possibility. So the statement is true.

(b) The profit - maximising output and price of a monopolist occur at output level at which it's marginal revenue is equal to it's marginal cost.

Therefore, MR = P + Q * dP/dQ Or, MR = P + P * Q/P * dP/dQ it can be calculated using the following equation, E_d = P/Q * dQ/dP taking inverse of the above equation and we get, 1/E_d = Q/P * dP/dQ therefore, MR = P + P * 1/E_d since, monopoly profit - maximising occurs when MR = MC we can write, MR = P + P * 1/E_d = MC or, P ( 1 + 1/E_d ) = MC or, P = MC / (1 + 1/E_d) the above formula can be used directly to determine a monopoly profit maximising price.

So, Market 1’s price elasticity of demand is e₁ = −2. Market 2’s price elasticity of demand is e₂ = −4. Assume that the monopolist has a constant marginal cost of 10. So, we can put the values in the above equation and then we get the prices.

Therefore, P = 10/ 1 + 1/(-2) for the market 1. Or, P = 10/ 1 - 1/2 Or, P = 10/ (2-1)/2 Or, P = 10/1/2 or, P = 10 * 2/1 = 20   

So the market 1's price will be 20

Therefore, P = 10/ 1+(-4) or, P = 10/1- 1/4 or, P = 10/(4-1)/4 or, P = 10/ (3/4) or, P = 10*4/3 = 40/3 = 13.33

This is for the market 2's price .

So the market 1's and 2's price will be 20 , 13.33.