The inverse demand equation for a monopoly firm is P = 60 - 0.015Q.The monopolist faces constant costs of production in the long run with LAC = LMC = $30.At the profit-maximizing price,the elasticity of demand is ________,which is __________ (elastic,inelastic,unit elastic)as expected.

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To find the profit-maximizing quantity and price, we first equate MR (Marginal Revenue) to MC (Marginal Cost). The inverse demand equation is P = 60 - 0.015Q. To find MR, we double the slope of the demand curve: MR = 60 - 0.03Q. Setting MR equal to MC (which is $30), we get 60 - 0.03Q = 30, solving for Q gives Q = 1000. Substituting Q = 1000 into the demand equation gives P = 60 - 0.015(1000) = 45. To find the elasticity of demand at this point, we use the formula E = (dQ/dP) * (P/Q). The derivative of the demand function with respect to Q (dQ/dP) is the inverse of the slope of the demand curve, which is -1/0.015 = -66.67. Therefore, E = (-66.67) * (45/1000) = -3.0, indicating that the demand is elastic at the profit-maximizing quantity and price.

The Inverse Demand Equation for a Monopoly Firm Is P