A monopolist faces a demand curve Q = 120 - 2p and has costs given by C(Q) = 20Q + 100
a. Write the monopolist's profits in terms of the price it charges.
b. Use the derivative (w.r.t. price) to determine the monopolist's profit-maximizing price.
c. Now, derive the monopolist's inverse demand based on the demand equation above. Write out the monopolist's profits in terms of quantity.
d. Use the derivative w.r.t. Q to determine the monopolist's optimal quantity. What price does the monopoly charge?
a. (p) = (120 - 2p)p - 20(120 - 2p) - 100
b. d/dp = 120 - 4p + 40 = 0 p* = 40
c. p = 60 - .5Q
Pi(Q) = (60 - .5Q)Q - 20Q - 100
d. dPi/dQ = 60 - Q - 20 = 0 Q = 40 and p = 120 - 2(40 ) = 40. The answer is the same whether deriving the optimality condition based on price or quantity.
You might also like to view...
Refer to the figure above. The market price of Good Y is ________
A) $10 B) $17 C) $22 D) $20
Negative income taxes have been a feature of our tax system since President Lyndon Johnson's "war on poverty" in the 1960s
Indicate whether the statement is true or false
A nonbinding price floor (i) causes a surplus. (ii) causes a shortage. (iii) is set at a price above the equilibrium price. (iv) is set at a price below the equilibrium price
a. (iii) only b. (iv) only c. (i) and (iii) only d. (ii) and (iv) only
Refer to the diagrams, which pertain to monopolistically competitive firms. Short-run equilibrium entailing economic loss is shown by:
A. diagram a only.
B. diagram b only.
C. diagram c only.
D. both diagrams a and c.