A monopolist produces a single good X but sells it in two separate markets. The demand function for each market is ?1 = 50 − 4x1 and ?2 = 80 − 3x2 where ?1 and x1, ?2 and x2, are the price and quantity in market 1 and 2, respectively. The cost function is ?? = 120 + 8x1 + 8x2. (a) Find the total revenue for the firm in terms of x1 and x2. (b) Find the profit function in terms of x1 and x2. (c) Write down the first and second order partial derivatives, using the function in (b)
A monopolist produces a single good X but sells it in two separate markets. The demand function for each market is ?1 = 50 − 4x1 and ?2 = 80 − 3x2 where ?1 and x1, ?2 and x2, are the price and quantity in market 1 and 2, respectively. The cost function is ?? = 120 + 8x1 + 8x2. (a) Find the total revenue for the firm in terms of x1 and x2. (b) Find the profit function in terms of x1 and x2. (c) Write down the first and second order partial derivatives, using the function in (b)
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.9P
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A monopolist produces a single good X but sells it in two separate markets. The demand
function for each market is
?1 = 50 − 4x1 and ?2 = 80 − 3x2
where ?1 and x1, ?2 and x2, are the price and quantity in market 1 and 2, respectively.
The cost function is ?? = 120 + 8x1 + 8x2.
(a) Find the total revenue for the firm in terms of x1 and x2.
(b) Find the profit function in terms of x1 and x2.
(c) Write down the first and second order partial derivatives, using the function in (b)
(d) Solve the system of equations
Derivative of pi/ derivative of x1= 0 and Derivative of pi/ derivative of x2= 0
(e) Show that the point (x1,x2) is a maximum.
(f) Find the maximum profit.
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