A monopolist w11ishes to maximize total revenue. She produces two outputs, (x1, x2) and faces the following demands for her products, X1 = 20 – 2p1, and X2 = 20 – 4p2 Where p1 and p2 are, respectively, the prices of the two goods. To produce one unit of x1 the monopolist must use one unit of land and one unit of capital. And, to produce one unit of x2 requires two units of land and one unit of capital. The firm has available 10 units of land and 6 units of capital. Specify the firm’s short-run maximization problem. Set up the Kuhn-Tucker conditions for maximization (you do not need to solve). Assume that the solution is x*1 = 5 1/3 (i.e. 16/3) and x*2 = 2/3. Explain which constraints are binding and whether the Lagrange multipliers are positive or zero and what they mean.
A monopolist w11ishes to maximize total revenue. She produces two outputs, (x1, x2) and faces the following demands for her products, X1 = 20 – 2p1, and X2 = 20 – 4p2 Where p1 and p2 are, respectively, the prices of the two goods. To produce one unit of x1 the monopolist must use one unit of land and one unit of capital. And, to produce one unit of x2 requires two units of land and one unit of capital. The firm has available 10 units of land and 6 units of capital. Specify the firm’s short-run maximization problem. Set up the Kuhn-Tucker conditions for maximization (you do not need to solve). Assume that the solution is x*1 = 5 1/3 (i.e. 16/3) and x*2 = 2/3. Explain which constraints are binding and whether the Lagrange multipliers are positive or zero and what they mean.
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.2P
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- A monopolist w11ishes to maximize total revenue. She produces two outputs, (x1, x2) and faces the following demands for her products,
X1 = 20 – 2p1, and
X2 = 20 – 4p2
Where p1 and p2 are, respectively, the prices of the two goods.
To produce one unit of x1 the monopolist must use one unit of land and one unit of capital. And, to produce one unit of x2 requires two units of land and one unit of capital. The firm has available 10 units of land and 6 units of capital.
- Specify the firm’s short-run maximization problem.
- Set up the Kuhn-Tucker conditions for maximization (you do not need to solve).
- Assume that the solution is x*1 = 5 1/3 (i.e. 16/3) and x*2 = 2/3. Explain which constraints are binding and whether the Lagrange multipliers are positive or zero and what they mean.
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