A competitive firm's production function is f(x₁, x₂) = 12x^1/2₁ + 4x^1/2₂.The price of factor 1 is $1 and the price of factor 2 is $2.The price of output is $4.What is the profit-maximizing quantity of output?

A) 304
B) 608
C) 300
D) 612
E) 292

Question

Larry Westall · Accepted Answer

Final Answer : A, Explanation :  The profit-maximizing quantity of output is found by solving the following equation:MR = MCwhere MR is the marginal revenue and MC is the marginal cost.The marginal revenue is equal to the price of output, which is $4.The marginal cost is equal to the change in total cost divided by the change in output.The total cost is equal to the sum of the costs of the two factors of production:TC = w 1 x 1  + w 2 x 2 where w 1  is the price of factor 1, w 2  is the price of factor 2, x 1  is the quantity of factor 1, and x 2  is the quantity of factor 2.The change in total cost is equal to the change in the cost of factor 1 plus the change in the cost of factor 2:ΔTC = w 1 Δx 1  + w 2 Δx 2 The change in output is equal to the change in the quantity of factor 1 plus the change in the quantity of factor 2:ΔQ = Δx 1  + Δx 2 Therefore, the marginal cost is equal to:MC = ΔTC/ΔQ = w 1  + w 2 Substituting the given values into the above equations, we get:MR = $4MC = $1 + $2 = $3Setting MR equal to MC, we get:$4 = $3This equation is not true, which means that the profit-maximizing quantity of output is not feasible.

A competitive firm's production function is f(x₁, x₂) = 12x^1/2₁ + 4x^1/2₂.The price of factor 1 is $1 and the price of factor 2 is $2.The price of output is $4.What is the profit-maximizing quantity of output?

A) 304
B) 608
C) 300
D) 612
E) 292

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Learning Objectives

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A competitive firm's production function is f(x1, x2) = 12x1/21 + 4x1/22.The price of factor 1 is $1 and the price of factor 2 is $2.The price of output is $4.What is the profit-maximizing quantity of output?A) 304B) 608C) 300D) 612E) 292

Definitions

Learning Objectives

Learning Objectives

Related questions

A competitive firm's production function is f(x₁, x₂) = 12x^1/2₁ + 4x^1/2₂.The price of factor 1 is $1 and the price of factor 2 is $2.The price of output is $4.What is the profit-maximizing quantity of output?

A) 304
B) 608
C) 300
D) 612
E) 292