In Problem 12, Al's production function for deer is f(x₁, x₂) , where x₁ is the amount of plastic and x₂ is the amount of wood used. If the cost of plastic is $4 per unit and the cost of wood is $4 per unit, then the cost of producing 8 deer is A) $16. B) $96. C) $256. D) $128. E) $32.

Question

Quizplus · Accepted Answer

To find the cost of producing 8 deer, we first need to find the amounts of plastic and wood needed to produce 8 deer. Since the production function is given as f(x₁, x₂) = 11ea6c55_6e79_1427_9875_bf171d0ad572_TB6162_11, we can assume that Al's production function exhibits constant returns to scale, which means that if we increase the inputs by a constant factor, the output will also increase by the same constant factor. Therefore, if Al needs x₁ plastic and x₂ wood to produce one deer, he will need 8 times as much to produce 8 deer. Substituting the values into the production function, we get: f(8x₁, 8x₂) = 11ea6c55_6e79_1427_9875_bf171d0ad572_TB6162_11 Now, let's assume that the cost of producing one unit of plastic or wood is $4. Therefore, the cost of producing x₁ plastic and x₂ wood will be: Cost = 4(x₁ + x₂) The cost of producing 8 deer will then be: Cost = 4(8x₁ + 8x₂) = 32(x₁ + x₂) Substituting this back into the production function equation, we have: f(x₁, x₂) = 11ea6c55_6e79_1427_9875_bf171d0ad572_TB6162_11 Multiplying both sides by 32, we get: 32f(x₁, x₂) = 32(11ea6c55_6e79_1427_9875_bf171d0ad572_TB6162_11) Substituting back the cost equation and simplifying, we get: Cost = 32f(x₁, x₂) Therefore, the cost of producing 8 deer will be 32 times the value of the production function with the given inputs. Since the value of the production function is not given, we cannot calculate the cost exactly. However, we know that the answer will be a multiple of 32. The only option that satisfies this condition is D) $128.

In Problem 12, Al's Production Function for Deer Is F(x1

In Problem 12, Al's Production Function for Deer Is F(x₁