Question

You have realized that the number of plants, y, that you can grow in your garden, depends on the amount of fertilizer, f, and water, h. 1In fact, you have noticed that your plants need twice as much fertilizer as water, and using any other ratio leads to input being wasted. Suppose that each unit of fertilizer costs w1 and each unit of water costs w2. What might be your production function? (There is more than one possible answer given the prompt, pick your favorite.)

Answer 1

The production function for the number of plants in the garden depends on the amount of fertilizer and water, with each unit of fertilizer costing twice as much as water. The total cost can be calculated using the production function and the cost of inputs.

Step-by-step explanation:

The production function for the number of plants, y, that can be grown in the garden, depends on the amount of fertilizer, f, and water, h. Since the plants need twice as much fertilizer as water, the production function can be expressed as y = 2f. The cost of fertilizer is w1 and the cost of water is w2, so the total cost can be calculated using the production function and the cost of inputs: Cost = w1 * f + w2 * (f/2).

For example, if each unit of fertilizer costs $10 and each unit of water costs $5, and you want to grow 10 plants, the production function becomes y = 20. The total cost would be Cost = $10 * 10 + $5 * (10/2) = $100 + $25 = $125.