Final answer:
To find where marginal product is greatest, we need information on input and output quantities, not just cost data. Costs help assess profitability but don't directly reveal maximal marginal product. Marginal product is typically highest where marginal cost begins to increase sharply, indicative of declining productivity.
Step-by-step explanation:
To find the level of output where the marginal product is the greatest, we need to understand the relationship between marginal cost (MC), average variable cost (AVC), and marginal product (MP). While the provided information about total cost, average total cost, and average variable cost is important for understanding profitability, it does not directly indicate the level of output at which marginal product is maximized. Marginal product is maximized at the point where it begins to decrease, which typically coincides with the point where marginal cost starts to increase at an increasing rate. Nevertheless, given the provided steps, we could infer that if the market price is greater than the average variable cost at the output level where MC equals marginal revenue (MR), the firm might be operating near the level where MP is greatest, because it would indicate the firm is in a profitable zone, possibly near the efficient scale of production. However, to pinpoint the exact level of output where marginal product is greatest, one would require data on physical output per additional unit of input, not just the costs associated with output levels. Without information on physical quantities of input and output, determining where the marginal product is highest from cost data alone is not feasible.