Final answer:
To calculate the highest level of profit, examine the profit curve in the graph and find the quantity of output at which the total revenue exceeds the total cost by the largest amount. The firm makes losses at low output levels, earns profits at moderate output levels, and incurs increasing losses at high output levels. The maximum profit occurs at an output between 70 and 80, where the profit equals $90.
Step-by-step explanation:
To calculate the highest level of profit for this problem, we need to find the quantity of output at which the total revenue exceeds the total cost by the largest amount. This will give us the maximum profit. We can determine this by examining the profit curve in the graph. The vertical gap between total revenue and total cost represents the profit, and the height of the profit curve at a particular output level indicates the amount of profit. The firm does not make a profit at every level of output; it makes losses from output levels 0 to around 30, earns profits from output levels 40 to 100, and then incurs increasing losses from output levels greater than 100. The maximum profit occurs at an output between 70 and 80, where the profit equals $90.
Profit is calculated by subtracting total cost from total revenue, and graphing this against the number of units produces the profit curve. The maximum profit, break-even points, fixed costs, and the scales on both axes must be clearly identified on the graph.
The profit function for a firm can be calculated by subtracting the total cost from the total revenue. Given the revenue function R(x) = 20x and the total cost function C(x) = 2x2 + 4x + 24, the profit function P(x) can be found by P(x) = R(x) - C(x). This quadratic function will generate a parabola when graphed, and its shape will indicate the break-even points (where the profit is zero), the maximum profit (the vertex of the parabola), and the behaviour of profit as the number of units x varies.
For the given example of a quantity of 40 units where the price is $16 and the average cost is $14.50, the firm's total revenue and cost can be visually represented in a graph as rectangles, where the height of the revenue rectangle exceeds the height of the cost rectangle, indicating economic profit. The graph also highlights the fixed costs, which are costs that do not vary with the quantity of output produced, such as the $24 in the total cost function, which is the y-intercept of the total cost curve.
To graph profit against the number of units, one needs to calculate P(x) for various values of x and plot these points on a coordinate axis, where x represents the number of units produced and sold (horizontal axis) and P(x) represents profit (vertical axis). The characteristics of the profit graph, including the maximum profit point and the break-even points, should be labeled accordingly, and the axes should be appropriately scaled to reflect the actual values of x and P(x).