This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
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a) Step 1: Identify the condition for profit maximization. A firm maximizes profit where marginal cost (MC) equals marginal revenue (MR) and the MC curve is rising (or cuts the MR curve from below).
Step 2: Analyze output level 40. At an output level of 40 units, the marginal cost (MC) curve intersects the marginal revenue (MR) curve. However, at this point, the MC curve is still falling. This means that for units immediately beyond 40, MR is greater than MC, indicating that producing more units would add more to revenue than to cost, thereby increasing total profit. Therefore, output level 40 is not the profit-maximizing level.
b) Step 1: Analyze the relationship between MR and MC beyond 90 units. The graph shows that the AR = MR line is constant at $80. At 90 units, the MC curve is below the MR curve (MC < MR). As output increases beyond 90 units, the MC curve starts to rise but remains below the MR curve for a range of output.
Step 2: Determine the production decision. Since MR > MC for output levels beyond 90 units up to the point where MC equals MR on the rising portion of the MC curve, each additional unit produced in this range adds more to total revenue than to total cost. This increases the firm's total profit. Therefore, the firm should produce beyond 90 units to reach the profit-maximizing output level.
c) i) Step 1: Identify the profit-maximizing condition on the graph. Profit maximization occurs where the marginal cost (MC) curve intersects the marginal revenue (MR) curve from below, meaning MC is rising at the point of intersection.
Step 2: Determine the output level and reason. From the graph, the AR = MR line is at $80. The MC curve intersects this line at two points. The first intersection is at 40 units where MC is falling. The second intersection, where MC is rising, occurs at an output level of 150 units. At this point, MR = MC, and the MC curve is rising, indicating the profit-maximizing output.
ii) Step 1: Analyze the revenue curves. The graph shows that the Average Revenue (AR) curve is equal to the Marginal Revenue (MR) curve, and both are represented by a horizontal line at a constant price of $80.
Step 2: Determine the market structure. A horizontal AR = MR curve indicates that the firm is a price taker and faces a perfectly elastic demand curve. This is characteristic of a perfectly competitive market, where individual firms have no control over the market price.
d) Step 1: Identify the equilibrium output level and price. The equilibrium (profit-maximizing) output level is 150 units (from c(i)). At this output, the price (P) is equal to AR = MR = $80.
Step 2: Calculate Total Revenue (TR).
Step 3: Determine Total Cost (TC) at equilibrium. At the profit-maximizing output of 150 units, observe the Average Total Cost (ATC) curve, labeled 'A' on the graph. At 150 units, the ATC curve also appears to be at 80. $$ TC = ATC \times Quantity $$ $$ TC = \80 \times 150 units = $12,000 $$
Step 4: Calculate profit or loss. At the equilibrium output level, the firm earns zero economic profit, which means it is breaking even or earning a normal profit. This occurs because the price (80) at the profit-maximizing output.
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This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.