Final answer:
To analyze the competitive firm's costs, total variable cost (TVC) equals 4q, and total fixed cost (TFC) is 16. ATC, AVC, and AFC are calculated per unit of output, and in long-run equilibrium, economic profits are zero with price, ATC, and MC all equal at the profit-maximizing output level.
Step-by-step explanation:
Cost Analysis for a Competitive Firm
A competitive firm's cost function is TC(q) = 4q + 16. From this, we can derive the total variable cost (TVC) and total fixed cost (TFC). Since the firm's total cost (TC) includes both variable and fixed costs, and the fixed cost (TFC) does not vary with output, we can surmise that TFC = 16 and TVC = TC - TFC = 4q. Thus, TVC = 4q.
We calculate average total cost (ATC) by dividing the total cost by the quantity produced, which yields ATC = (4q + 16) / q. Simplifying gives us ATC = 4 + 16/q. For average variable cost (AVC), we divide the total variable cost by the quantity produced, which gives AVC = 4q / q = 4. Lastly, average fixed cost (AFC) can be determined by dividing total fixed cost by the quantity, resulting in AFC = 16/q.
Based on the given marginal cost (MC) function MC = 8q, we can graph the ATC, AVC, and MC curves. The ATC and AVC curves are typically U-shaped, while the MC curve is upward-sloping, indicating that marginal costs increase as more units are produced.
In long-run equilibrium for perfectly competitive firms, economic profits tend to be zero because firms enter and exit the industry until price equals the minimum of the ATC curve. This means the price, average total cost, and marginal cost are all equal at the profit-maximizing level of output in the long run: P = ATC = MC.