U3: Production, Costs, and Elasticities

3.1: The Production Function

Key Terms

● Production function: Relates physical output of a production process to physical input or factors of production.

● Marginal cost: The increase in cost that accompanies a unit increase in output; the partial derivative of the cost function with respect to output; additional cost associated with producing one more unit of output.

● Output: quantity produced, created, or completed.

● Rental rate: The price of capital.

● Marginal product: The extra output from using one or more units of input.

● Capital: Already-produced durable goods available for use as a factor of production, such as steam shovels (equipment) and office buildings (structures).

○ In the short run, economists assume that the level of capital is fixed.

● Labor: The human work that goes into production.

○ Typically economists assume that labor is a variable factor of production.

Key Takeaways

● The production function describes a boundary or frontier representing the limit of output obtainable from each possible combination of inputs.

● Firms use the production function to determine how much output they should produce given the price of a good, and what combination of inputs they should use to produce given the price of capital and labor.

● The production function also gives information about increasing or decreasing returns to scale and the marginal products of labor and capital.

● One consequence of the law of diminishing returns is that producing one more unit of output will eventually cost increasingly more due to inputs being used less effectively.

● The marginal cost curve will initially be downward sloping, representing added efficiency as production increases. If the law of diminishing returns holds, the marginal cost curve will eventually slope upward and continue to rise.

● The marginal product of an input is the amount of output that is gained by using one additional unit of that input. It can be found by taking the derivative of the production function in terms of the relevant input.

3.2 Short-Run Production Costs

Key Terms

● Fixed Costs: costs that don’t change with the amount produced

○ ex. pizza oven for a pizza company or employee salaries

● Variable Costs: Costs that do change with the amount produced

● Total Cost: Total Fixed Costs (TFC) plus Total Variable Costs (TVC)

Marginal Cost

○ Additional cost of one additional output

○ Change in Total Cost (∆ TC) divided by Change in Units of Labor (∆ Qs)

○ Marginal Cost Curve = Supply Curve

○ MC Curves shift whenever a variable cost changes, or a per-unit tax/subsidy is placed on the good. If a variable cost (labor) increases or a per-unit tax is placed on the good, then MC shifts up. If a variable cost decreases (workers get more productive), or a per-unit subsidy is given, then MC shifts down.

○ Fixed costs don’t shift MC, nor do lump-sum taxes/subsidies. Hence, they do not affect the profit-maximizing quantity for the firm.

Average Costs

● Average Fixed Cost: the fixed cost per unit of output

○ Total Fixed Cost (TFC) divided by Units of Labor (Q)

○ Average Total Cost (ATC) subtracted by Average Variable Cost (AVC)

● Average Variable Cost: the variable cost per unit of output

○ Total Variable Cost (TVC) divided by Units of Labor (Q)

○ Average Total Cost (ATC) subtracted by Average Fixed Cost (AFC)

● Average Total Cost:

○ Average Variable Cost (AVC) plus Average Fixed Cost (AFC) 

3.3 Long-Run Production Costs

● In the short-run, at least one cost is held fixed. In the long run, all costs are variable.

● Depending on whether a firm has increasing, constant, or decreasing returns to scale, the output could increase, remain constant, or decrease as inputs increase

○ Returns to scale shows what happens to a firm’s production in the long-run

● Economies of scale means that as (output) production increases, the Long-run Average Total cost (LRATC) falls as more is produced (due to specialization)

○ As production continues and you are supplying more, your fixed costs become more spread out and you’re driving the average down

○ The firm can buy techniques to produce goods with lower cost per item

○ If you double your inputs, your output will more than double

● Constant returns to scale means that the LRATC remains constant as more output is produced

○ The firm is so efficient now that it can’t reach a lower cost per item

● Diseconomies of scale means that the LRATC increases as more output is produced

○ The firm is now too big and it must now pay more due to large numbers of employees or factories which, in turn, pushes the cost per item upwards

3.4 Types of Profit

● Economic profit = profit = π = TR - TC = (P - ATC)Q

○ Includes opportunity cost (non-monetary costs)

○ TC = implicit cost + explicit cost = ATC x Q

● Accounting profit = TR - explicit cost = π - Implicit Costs = revenue

○ (implicit costs = opportunity costs)

3.5 Profit Maximization

● Firms are willing to produce as long as MR ≥ MC up until the last unit produced

○ “Optimal Output Rule” → Firms profit maximize where MR = MC

3.6 Firms’ Short-Run Decisions to Produce and Long-Run Decisions to Enter or Exit a Market

Short Run

● Shutdown rule:

○ In the short run, a firm should produce as long as P ≥ AVC. If a firm’s AVC is higher than the price, they are better off shutting down in the short run and only paying their fixed costs than continuing to produce and paying their fixed and variable costs

○ Total revenue is less than TVC

Long Run

● Exit Rule: Exit in the long-run when π < 0 (when you are incurring losses)

○ Productive Efficiency: they produce the quantity that is the lowest cost (minimum ATC).

○ Allocative Efficiency: they produce the optimal quantity that the society wants (P=MC).

Short-Run vs. Long-Run Production

● From short-run to long-run

○ If the firm is operating in a constant cost industry, then the entry and exit of firms does not change ATC. An example would be if you had unlimited workers, so when a new business opened, it wouldn’t affect the ATC for each firm

○ When firms earn economic profit, there is incentive for other firms to enter the market. This shifts the supply in the market to the right, which lowers the price until P=ATC

○ Firms will enter the market until the firm earns 0 economic profit

■ If the price is < the equilibrium price but quantity > AVC, MR would decrease (because MR = P), output would decrease (because MC = MR at a lower quantity), and short-run total costs and short-run total revenue would decrease because the quantity decreased and price fell.

○ Increasing cost industry - if firms enter due to the existence of profit, then the ATC increases. In addition, as output in the industry increases, the LRATC increases. This is due to firms competing for resources and an increase in supply causes the price to decrease in the market.

● Perfectly Competitive Firm at a Loss

○ Price is less than ATC, so the firm is earning an economic loss

○ Since Price > AVC, the firm continues to operate in the short-run

● If the firm is operating in a constant cost industry, then entry and exit of firms does not change LRATC (it’s constant). If firms are at a loss, some firms will exit the market. This causes supply to decrease, which raises the price until P = ATC.

● If the firm is operating in a decreasing cost industry, as firms exit the marketplace and the output in the industry increases, the LRATC would decrease (and the LRATC cost curve would shift upward). This is due to the fact that there would be less firms competing for resources. Price would increase due to a decrease in supply, and the ATC would decrease.

● Perfectly Competitive Firm in the Long-Run

○ Price = ATC, so the firm is earning 0 economic profit

○ Firms in the long-run equilibrium earn 0 economic profit (normal profit)

○ Firms are allocatively efficient (P=MC) but also productively efficient (ATC is at minimum)

○ P = MR = MC = ATC

3.7 Perfect Competition

Characteristics

○ Many buyers and sellers

○ Identical Products

○ No/low barriers to entry (firms can freely enter or exit the market)

○ No advertisements

○ Firms are “price-takers”; they take the market price as given. Firms have no control over price.

○ No economic profit in the long run (which is why we say you have normal profit when you have 0 profit)

○ The long-run supply curve for the industry is perfectly elastic, firms can supply all of their output at a constant price determined in the market

Case #1: Normal Profit

Case #2: Positive Economic Profit

Case 3: Negative Economic Profit (Losses)

● The typical LRATC curve is also U-shaped, reflecting increasing returns to scale when it has a negative slope, constant returns to scale when it has a horizontal slope, and decreasing returns when it has a positive slope.