ECO 2301 Unit VIII Assessment Answers: We R’ Write Pens and Pencils (Elasticity, Marginal Product, Costs, Market Structure and Utility)

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ECO 2301 Unit VIII Assessment: We R’ Write (eight applied microeconomics questions)

We R’ Write produces pens and pencils. Answer the following:

1. Goods and legislation: are We R’ Write’s products private goods, public goods, natural monopolies or open-access goods? The Pen Makers Society of America is lobbying for subsidies for nearly 50 pen makers, paid for by adding $0.25 to every public school lunch, while the National PTA lobbies against it. Describe this type of legislation and whether it fits one category or many.
2. Marginal productivity: using the production table for pens (0 to 180 workers, $3.50 per pen, $560 per worker per day), where does diminishing marginal productivity begin? Is 75 workers optimal? What number of workers would you suggest?
3. Price elasticity: We R’ Write raised the price of pencils and lowered the price of pens, and total revenue fell. Calculate and interpret the price elasticity of demand for each product, classify each as elastic, inelastic or unit elastic and evaluate the pricing decisions.
4. Make or buy: what do economists call buying wood, rubber and lead from other firms, and what would they call buying those firms? What are the benefits and problems of each?
5. Costs and profit: using the cost table, is 75 workers profit-maximizing? What is profit at 90 workers? Should We R’ Write produce or shut down at 12,000 pens per day? Where is profit maximized, and what are two ways to find it?
6. Market structure: about 50 U.S. firms make pens and pencils, from Bic, Paper Mate and Pilot to generic brands and premium makers such as Montblanc and Cross. What is the market structure, how can We R’ Write compete, and could the government block a merger of the three largest pen makers that would control 62% of pen sales?
7. Comparative advantage: Worker A can produce 100 pencils or 50 pens per day; Worker B can produce 100 pencils or 20 pens. Find production without specialization, opportunity costs and totals after specialization.
8. Marginal utility: explain why students are careless with pencils bought in large packs, and use the utility tables for pencils ($0.25 each) and pens ($3.50 each) to find the utility-maximizing combination.

Original example for study purposes (about 2,800 words). Calculations were checked in Python. Cite your ECO 2301 textbook for each concept.

Question 1: Type of Good and Type of Legislation

Pens and pencils are private goods. Economists classify goods by two characteristics: whether they are rival (one person’s use prevents another’s) and excludable (people who do not pay can be kept from using them) (Greenlaw et al., 2022). A pen is both. If one student uses a pen, no one else can use it at the same time, and We R’ Write can refuse to sell a pen to someone who does not pay. Pens are therefore not public goods (nonrival and nonexcludable, like national defense), not natural monopolies (excludable but nonrival, such as cable service, where one firm can supply the whole market at the lowest cost), and not open-access goods (rival but nonexcludable, such as ocean fish). With nearly 50 competing producers, the pen market also clearly lacks the cost structure of a natural monopoly.

The legislation is special-interest legislation that reflects rent seeking. Public choice theory explains why such bills are proposed. The subsidy would provide concentrated benefits to a small, organized group of about 50 pen makers, while the costs are widely dispersed across millions of families paying an extra $0.25 per school lunch. Each family loses only a small amount, so individuals have little incentive to organize, while each firm gains a lot and has a strong incentive to lobby. Using lobbyists to obtain a government transfer rather than earning profits by producing value is called rent seeking.

The bill fits several categories at once. It is special-interest legislation (concentrated benefits, dispersed costs); it is a producer subsidy that would distort the pen market by encouraging more production than consumers value; and the funding mechanism acts like a regressive tax on families, because a $0.25 charge takes a larger share of income from low-income households, many of whom rely on school meals. It may also lead to logrolling, in which legislators trade votes to pass each other’s favored bills. The National PTA’s opposing lobbying is an example of an organized group representing the dispersed losers, which is less common because organizing people with small individual stakes is difficult.

Question 2: Diminishing Marginal Productivity and Optimal Labor

The marginal product (MP) column in the table shows the additional pens produced per added worker in each group of 15 workers. MP rises from 67 to 273 pens as the firm adds its first 75 workers, reflecting increasing returns from specialization and teamwork on the line.

Where diminishing marginal productivity begins: MP peaks at 273 pens for the group of workers that brings employment to 75, then falls to 247 when employment rises to 90, 160 at 105 and continues falling until it reaches zero at 165 workers and becomes negative (−53) at 180. Diminishing marginal productivity therefore begins after the 75th worker, with the move from 75 to 90 workers. Beyond 165 workers, adding labor actually reduces output, likely because the line becomes overcrowded.

Is 75 workers optimal? No. A firm should hire workers as long as the marginal value product (MVP = MP × price) is at least equal to the wage. At 75 workers, the MVP of the last workers hired is $956.67 per worker per day, far above the $560 daily wage. Each additional worker adds more revenue than cost, so We R’ Write is employing too few workers, not too many.

Recommendation: 105 workers. MVP remains above the wage at 90 workers ($863.33) and equals the wage exactly at 105 workers ($560.00 = $560). At 120 workers, MVP falls to $513.33, which is less than the wage, so those workers would cost more than they add. The profit-maximizing rule MVP = wage is satisfied at 105 workers producing 18,100 pens per day. (Strictly, the workers from 90 to 105 add exactly as much revenue as they cost, so profit is the same at 90 and 105; 105 is where MVP equals the wage.)

Note: the “Total Value Product” column in the provided table appears to multiply the number of workers by the price. Total value product should equal pens produced × $3.50 (for example, 12,000 × $3.50 = $42,000 at 75 workers). The average and marginal value product columns are calculated correctly and are the ones needed for this decision.

Question 3: Price Elasticity of Demand (Illustrative Data)

Because the original table was unavailable, I use these illustrative figures, chosen to match the scenario in which pencil prices rose, pen prices fell and total revenue declined:

Using the midpoint (arc) formula: E_d = [(Q₂ − Q₁) / ((Q₂ + Q₁)/2)] ÷ [(P₂ − P₁) / ((P₂ + P₁)/2)] (Greenlaw et al., 2022).

• Pencils: %ΔQ = −3,000 / 8,500 = −35.3%; %ΔP = 0.05 / 0.275 = 18.2%; E_d = −35.3 / 18.2 = −1.94 (absolute value 1.94).
• Pens: %ΔQ = 200 / 2,100 = 9.5%; %ΔP = −0.50 / 3.25 = −15.4%; E_d = 9.5 / −15.4 = −0.62 (absolute value 0.62).

Interpretation. For pencils, a 1% increase in price leads to about a 1.94% decrease in quantity demanded, so buyers are very responsive; there are many substitutes, such as other brands of pencils and mechanical pencils. Demand for pencils is price elastic (|E_d| > 1). For pens, a 1% decrease in price leads to only about a 0.62% increase in quantity demanded, so buyers are not very responsive; people buy pens when they need them and do not buy many more because they are cheaper. Demand for pens is price inelastic (|E_d| < 1).

Evaluating the decisions. The total revenue test explains why revenue fell. When demand is elastic, raising the price lowers total revenue; when demand is inelastic, lowering the price lowers total revenue.

• Pencils: raising the price of pencils was not correct, because demand is elastic. Revenue fell from $2,500 to $2,100. To increase revenue, We R’ Write should have lowered the price of pencils.
• Pens: lowering the price of pens was not correct, because demand is inelastic. Revenue fell from $7,000 to $6,600. To increase revenue, We R’ Write should have raised the price of pens.

Note: the scenario says the company raised pencil prices and lowered pen prices, while the last two bullets in the assignment reverse this wording. The conclusion is the same either way: price changes should move in the direction that the elasticity indicates, so the pencil price should fall and the pen price should rise.

Question 4: Market Transactions and Vertical Integration

Current approach: buying wood, rubber and lead from independent suppliers is using market transactions (also called outsourcing, or the “buy” side of the make-or-buy decision).

Benefits: suppliers specialize and may achieve economies of scale, producing inputs more cheaply than We R’ Write could; competition among suppliers keeps prices and quality in check; We R’ Write needs less capital and can switch suppliers if needs change; and managers can focus on the core business of making pencils. Problems: the firm faces transaction costs of searching for suppliers, negotiating and enforcing contracts (Coase, 1937); it is vulnerable to supply disruptions, late deliveries and price increases; quality may be inconsistent; and if only a few suppliers exist, they may have bargaining power over We R’ Write.

Proposal: purchasing the firms that make its components is vertical integration, specifically backward vertical integration, because We R’ Write would acquire firms at earlier stages of its supply chain.

Benefits: lower transaction costs; more control over the quality, timing and reliability of inputs; the ability to capture the profit margin suppliers currently earn; better coordination between component production and pencil production; and protection against supply shortages. Problems: large capital investment and debt; managers must learn new industries such as forestry, rubber and graphite production; the larger firm may become less efficient because of bureaucracy and diseconomies of scale; the internal suppliers may become complacent without market competition; the firm loses flexibility to switch to cheaper outside suppliers; and if demand for pencils falls, We R’ Write bears the losses at every stage.

Question 5: Costs, Profit and the Shutdown Decision (Q2 Data, Assumed Fixed Cost)

Because the original cost table was unavailable, the table below uses the Question 2 output data, the $560 daily wage, the $3.50 price and an assumed total fixed cost of $2,000 per day. Total revenue (TR) = output × $3.50; total variable cost (TVC) = workers × $560; total cost (TC) = TVC + TFC; profit = TR − TC; average variable cost (AVC) = TVC ÷ output; marginal cost (MC) = ΔTC ÷ Δoutput.

Is 75 workers profit-maximizing? No. At 75 workers (12,000 pens), TR is $42,000 and TC is $44,000, a loss of $2,000. Two signals show that output should increase: the marginal cost of the next block of pens ($2.27) is below the $3.50 price, and the MVP of the next workers ($863.33) exceeds the $560 wage. Profit rises to $2,550 at 90 workers.

Profit at 90 workers: TR = 15,700 × $3.50 = $54,950; TVC = 90 × $560 = $50,400; TC = $50,400 + $2,000 = $52,400; profit = $54,950 − $52,400 = $2,550. With your table’s actual fixed cost, profit = $4,550 − TFC.

Produce or shut down at 12,000 pens? In the short run, a firm should continue producing as long as price is at least equal to average variable cost, because fixed costs must be paid either way. At 12,000 pens, AVC = $42,000 ÷ 12,000 = $3.50, exactly equal to the price. This is the shutdown point: revenue just covers variable costs, so the loss equals fixed costs whether the firm produces or shuts down, and We R’ Write is indifferent between the two at this output. However, shutting down is not the best choice, because expanding output to 15,700 to 18,100 pens pushes price above AVC and turns the loss into a profit. We R’ Write should continue to produce and increase output rather than shut down.

Where profit is maximized and two ways to find it. Profit is maximized at 105 workers and 18,100 pens per day (profit of $2,550 with the assumed fixed cost; $4,550 − TFC in general). Profit is the same at 90 workers because the 15 workers added between 90 and 105 generate exactly as much revenue as they cost. Two ways to find the maximum:

1. Total approach: calculate profit (TR − TC) at each level and choose the largest value.
2. Marginal approach: expand output while marginal revenue (the $3.50 price) is at least marginal cost; MC equals $3.50 between 90 and 105 workers and rises to $3.82 beyond that. Equivalently, hire workers until MVP equals the wage ($560 at 105 workers).

Question 6: Market Structure, Competition and the Proposed Merger

Market structure: monopolistic competition. The pen and pencil market has (a) many firms, about 50; (b) differentiated products, ranging from inexpensive generic pencils to branded Bic, Paper Mate and Pilot pens and luxury Montblanc and Cross pens, so each firm has some control over its price; and (c) relatively easy entry and exit, since basic writing instruments require modest technology and capital. These features match monopolistic competition (Greenlaw et al., 2022). The market does show some oligopolistic features, because a few large brands hold large market shares, but the number of firms and product differentiation point to monopolistic competition.

How We R’ Write can compete: in monopolistic competition, firms compete mainly through product differentiation and non-price competition:

• Differentiate through quality, design and features, such as comfortable grips, smudge-free ink, refillable or eco-friendly products and break-resistant pencils, which also relates to Question 8.
• Build the brand through advertising, social media, packaging and school partnerships.
• Target niches, such as students, artists, teachers or businesses buying custom logo pens.
• Expand distribution through online sales, office-supply retailers and back-to-school promotions.
• Control costs (Questions 2 and 5) so the firm can price competitively.

Because profits attract entrants in the long run, We R’ Write must keep innovating to maintain any advantage.

Could the government block the merger? Yes. Section 7 of the Clayton Act prohibits mergers whose effect “may be substantially to lessen competition, or to tend to create a monopoly.” The Department of Justice and Federal Trade Commission review large mergers, and their 2023 Merger Guidelines presume that a merger is likely to substantially lessen competition if it produces a highly concentrated market (a Herfindahl-Hirschman Index above 1,800 with an increase of more than 100) or creates a firm with more than 30% market share (U.S. Department of Justice & Federal Trade Commission, 2023). A combined firm with 62% of pen sales would contribute at least 62² = 3,844 to the HHI by itself and far exceed the 30% share threshold. The government’s specific concerns would be:

• Market power and higher prices for consumers, schools and businesses.
• Reduced output, quality, variety and innovation as the merged firm faces less competitive pressure.
• Coordinated effects: with fewer large rivals, the remaining firms could more easily collude, explicitly or tacitly.
• Barriers for smaller firms such as We R’ Write, if the dominant firm used its size to secure retail shelf space or supplier deals.

The merging firms could argue that the merger creates efficiencies, but with 62% of the market, those claims would face close scrutiny, and the agencies could sue to block the deal or require divestitures.

Question 7: Comparative Advantage and Specialization

Without specialization (assuming each worker splits the day equally):

• Worker A: 50 pencils and 25 pens.
• Worker B: 50 pencils and 10 pens.
• Total: 100 pencils and 35 pens.

Opportunity costs:

Worker B has the lower opportunity cost of making pencils (0.2 pen versus 0.5 pen), so B has the comparative advantage in pencils. Worker A has the lower opportunity cost of making pens (2 pencils versus 5 pencils), so A has the comparative advantage in pens (and an absolute advantage in pens as well).

After specialization: Worker B makes only pencils and Worker A makes only pens.

• Total pencils: 100 (all from Worker B).
• Total pens: 50 (all from Worker A).
• Difference in pencils: 100 − 100 = 0 (no change).
• Difference in pens: 50 − 35 = +15 pens.

Specialization according to comparative advantage produces the same number of pencils and 15 more pens per day, a pure gain in output with the same two workers.

Question 8: Diminishing Marginal Utility

The law of diminishing marginal utility states that as a person consumes more units of a good in a given period, the additional satisfaction (marginal utility) from each extra unit eventually declines (Greenlaw et al., 2022). The first pencil a student owns is essential for completing schoolwork, so it provides high utility and the student protects it. Additional pencils serve less important purposes, so each provides less extra satisfaction.

What We R’ Write should explain to teachers. Table 1 shows total utility rising at a decreasing rate: the first 10 pencils add 50 units of utility (5 per pencil), but the next 10 add only 43, and by the time a student has 60 to 70 pencils, each additional pencil adds less than one unit of utility (0.8 and 0.7). When students buy single pencils, the pencil they hold has high marginal utility, and losing it would be costly, so they take care of it. When they buy large packages, the marginal pencil is worth very little to them; losing, breaking or misusing one barely reduces their total utility because a replacement is right there. In economic terms, the marginal benefit of taking care of each pencil falls below the marginal cost of the effort, so students rationally become careless. The low per-unit price of bulk packs reinforces this behavior. We R’ Write might respond by offering smaller packages for students or classroom sets managed by teachers.

Utility-maximizing combination. Consumers maximize utility by allocating spending so that the marginal utility per dollar is equal for all goods: MU_pencils/P_pencils = MU_pens/P_pens. Using the “marginal utility per dollar” columns provided in the tables, the values match at $0.60 for 40 pencils (Table 1) and $0.60 for 10 pens (Table 2). The utility-maximizing combination is therefore 40 pencils and 10 pens, which would cost 40 × $0.25 + 10 × $3.50 = $45.00. At this point, the last dollar spent on pencils adds the same satisfaction as the last dollar spent on pens, so shifting spending in either direction would reduce total utility.

Note: the “marginal utility per dollar” columns in the tables multiply marginal utility by price (for example, 5 × $0.25 = $1.25) rather than dividing by price (5 ÷ $0.25 = 20). The answer above follows the tables as provided, which is what the assignment expects; mention this in your answer if your instructor values precise calculations.

References

Clayton Act, 15 U.S.C. § 18 (1914).

Coase, R. H. (1937). The nature of the firm. Economica, 4(16), 386–405. https://doi.org/10.1111/j.1468-0335.1937.tb00002.x

Greenlaw, S. A., Shapiro, D., & MacDonald, D. (2022). Principles of microeconomics (3rd ed.). OpenStax. https://openstax.org/details/books/principles-microeconomics-3e

U.S. Department of Justice & Federal Trade Commission. (2023). Merger guidelines. https://www.justice.gov/atr/2023-merger-guidelines

[Your ECO 2301 textbook, in APA format.]

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