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Introduction to Factor Markets - Microeconomics

  1. A firm's short-run production function is given by Q=100L−2L2Q = 100L - 2L^2, where L is the number of workers and Q is total output. The firm sells its product in a competitive market for $3 per unit and hires workers in a competitive market for a wage of $60 per worker. How many workers should the firm hire to maximize profit?
    Answer: 20 To maximize profit, the firm should hire workers until Marginal Revenue Product (MRP) equals the wage (Marginal Factor Cost). 1. Find Marginal Product (MP): MP = dQ/dL = 100 - 4L. 2. Find MRP: MRP = MP Price = (100 - 4L) $3 = 300 - 12L. 3. Set MRP equal to the wage: 300 - 12L = $60. 4. Solve for L: 240 = 12L, which gives L = 20. The firm should hire 20 workers.
  2. For which of the following firms is the value of the marginal product of labor (VMPL) most likely to be significantly greater than its marginal revenue product of labor (MRPL)?
    Answer: The sole provider of patented prescription medication used to treat a rare disease. VMPL is calculated as Marginal Product (MP) times Price (P), while MRPL is MP times Marginal Revenue (MR). These two values are equal only when P = MR, which occurs in perfectly competitive product markets. For any firm with market power (monopoly, oligopoly, monopolistic competition), P > MR, which means VMPL > MRPL. The firm with the most market power will have the largest gap between P and MR, and thus the largest gap between VMPL and MRPL. The sole provider of a patented drug (a monopolist) has the most market power among the choices.
  3. If electronics firms suddenly receive large export orders requiring them to increase their machinist workforce by 40% immediately, what is the most likely short-run outcome in this labor market?
    Answer: Wage rates will rise across all industries as electronics firms bid workers away from textile and automotive sectors In the short run, the supply of skilled machinists is fixed (training takes 18 months). Electronics firms need 40% × 300 = 120 additional machinists immediately. Since new workers cannot be trained quickly, electronics firms must bid workers away from other industries, raising wages. This creates upward pressure on wages across all industries as firms compete for the fixed pool of workers. Choice B ignores that wage increases in one sector affect the entire market. Choice C is impossible since training takes 18 months. Choice D incorrectly assumes automotive firms will outbid electronics firms who are driving the demand increase.
  4. Which of the following events would cause a movement upward along a firm's demand curve for labor, resulting in fewer workers hired?
    Answer: A rise in the market wage rate for labor. The firm's demand curve for labor is its marginal revenue product (MRP) curve. A movement along this curve is caused by a change in the price of the factor itself, i.e., the wage rate. A rise in the wage rate represents a movement upward along the stationary MRP curve to a point where the firm demands a lower quantity of labor. Changes in product price, the price of other inputs, or the marginal product of labor itself would all cause the entire labor demand (MRP) curve to shift.
  5. An online retail company uses both human workers for customer service and an AI-powered chatbot system. The company determines that the marginal revenue product of the last human agent hired is $30 per hour, while the marginal factor cost is $25 per hour. For the chatbot system, the marginal revenue product of the last unit of processing power is $40 per hour, while its marginal factor cost is $40 per hour. To maximize profits, this company should:
    Answer: increase the use of human agents and keep the use of the chatbot system constant. A firm maximizes profit by employing each factor up to the point where the factor's MRP equals its MFC. For human agents, MRP ($30) > MFC ($25), so the firm should hire more human agents. For the chatbot system, MRP ($40) = MFC ($40), which means the firm is already employing the profit-maximizing amount of this factor. Therefore, the optimal strategy is to increase the use of human agents while maintaining the current level of chatbot usage.
  6. According to the marginal productivity theory of income distribution, in a competitive market, a worker's wage is determined by:
    Answer: the value of the marginal product of the last worker hired. The marginal productivity theory posits that firms will hire workers up to the point where the cost of the last worker (the wage) is equal to the revenue that worker generates at the margin. In a competitive market, this is the Value of the Marginal Product (VMP), which is the Marginal Product of the last worker multiplied by the market price of the output. Therefore, wages are determined by the marginal contribution of the last worker to the firm's output, valued at the market price.
  7. A car manufacturing firm experiences two simultaneous events: the market price of cars increases due to higher consumer demand, and the firm adopts a new robotic assembly line that is a substitute for human labor. What is the net effect on the firm's demand for labor?
    Answer: The effect on the demand for labor is ambiguous. The two events have opposing effects on the demand for labor. First, the higher market price for cars increases the Marginal Revenue Product (MRP = MP * P) of labor, shifting the labor demand curve to the right. Second, adopting a substitute technology (robotics) means that for any given level of output, the firm will use more robots and less labor. This shifts the labor demand curve to the left. Since one effect increases labor demand and the other decreases it, the net effect is ambiguous without knowing the magnitude of each change.
  8. In a monopsony labor market, a firm's marginal factor cost curve lies above its labor supply curve. If the firm currently employs 100 workers at a wage of $20 per hour, and increasing employment to 101 workers requires raising the wage to $20.50 for all workers, what is the marginal factor cost of the 101st worker?
    Answer: $70.50, reflecting both the wage paid to the new worker and increased costs for existing workers Marginal factor cost (MFC) includes both the wage paid to the new worker ($20.50) and the additional cost of raising wages for all existing workers (100 × $0.50 = $50). Total MFC = $20.50 + $50 = $70.50. Choice A only considers the new worker's wage. Choice C only considers the wage increase per worker. Choice D incorrectly calculates as $0.50 × 100 + $20.50 = $50.50, missing the proper MFC calculation.
  9. A profit-maximizing firm currently employs labor such that the marginal revenue product of labor is $40 and the market wage is $35. The marginal product of the last worker hired is 8 units of output. Which of the following actions should the firm take?
    Answer: Hire more labor because its marginal revenue product exceeds the wage rate. The rule for profit maximization in factor markets is to hire inputs until the marginal revenue product (MRP) equals the marginal factor cost (MFC). Here, the MRP is $40 and the MFC (the wage) is $35. Since MRP > MFC, the last worker added more to revenue ($40) than to cost ($35), increasing profit by $5. The firm can continue to increase its profit by hiring more labor, as long as the MRP of additional workers remains above the wage. It should stop hiring only when MRP falls to equal the wage.
  10. A competitive firm sells its product for $5 per unit and pays a wage of $150 per day. It is currently employing 10 workers. The marginal product of the 10th worker is 35 units, and the marginal product of the 11th worker would be 25 units. What would be the effect on daily profit if the firm hired the 11th worker?
    Answer: Profit would decrease by $25. To find the effect on profit, we compare the marginal revenue product (MRP) of the 11th worker to their marginal factor cost (MFC). The MFC is the wage, which is $150. The MRP of the 11th worker is their marginal product multiplied by the product price: MRP = 25 units * $5/unit = $125. The change in profit is MRP - MFC = $125 - $150 = -$25. Since the cost of the worker is greater than the revenue they generate, hiring the 11th worker would decrease daily profit by $25.
  11. Firm A and Firm B produce the same product and sell it in a perfectly competitive market. They also hire from the same competitive labor market. Due to superior management, for any given number of workers, the marginal product of labor is always higher at Firm A than at Firm B. Which of the following must be true?
    Answer: Firm A's labor demand curve will be to the right of Firm B's labor demand curve. When analyzing labor demand in perfectly competitive markets, remember that a firm's labor demand curve is derived from the marginal revenue product of labor (MRP_L), which equals the marginal product of labor times the product price. Since both firms sell in the same perfectly competitive market, they face identical product prices. However, Firm A has superior management that makes labor more productive at every employment level. This means Firm A's marginal product of labor is higher than Firm B's for any given number of workers. Since MRP_L = MP_L × Price, and price is the same for both firms, Firm A will have a higher marginal revenue product at every employment level. This shifts Firm A's entire labor demand curve to the right of Firm B's curve, making choice A correct. Choice B is incorrect because both firms hire from the same competitive labor market, so they face identical wage rates (marginal factor cost). The labor supply to each firm is perfectly elastic at the market wage. Choice C misunderstands profit maximization. Each firm hires where MRP_L equals the wage rate. Since Firm A has higher MRP_L at every employment level, it will actually hire more workers than Firm B, not the same number. Choice D gets the relationship backwards. Firm A's superior productivity means it will hire more workers (since labor is more valuable there), while Firm B will hire fewer workers due to lower productivity. Remember: In competitive markets, higher productivity shifts labor demand rightward, leading to higher employment at that firm, not lower.
  12. If the price of a variable input decreases, which of the following will occur?
    Answer: The firm's marginal cost curve will shift downward, and the firm will move down along its demand curve for the input. A decrease in the price of a variable input (a factor of production) has two main effects. First, it lowers the firm's marginal costs of production at all levels of output, causing the MC curve to shift downward. Second, the demand curve for an input is the MRP curve. A change in the input's own price does not shift the demand curve for that input; rather, it causes a movement along the curve. A lower price for the input means the firm will move down and to the right along its fixed MRP curve, increasing the quantity of the input it hires.
  13. A firm is using capital and labor to produce output. The price of capital is $200 per unit and its marginal product is 40 units. The price of labor is $50 per unit and its marginal product is 12 units. To minimize the cost of producing its current level of output, the firm should:
    Answer: use less capital and more labor. The least-cost rule for combining inputs is that the marginal product per dollar spent should be equal for all inputs: MPk/Pk = MPl/Pl. Let's check the current situation: - For capital: MPk/Pk = 40 / $200 = 0.2 units per dollar. - For labor: MPl/Pl = 12 / $50 = 0.24 units per dollar. Since 0.24 > 0.2, the firm gets more output per dollar from labor than from capital. To minimize costs, it should reallocate spending from capital to labor—using less capital and more labor—until the two ratios are equal.
  14. In a labor market where workers have different skill levels, high-skilled workers earn $50/hour and low-skilled workers earn $20/hour. A firm's production function shows that 2 high-skilled workers can produce the same output as 5 low-skilled workers. If the firm currently employs 10 high-skilled and 20 low-skilled workers, what adjustment would minimize total labor costs while maintaining current output?
    Answer: Replace 5 low-skilled workers with 2 high-skilled workers since high-skilled workers provide better cost-effectiveness per unit output Cost per unit of effective labor: 2 high-skilled workers cost 2×$50 = $100 for the same output as 5 low-skilled workers costing 5×$20 = $100. Wait, these are equal, suggesting the firm is already at optimum. But let me check the current situation: 10 high-skilled + 20 low-skilled workers. The 20 low-skilled workers could be replaced by 20/5 × 2 = 8 high-skilled workers. Current cost: 10×$50 + 20×$20 = $500 + $400 = $900. If we replace 5 low-skilled ($100) with 2 high-skilled ($100), cost stays the same but we might achieve better flexibility. Actually, since costs are equal per effective unit, the firm is indifferent, making C correct.
  15. A widely publicized medical study concludes that consumption of grapefruit has significant negative health effects. Which of the following is the most likely immediate consequence in the related factor markets?
    Answer: The demand for agricultural land suitable for growing grapefruit will decrease. The demand for a factor of production is a derived demand, meaning it stems from the demand for the final product. The negative health study will decrease the demand for grapefruit. This leads to a lower price for grapefruit, which in turn reduces the marginal revenue product (MRP) of the factors used to produce it (like land). A lower MRP for land means the demand curve for that land shifts to the left, causing demand to decrease.
  16. A firm's production technology improves, causing the marginal product of each worker to increase by 20%. The firm sells its product in a perfectly competitive market. What is the effect of this technological improvement on the firm's demand for labor?
    Answer: The labor demand curve shifts to the right, with the new MRP being 20% higher at every quantity of labor. A firm's demand for labor is its marginal revenue product (MRP) curve, where MRP = Marginal Product (MP) * Price (P). If the MP of each worker increases by 20%, and the product price P remains constant, the MRP at every level of employment will also increase by 20%. This causes the entire labor demand curve to shift to the right, indicating that the firm is willing to hire more workers at any given wage.
  17. A competitive firm producing widgets notices that when it increases its labor input from 10 to 11 workers, its total revenue increases from $1,000 to $1,080. If the market wage rate is $75 per worker, what can be concluded about the firm's hiring decision in the short run?
    Answer: The firm should hire the 11th worker because the marginal revenue product of labor exceeds the wage rate by $5 The marginal revenue product of labor (MRPL) is the change in total revenue from hiring one additional worker: $1,080 - $1,000 = $80. Since MRPL ($80) > wage rate ($75), the firm should hire the 11th worker, earning $5 in additional profit. Choice B incorrectly states MRPL < wage. Choice C correctly identifies that the firm should hire but incorrectly states the profit margin as $80 instead of $5. Choice D is wrong because MRPL ≠ wage rate.
  18. A firm uses both labor and capital as inputs, and they are substitutes in production. If the price of capital falls, what is the impact on the firm's demand for labor?
    Answer: The net effect is ambiguous, as the substitution and output effects work in opposite directions. A fall in the price of capital has two effects on the demand for labor. The substitution effect: capital is now relatively cheaper, so the firm substitutes away from labor and towards capital, decreasing the demand for labor. The output effect: lower capital costs reduce the firm's overall marginal cost of production, making it profitable to increase output. To increase output, the firm will use more of all inputs, including labor, which increases the demand for labor. Since the substitution effect decreases labor demand and the output effect increases it, the net impact is ambiguous without knowing the relative magnitudes of the two effects.
  19. From the perspective of a single small firm hiring in a perfectly competitive labor market, the supply curve for labor is:
    Answer: perfectly elastic at the market wage rate. In a perfectly competitive labor market, there are many firms hiring and many workers with identical skills. A single small firm is a 'wage taker,' meaning it is too small to influence the market wage. It can hire as many workers as it wants at the prevailing market wage. This situation is represented by a horizontal (perfectly elastic) labor supply curve at the level of the market wage.
  20. The demand for labor is called a derived demand because:
    Answer: it is contingent upon the demand for the product or service that the labor produces. The term 'derived demand' signifies that the demand for a factor of production (like labor) is not for its own sake but exists only because there is a demand in the market for the final goods or services that the factor helps to create. If the demand for the final product falls, the demand for the inputs used to make it will also fall, and vice versa.

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