Monopsony in Rural Nursing Assistant Wages
Clay County has one dominant employer of nursing assistants, a regional hospital that hires about 60% of them; the remaining clinics are too small to affect the market wage. The hospital's human-resources office estimates the local labor supply and the marginal revenue product (MRP) of nursing assistants: Hourly wage $15, 100 workers willing to work; $16, 120; $17, 140; $18, 160. MRP per hour: 100 workers, $30; 120 workers, $26; 140 workers, $22; 160 workers, $18. The hospital currently pays $16 and employs 120 assistants. A county living-wage proposal would set a minimum hourly wage of $17 for nursing assistants. The hospital argues that any minimum wage will force it to cut staff, citing its tight budget. Local advocates counter that the hospital is not a wage taker and that a modest floor could raise pay without reducing employment.
1. Compute the marginal factor cost of moving from 100 to 120, 120 to 140, and 140 to 160 workers. What wage and employment does the hospital choose if it acts as a monopsonist?
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Marginal factor cost is the change in total wage cost divided by the change in workers. From 100 to 120: total cost rises from 100 x $15 = $1,500 to 120 x $16 = $1,920, so MFC = $420/20 = $21. From 120 to 140: $1,920 to 140 x $17 = $2,380, so MFC = $460/20 = $23. From 140 to 160: $2,380 to 160 x $18 = $2,880, so MFC = $500/20 = $25. A monopsonist hires up to the point where MRP is at least MFC. At 100 workers MRP is $30; at 120 it is $26, still above MFC of $21, so expand. At 140 MRP is $22, below MFC of $23, so do not expand. The hospital hires 120 workers and pays the supply wage of $16. It does not pay MRP; it pays the lowest wage needed to attract 120 workers.
2. What wage and employment would a competitive labor market produce? Compare with the monopsony outcome and identify the efficiency loss.
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A competitive labor market hires where supply equals demand (MRP). At 140 workers the supply wage is $17 and MRP is $22, so firms would want to expand. At 160 workers the supply wage is $18 and MRP is $18, so the competitive outcome is 160 workers at $18. Compared with monopsony (120 workers at $16), the competitive market has 40 more workers and a $2 higher wage. The monopsony outcome is inefficient because the MRP of the 121st to 140th workers exceeds the wage needed to attract them; the hospital restricts employment to hold down the wage. The efficiency loss is the area between the MRP schedule and the labor supply schedule from 120 to 160 workers. Using the discrete points, the gap is $10 at 120, $5 at 140, and $0 at 160; roughly $200 per hour.
3. Evaluate the hospital's claim that a $17 minimum wage would force layoffs. What if the minimum were $18? What if it were $20?
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At a $17 minimum, the hospital faces a horizontal MFC of $17 for up to 140 workers, the number willing to work at $17. MRP at 140 is $22, which exceeds $17, so the hospital still wants 140 workers. Employment rises from 120 to 140, and the wage rises from $16 to $17. The hospital's claim of layoffs is wrong in this range because it was restricting employment to avoid raising the wage for all workers; the minimum wage removes that incentive. At $18, supply is 160, MFC is $18 up to 160, and MRP at 160 is $18, so employment rises to the competitive level of 160. At $20, the supply schedule beyond 160 is not given, but if supply continues upward, the hospital will hire fewer than 160; employment could still be above 120 depending on supply elasticity. The standard layoff prediction applies only when the minimum exceeds the competitive wage.