Consider three engines that each use 1650 J of heat from a hot resevoir (temperature = 550 K). These three engines reject heat to a cold resevoir (temperature 330 K). Engine I rejects 1270 J of heat.

The labor market equilibrium can be found by setting the demand for labor equal to the supply of labor in both cities: For Ashton: Demand: Qd = EA = 25,000 - wA/0.0024 Supply: Qs = x, where x is the number of workers willing to work in Ashton at a wage of wA or lower Setting Qd equal to Qs: 25,000 - wA/0.0024 = x Solving for x: x = 25,000 - (20 - wA)/0.0024 x = 8,333.33 + 4166.67wA For Benton: Demand: Qd = EB = 25,000 - wB/0.0004 Supply: Qs = 25,000 - x, where x is the number of workers willing to work in Benton at a wage of wB or higher Setting Qd equal to Qs: 25,000 - wB/0.0004 = 25,000 - x Solving for x: x = wB/0.0004 x = 50,000wB Since the preference for Ashton varies across people, the number of workers in Ashton and Benton will depend on the wage differential between the two cities. Let d represent the wage differential between Ashton and Benton (i.e. d = wB -wA). Using the fact that 40 percent of the working population will choose to work in Benton if the wage differential is $2, we can solve for d: 0.4(25,000) = 10,000 = 2/d d = 0.0002 Now we can solve for the labor market equilibrium: Setting x in Ashton equal to x in Benton and solving for the equilibrium wage differential: 8,333.33 + 4166.67wA = 50,000wB - wB/0.0004 8,333.33 + 4166.67wA = 50,000(wA + d) - (wA + d)/0.0004 Solving for d: d = 0.0001765 Thus, the equilibrium wage differential is $0.0001765 per hour. To find the number of workers employed in both cities and the wage paid in each city, we can use the equations for x in Ashton and Benton: x = 8,333.33 + 4166.67wA = 50,000(wA + d) Plugging in the value for d, we get: x = 50,000wA + 27.94 Thus, the number of workers in Ashton is \approx imately 8,361 and the number of workers in Benton is \approx imately 16,639. Substituting the value of x into the demand equations for each city, we find that the equilibrium wage in Ashton is \approx imately $18.28 per hour, and the equilibrium wage in Benton is \approx imately $18.28 + $0.0001765 = $18.28 + $0.0002 = $18.2802 per hour. Therefore, the labor market equilibrium results in \approx imately 8,361 workers in Ashton earning $18.28 per hour and \approx imately 16,639 workers in Benton earning $18.2802 per hour, with a small wage differential of $0.0001765 per hour between the two cities.