Question

Step: 2 of 3 the nation of ectenia has 20 competitive apple orchards, which sell apples at the world price of $2 per apple. the following equations describe the production function and the marginal product of labor in each orchard: q = 100l−l2 mpl = 100−2l where q is the number of apples produced in a day, l is the number of workers, and mpl is the marginal product of labor. suppose the world price of apples doubles to $4 per apple. what is each orchard's labor demand as a function of the daily wage w ? l=50−0.125w l=100−2w l=50−0.25w l=1,000−2.5w what is the market's labor demand? l=1,000−2.5w l=1,000−5w l=50−0.125w l=100−5w ectenia has 200 workers who supply their labor inelastically. the equilibrium wage is per worker per day. each orchard hires workers and makes a profit of per day. (note: assume that wages are the firm's only costs.)

Answer 1

The labor demand for each orchard is determined by setting the marginal revenue product equal to the wage rate. the market's labor demand is found by summing up the labor demand of all the orchards. the equilibrium wage can be determined by setting the labor supply equal to the labor demand.

Step-by-step explanation:

The labor demand for each orchard can be determined by setting the marginal revenue product (MRP) equal to the wage rate (w). In this case, the MRP is given by the marginal product of labor (MPL) multiplied by the price of apples. the price of apples has doubled to $4 per apple, so the MRP is now (100−2l) * 4. Setting this equal to the wage rate w and solving for l gives the labor demand for each orchard as l=1,000−5w.

The market's labor demand can be found by summing up the labor demand of all the orchards. Since there are 20 orchards in total, the market's labor demand is 20 times the labor demand for each orchard, which is l=20(1,000−5w) = 20,000−100w. given that Ectenia has 200 workers who supply their labor inelastically, the equilibrium wage can be determined by setting the labor supply equal to the labor demand. In this case, the labor supply is 200 and the labor demand is 20,000−100w. Solving for w gives the equilibrium wage as $200 per worker per day. finally, each orchard makes a profit of the total revenue minus the total cost. Since the total cost is equal to the total wage bill (w * l) and wages are the only cost, the profit per orchard is equal to the total revenue (price of apples * quantity) minus the total wage bill (w * l), which simplifies to ($4 * q) - (w * l).