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- Consider the market for labor where both firms and workers are price takers. Output is produced using capital and labor.The marginal product of labor can be described by: 200 – 4L, where L is the number of workers hired. The price of the good produced is 5 per unit. a. Illustrate the demand for labor. Be sure to note the specific value of the vertical intercept. b. Suppose that the competitive firm must pay 100 for each worker. Determine the number of workers hired. (Determine the total income to capital. Show your work for both parts. c. Suppose that the price of the good rises but that the wage remains the same. Illustrate how the optimal choice of labor would change. No need to do the explicit calculation; just show the outcome and briefly explain.A firm faces perfectly elastic demand for its output at a price of $6 per unit of output. The firm, however, faces an upward-sloping labor supply curve of E = 20w - 120 where E is the number of workers hired each hour and w is the hourly wage rate. Thus, the firm faces an upward-sloped marginal cost of labor curve of MCE = 6 + 0.1E Each hour of labor produces five units of output. How many workers should the firm hire each hour to maximize profits? What wage will the firm pay? What are the firm’s hourly profits?Suppose that the demand for electricians in a particular town can be given by the equation: L = 10,000 - 20W where L = the number of hours of electrician services and W = the hourly wage rate for electricians. a. What is the own-wage elasticity of demand for electricians when W = $125 per hour -- the equilibrium wage rate? b. Is the demand curve elastic or inelastic at this point? c. How will Aggregate Earnings of electricians be affected by a 10% increase in wages from this equilibrium point? d. What effect will each of the following have on the own-wage elasticity of demand for electricians at the equilibrium wage? i. An increase in the price elasticity of demand for electrical services ii. An increase in the equilibrium wage (with the same labor demand curve specified in this problem) iii. A dramatic increase in handymen in this town (which can be thought of as substitutes in the production for electricians)
- Consider the general supply function: Qs=60+5p-12Pl+10F Where Qs = quantity supplied, p = price of the commodity, pl = price of a key input in the production process, and F = number of firms producing the commodity. 1. Interpret the slope parameters on p, pl, ane F. 2. Derive the equation for the supply function when pI = $90 and F = 20. 3. Sketch the graph of the supply function in part b. At what price does the supply curve intersect the price axis? Give an interpretation of the price intercept of this supply curve. 4. Using the supply function from part b, calculate the quantity supplied when the price of the commodity is $300 and $500.Consider the labour market for farms during the harvest season. Assume the market is perfectly competitive, with a labour demand function QD = 10-P and a labour supply function QS = 3P, where P is the wage. a) What are the consumer (farm owners) surplus and producer (farm workers) surplus in equilibrium? b) What is the price elasticity of demand at the equilibrium? c) Suppose the government subsides the farm owners (consumers) $1 for every unit of labour purchased. Then, compute the quantity of labour traded in the market, the wage received by the workers and the wage paid by the farm owners. d) Calculate the consumer surplus and producer surplus in the presence of the subsidy in part c).A company called Tramlaw has become the only employer in the local market for retail labor. The marginal value (extra profit before wages) of hiring an additional worker-hour is ?? = 60 − ?, where ?? is marginal value and ? is the hours of labor worked. The supply of workers is given as ? = ? 2 , where ? is the wage (the price of labor). Assume Tramlaw pays all retail workers in this market the same wage. For parts (a) and (b), ignore the numbers and equations (though you could use the equations as hints). a. Explain in words why Tramlaw’s marginal cost of hiring an additional worker-hour is higher than supply, which represents the marginal cost to the worker of providing an additional hour of labor. b. Draw a market diagram of Tramlaw’s local labor monopsony, including marginal value (MV), supply (S), and marginal cost (MC). Graphically indicate the monopsonist’s profit-maximizing quantity of labor ??, wage ??, the efficient quantity of labor ? ∗ , and any deadweight loss (DWL)…
- onsider the supply function: Qs = 60 + 5P – 12 PI + 10F , Where Qs = quantity supplied, P = price of the commodity, PI = price of a key input in the production process, and F = number of firms producing the commodity. Interpret the slope parameters on P, PI, and F. Derive the equation for the supply function when PI =$90 and F = 20. Sketch a graph of the supply function in part b. At what price does the supply curve intersect the price axis? Give an interpretation of the price intercept of this supply curve. Using the supply function from part b, calculate the quantity supplied when the price of the commodity is $300 and $500. Derive the inverse of the supply function in part b. using the inverse supply function; calculate the supply price for 680 units of the commodity. Give an interpretation of the supply price.Suppose that in a competitive output market, firms hire labor from a competitive labor market (so that the profit maximization conditions for hiring labor are as we discussed in class). If the supply of this kind of labor decreases, we would expect which of the following regarding the equilibrium wage, W, and the equilibrium quantity of labor, L, employed? Group of answer choices a) a decrease in W and a decrease L b) a decrease in W and a decrease L c) an increase in W and a decrease L d) a decrease in W and no change in L e) increase in W and an increase in LSolving for the equilibrium wage and quantity is a multi-step procedure. First, you will need the marginal resource cost (MRC) curve. This curve gives the marginal cost of hiring an additional nurse (in cost per hour). Since attracting an additional nurse requires raising the wage rate for all nurses, this cost is above the wage rate required for that additional nurse. If the inverse supply curve is given as W = a + bQs, the marginal resource cost is: MRC = a + 2bQs Essentially, it has the same y-axis intercept as the inverse supply curve, but twice the slope. With a single buyer there isn’t a demand curve, but what we would think of the demand curve is the marginal value curve. In this case, it gives the marginal value product (in dollars per hour) of nurses. Hence, you can replace W in the inverse demand function with MVP. To find the quantity of nurses hired, set MRC = MVP and solve: Q. 6. With a monopsony, how many nurses are hired?
- Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure. U(c,l) = lnC + 4lnl Derive worker’s uncompensated labour supply function (for labour market participants and non-participants) and the uncompensated labour supply elasticity (for labor market participants) with respect to wage as a function of non-labour income and wage.Suppose that in a competitive output market, firms hire labor from a competitive labor market (so that the profit maximization conditions for hiring labor are as we discussed in class). If the demand for the product these firms sell increases, so that the market price of this product increases, we would expect which of the following regarding the equilibrium wage, W, and the equilibrium quantity of labor, L, employed? Group of answer choices a) a decrease in W and no change in L b) a decrease in W and a decrease L c) an increase in W and a decrease L d) a decrease in W and an increase L e) an increase in, W, and an increase in LA firm faces a perfectly elastic demand for its output at a price of $6 per unit of output. The firm, however, faces an upward-sloped labor supply curve ofE = 20w - 120where E is the number of workers hired each hour and w is the hourly wage rate. Thus, the firm faces an upward-sloped marginal cost of labor curve ofMCE = 6 + 0.1EEach hour of labor produces five units of output. How many workers should the firm hire each hour to maximize profits? What wage will the firm pay? What are the firm’s hourly profits?