Hi. Kindly help me solve these problems. Strictly answer all questions

4. Suppose that in the short run a firm has a production function relating workers to output per hour: Q = 10L Where L is hours of labor. Suppose also that the firm sells its product in a perfectly competitive output market, at a price of $8 per unit produced a. Suppose that the firm is a monopsonist in the labor market, facing a labor supply curve that can be written as: L = 2W (for W = wage per hour). Derive the marginal value product of labor as a function of L (from the production function and price), and derive the marginal expenditure on labor as a function of L from the labor supply curve. (It might help to figure out total expenditure on labor as a function of L, and then take the derivative with respect to L.) How many hours of labor will the firm want to hire in this case? What will the wage be? b. Continuing with the monopsony case, suppose the firm faced a more inelastic labor supply curve: L = W Econ 4010 Fall 2019, Problem Set 3, p. 3 Now, given the same production function and the same perfectly competitive price in the output market, how many hours of labor will the firm employ, and at what wage?3. Competitive equilibrium model, Consider a market populated by 20 identical firms, with marginal product of labor MP-50-2L, selling its product at p-$2. The market supply of labor is given by w-5+0.05L. a. What is the firm's demand for labor, expressed as w-f(L) (hint: use VMP)? What is the market's demand? Illustrate both on separate graphs. b. What is the equilibrium market wage and employment in this market? .. . How many workers will an individual firm employ? Illustrate in side-by-side market/firm graphs c. Supposed the demand for labor has decreased, which is reflected in a lower equilibrium product price p-$1.50. How will this affect equilibrium employment and wage? Calculate and illustrate, contrasting the original and new equilibriums. d. If nominal wages are sticky, and stay at original levels (i.e., the first equilibrium), will this result in unemployment? If so, what will be the number of laid-off workers? Provide numerical answers and illustrate. 4. Monopsony model. Minimum wage, Consider a market that is a structural monopsony (Le, a company town) with labor demand w = 20 - 0.2L, and supply w - 4 + 0.2 L. a. Find equilibrium if the market were perfectly competitive, Illustrate b. Now, find marginal cost schedule/expression for the monopsonistic employer and solve for monopsony equilibrium. Illustrate. c. Suppose the minimum wage MW-$10 was introduced in the market. How will the minimum wage affect the market if it were i) competitive and il) monopsonistic" Illustrate and discuss. If2. A firm produces output using only one input, labor. Its production function is f(L) = 21L - L? It sells its output in a competitive product market at a price of 1. The firm is not a price-taker in the input market. Instead, it faces an upward-sloping supply of labor; the inverse labor supply function is given by w (L) = 9+ L. a) Find the firm's optimal employment level, and the wage it pays to its workers. b) Find the level of employment and the wage that the firm would pay to its workers if, for some reason, it behaved like a competitive firm. How does this compare to your answer in part a)? c) Let u = = be the wage markdown of a monopsonistic firm, i.e., the wage paid by a monopsonistic firm relative to the marginal revenue product of labor. a. Show that H = 1 1+1) . Where nw is the elasticity of the labor supply curve with respect to the wage. b. What is new for a firm that is a price-taker in the input market? What is the markdown? c. What is the markdown for the firm described in parts a)-b)? d) An upward sloping supply of labor is often associated with a monopsonistic firm, i.e., a form that this is the sole buyer of labor in a given market. What other features of the labor market can lead to firms facing an upward sloping supply of labor, even if they are not the sole buyers of labor in the market? e) Assume that a new internet platform is introduced in the market in which the firm operates. This platform allows employees to post reviews about their employers, including salary, working conditions, workplace culture, and more. How do you think the introduction of this platform will affect the firm's labor supply elasticity What will happen to wages?General Topology Info: 2B. Metrics on C(I) Let C(I) denote the set of all continuous real-valued functions on the unit interval I and let xo be a fixed point of I. 1. p(f, g) = sup. If(x) - g(x) is a metric on C(I) 2. o(f, g) = Solf(x) - g(x) dx is a metric on C(I). 3. "(f, 9) = If(xo) - sixall is a pseudometric on C(D). Problem: 4F. Spaces of functions Consider the set R' of all real-valued functions on the unit interval. 1. For each fe R', each finite subset F of I and each positive o, let U( f, F. O) = (9 ER'| (g(x) - feel