Consider a firm which produces q units of output using L units of labour and whose market demand for labour is given by L* = 57- w/(14p), if w/(14p)<57 and L*=0, otherwise where p denotes the price of output and w denotes the price of labour. What is the change in the profit of the firm if the price of labour changes from w= 1 to w = 4 assuming the price of output is p=57?
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Consider a firm which produces q units of output using L units of labour and whose market demand for labour is given by L* = 57- w/(14p), if w/(14p)<57 and L*=0, otherwise where p denotes the price of output and w denotes the price of labour. What is the change in the profit of the firm if the price of labour changes from w= 1 to w = 4 assuming the price of output is p=57?
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- Consider a firm that uses labour and capital as inputs for production accord- ing to some production technology y = f(K, L). Let c(y, w, r) be the cost of producing y units of output if the wage rate is w and the cost of capital is r. Let L* and K* be the optimal capital and labour demand for producing y units. Prove that dc(y, w, r) dc(y, w, r) _ K. L* and = K*. dw drSuppose that the production function of a salmon farming firm is given by F(L) = 4*root(L) and it faces a price for its product of P = 200. Moreover, the firm acts as a monopsony in the labour market - located in a small town in the south - and the supply curve is w(L) = 3 + L. We ask: (a) Determine the output and level of hiring. (b) How many workers should this firm hire from the point of view of the social optimum?Imagine there is a firm that only uses labor to produce goods and that its production function is given by Y(L)=5L-L^2. The price of the firm’s output is equal to 1. Let’s assume the firm is a price taker on the product market but is a local monopsony for employment. Imagine that its marginal cost is given by 2+L. Imagine that labor supply is given by 1+L How much labor does the firm want to use? What will be the wage it pays? How many people will work if the government imposes a minimal wage of 2.25? How will this affect the firm’s profit? Calculate and compare before and after the introduction of the minimum wage.
- 7. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What are the demand functions for labor 1(v,w.p) and capital k(v,w,p)? [Show your work] 8. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What is the supply function q(v,w,p)? [Show your work]The outputs of firms 1 and 2 are given by Q = 3L and Q2 =4L respectively 0.6 0.6 where the L's stand for labour (measured in hours). If the total labour supply is 350 what would be the total output (Q, + Q2) if (a) labour was split equally between the two firms. (b) labour was allocated efficiently between the two firms. MacBook AirWidget Factory INC. in Wisconsin has the follwing production function F(L,K)= 2L1/2K1/2L represent the number of labour hours. workers at this factory are paid an hourly wage of 30$ and they rent capital at 25$ per hour. Since this is a competative market, the factory output gets per is output is $50 per unit. let's pretend the firm operate in the short run with capital fixed at 900, how many factory workers would widget factory inc. employ? what is their profit rate?
- A firm pays a price w for each unit it employs of its labor x. It also incurs fixed costs equal to F. If the firm receives a price p for each unit of output produced, and it produces output given by f(x) = 4x¹/4, how much of labor x should it employ to maximize profits? Verify whether your answer is indeed a maximum.Suppose a price-taking profit-maximising firm produces output in the short run using only labour as a variable factor. Output (Q) and labour input (L) are related by the equation: Q Where & a positive constant, the price of output is given and denoted by p, and the wage is given and denoted by w. The firm seeks to maximise profits, given by pQ – wL. Show that the first order condition for a profit maximum may be written as: イー apL' (4)文 and hence show that in this case the firm's demand for labour is given by Further, by examining the second-order conditions explain carefully the requirement thatIn this question you will derive a simple labour demand curve. Suppose that the number of calculators a firm can produce per hour (TP) given a certain number of workers (L), is given by: TP = 396 ln(L +17) + 13L The cost of using each worker is just their hourly wage (w). So the total labour cost is C = wL. If the price of each calculator is $11, find the profit maximizing wage as a function of number of workers used (L). W=
- 2. Consider a representative firm that aims at maximizing its profit by choosing the real wage (w), capital input (K) and labour input (L) optimally. The profit function of the firm is given by: I = F(K, e(w)L) – rK – wL The effort function of the representative firm takes the following form: (w-wa e(w) = wa 0< 0 < 1 %3D where W and Wa denote the representative firm's optimal real wage and employees' alternative wage, respectively. (a) Solve the model for the Solow condition and discuss how the optimal wage depends on the model parameters. (b) Discuss by justifying on theoretical grounds the impact of four non-wage factors that affect workers efforts.(a) Let f: R→ R+ be a a firm's differentiable production function satisfying the usual assumptions. Suppose that x = R¹ is a vector of inputs and that w € R¹ are the factor prices. Let p E R+ denote the output price. The profit of the firm is given by: π(p, w) = max [pf (x) - wx]. Derive and explain Shephard's lemma: ƏT θω; (b) Now let f: R² → R₁ be defined by: :-xi (p, w). == ƒ (x) = x1 x3. Suppose this firm is a price taker in the output market and in the factor market. The output price is p and the factor prices are w = (1,1). Derive the firm's supply function. (c) Suppose now that x₁ is fixed at x₁ = 1. Derive the short run supply function. Which is more elastic, the short-run supply or the long-run supply? For what output level is x₁ = 1 the optimum plant size? (d) Suppose that p = 4 and that the government imposes a lump sum tax T = 2.50 on the firm if it produces positive output. What will the firm's output be i) in the long-run and ii) in the short-run where x₁ is fixed at 1?…A firm's production function is Q = 5 + 25L - .5L2 + 30K – K2, and its demand function is PQ MRQ = d = $30. The prices of L and K are PL = $6 and PK = $12. Use Excel Solver to find the profit-maximizing and cost minimizing amounts of L and K to employ. The profit- maximizing and cost minimizing amount of L is: A. L = 16. %3| L = 25. C. L = 38. D. L = 42. B.