Suppose that wood industry is a perfectly competitive industry that involves 160 identical firms. The production function of each of these identical firms is as follows: 1 1 q = KZLZ where K denotes capital and L denotes labor with the corresponding prices: PK = 10 and P, 12. Suppose that capital is fixed K=12 and market %3D %3D demand function is given as follows: QD = 1,600 - 20P %3D What is the economic profit at the equilibrium, respectively?
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- Suppose a firm’s total cost is C = rK + (q 2 /2K), where K = the firm’s capital (plant size), q is output and r is the price of a unit of capital. 1. What is short-run average total cost (C/q) and what is marginal cost dC/dq, assuming K is fixed at K0 (2 points) 2. Suppose K is not fixed, but output is fixed at q0. Given this exogenous output and exogenous price of capital r0, what level of capital (K*) is most efficient – that is, minimizes total cost C? Do not forget to check the second order condition (4 points) 3. Find and interpret ∂K*/∂r.A purely competitive firm has a single variable input L (labor), with the wage rate W0 per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P0. (a) write the production function, revenue function, cost function, and profit function of the firm. (b) What is the first-order condition for profit maximization? Give this condition an economic interpretation. (c) What economic circumstances would ensure that profit is maximized rather thatn minimized?Modified True or False: State whether each statement is true or false. If the statement is false, briefly explain why it is so, and then restate it to make it true. The shapes of long-run cost curves follow directly from the assumption of a fixed factor of production, which implies diminishing returns. The optimal scale of plant is the scale of plant that maximizes average cost. In the long-run competitive equilibrium, each individual firm chooses a scale of operations that minimizes its long-run average cost. Answer correctly and explain within 30mins will give you positive feedback.
- The graph below shows a particular firms marginal revenue (mr) marginal cost (mc) and average total cost (atc) curves, where the market is competitive. Suppose that a new management team is brought in and that this team is initially less concerned about maximizing profits than it is simply about making a profit. What range of production quantities will allow the firm to operate while earning a profit? Give you're answer by dragging the qmin to Qmax lines into their correct positions. The output will need to lie somewhere between those limits.In the graph below, you can see the iso-cost curve and the iso-quant curve for the firm to produce q = 1000 units of output. Note that the vertical axis shows the quantity of capital while the horizontal axis shows the quantity of labor. Suppose that the firm is producing 1000 units of output at point A, using 200 units of capital and 100 units of labor. (i) As an outside consultant, what actions would you suggest to management to improve profits? (ii) What would you recommend if the firm were operating at point B, using 100 units of capital and 200 units of labor? Explain your answer.A purely competitive firm has a single variable input < (labor), with the wage rate. W0 per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P0. (a) write the production function, revenue function, cost function, and profit function of the firm. (b) what is the first-order condition for profit maximization ? Give this condition an economic interpretation. (c) What economic circumstances would ensure taht profit is maximized rather tahtn minimized?
- Answer the given question with a proper explanation and step-by-step solution. Ned’s Tuna has the following production function: q = K3/4L1/4, Where q is the number of tunas per hour, L is the number of workers and K is the number of boats. Suppose that w = $20/hour (PL) and r = $30/hour (PK). a. Find Ned’s marginal product of labor (MPL). Does it exhibit diminishing marginal returns? b. Find Ned’s marginal product of capital (MPK). Does it exhibit diminishing marginal returns? c. Find and draw an isocost function for CSuppose the production function is given by Q=K1/2L1/2, and that Q=30 and K = 36. How much labor isemployed by the firm?A. 49 B.6 C.36 D.25Use second image for reference, for part b here is referene; The maximum profit is found at the tangency between the production function and the isoprofit line. In other words, the slope of the production function and the slope of the isoprofit line must be the same. This is written as MPL = w where w is the slope of the isoprofit line. Then we get sqrt1 / 2L = w => 1/2w = sqrtL => L*D = 1/4w^2
- QUESTION 1a. Is it possible to have diminishing returns to a single factor of production and constant returnsto scale at the same time? Discuss.b. Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you aboutthe nature of the production function? What does each of these shapes tell you about theMRTS?QUESTION 2a. A firm faces the following average revenue (demand) curve:P = 120 − 0.02Qwhere Q is weekly production and P is price, measured in cents per unit. The firm’s costfunction is given by C = 60Q + 25,000. Assume that the firm maximizes profits.i. What is the level of production, price, and total profit per week?ii. If the government decides to levy a tax of 14 cents per unit on this product, what will be thenew level of production, price, and profit?b. The United States currently imports all of its coffee. The annual demand for coffee by U.S.consumers is given by the demand curve Q = 250 – 10P, where Q is quantity (in millions ofpounds) and P is the…(a) Show that the production function Q = (Kα + Lα)β, where Q is output, K is capital input, L islabour input and α > 0 and β > 0 exhibits diminishing returns when α < 1 and increasing returns to scale when αβ > 1.(b) Specify a translog cost function for two inputs and show that the input shares depend on inputprices.2.1 Consider N firms each with the constant-returns-to-scale production function Y = F (K, AL), or (using the intensive form) Y = ALf (k). Assume f'(•) > 0, f"(•) < 0. Assume that all firms can hire labor at wage wA and rent capital at cost r, and that all firms have the same value of A.(a) Consider the problem of a firm trying to produce Y units of output at minimum cost. Show that the cost-minimizing level of k is uniquely defined and is independent of Y, and that all firms therefore choose the same value of k.(b) Show that the total output of the N cost-minimizing firms equals the output that a single firm with the same production function has if it uses all the labor and capital used by the N firms. 2.2 The elasticity of substitution with constant-relative-risk-aversion utility. Consider an individual who lives for two periods and whose utility is given by equation (2.43). Let P1 and P2 denote the prices of consumption in the two periods, and let W denote the value of the…
