3. Consider a firm that produces a single output Q using two inputs, q1 and 92. The production technology is the Cobb-Douglas: Let pi be the price of q₁, and p2 be the price of 92. Assume that the price of the output Q is 1. Given: Implicit function theorem Implicit function theorem. - Consider an equation F(x₁... Xm. y) = 0. If an implicit function y = f (x₁..... Xm) exists, then the desired derivatives can be found by
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- 1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…Exercise A.5 A company operates with production function q-K¹/2 [1/2 a) What type of returns to scale does this production function present? As production varies, how would you expect long-term average costs to evolve? b) Assume that the firm's capital equipment is fixed and equal to K = 100 units. Find the firm's short-run production function and the marginal productivity of labour and graph these functions. As production varies, how would you expect marginal costs to evolve in the short term? c) If the prices of capital and labour are r = 8€ and w = 2€ respectively, obtain the expression of the short-run total cost function of the firm. b) Obtain the expressions of the functions of short-term average total costs, average variable costs and marginal costs of this company. Find the production level for which the average total cost is minimized and the corresponding average total cost level. d) Indicate the value of the average total cost, the average variable cost and the marginal cost…1. Let a firm’s cost function be c(y1, y2) = F + αy1y2 + y21 + y22, where α is some constant.a) What restriction on α is required to guarantee that this cost function exhibits economies ofscope?b) What restriction on α is required to guarantee that this cost function exhibits cost complementarities in both goods? Note that you’ll need to verify cost complementarities for y1 andy2.2. Given the industry demand function X(p) = 100 − 2p, consider the following scenarios:• The market is a perfectly competitive market. Assume there are identical firms with marginalcost of 12 in this perfectly competitive market.• The market is dominated by one monopolist with a marginal cost of 12. This monopolist isable to achieve 1st degree pricing.• The market is dominated by one monopolist with a marginal cost of 12, but the monopolistis able to achieve only 2nd degree pricing. Assume the menu offers only 2 choices:(Q∗1 = 30, p∗1 = 35), and (Q∗2 = 60, p∗2 = 20).• The market is dominated by one monopolist…
- 1. The total cost of producing a quantity q is C(q). The average cost a(q) is given in figure below. The following rule is used by economists to determine the marginal cost C'(q0), for any qo: Construct the tangent line ti to a(q) at qo. Let t, be the line with the same vertical intercept as t, but with twice the slope of t, . Then C'(q0), is the vertical distance shown in figure below. Explain why this rule works. $/unit a(q) t2 t1 C'(qo)3. Suppose a firm has a well-behaved technology and it can produce 38 units of output using the input bundles (x1, x2) = (16,8) and (x1, x2) = (4,24). – Will the bundle (x1, x2) = (13,12) produce more output, less output, or the same amount of output? (Explain your answer.)Question: Orla manages a loom that produces flags (F) using thread (T) and dye (D) as inputs. Herproduction function is given by: Q(T,D) = (T1/2 D1/2)1/2*For this problem, assume F, T, and D are infinitely divisible so you don’t need to worryabout restricting to whole-number answers. a.) Does Orla’s production function exhibit increasing, constant, or decreasing returns toscale? Explain. b.) Set up Orla’s cost-minimization problem to find the lowest-cost combination of inputsrequired to produce a specific level of output (bar Q) given factor prices PT and PD. (Note: You can write this either as a minimization subject to constraints or in Lagrangian form. *You do not need to solve it.)
- 1.Suppose a chair manufacturer is producing in the short run (with its existing plant andequipment). The manufacturer has observed the following levels of production correspondingto different numbers of workers:Number of Workers Number ofChairs 1 10 2 18 3 24 4 28 5 30 6 28 7 25a. Calculate the marginal and average product of labor for this production function.b. Does this production function exhibit diminishing returns to labor? Explain.c. Explain intuitively what might cause the marginal product of labor to becomenegative.Homework 2.1 Suppose a business manager of the factory wants to assess in terms of elasticity of demand, whetherthe products that his business is producing are complement goods or substitute goods inconsumption. So please explain which are the factors need to consider the long-run average cost curve in terms of usage of input?7. Suppose that the profit from the production and sale of x units of a product is given by x2 - 200. 100 p(x) = 180x In addition, suppose that for a certain month, the number of units produced on day t of the month is x = q(t) = 1000 + 10t. a) Find (p o q)(t) to express the profit as a function of the day of the month. b) Find the number of units produced, and the profit, on the fifteenth day of the month.
- QUESTION 3 P D X A S S2 0 5 10 15 20 25 30 35 This graph is representing the equilibrium change when input prices decrease. Other things being equal. O True O FalseProblem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy