Consider the following function: f(x,y,w) =(x2/y) + (2w2/x). Is this homogeneous? If so, to what degree? Please show the steps to solving this.
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Consider the following function: f(x,y,w) =(x2/y) + (2w2/x). Is this homogeneous? If so, to what degree? Please show the steps to solving this.
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- After an analysis of a large number of small businesses with two to nine employees, it was determined that, in a certain market sector, the operating costs C, in thousands of dollars, could be modeled by the function(pic#2)...., where p is the number of employees working for the firm. On the other hand, the realized revenue, R, of a firm could be determined as a function of the operating costs C, where R=(pic#1)... R and C are expressed in thousands of dollars. a) Based on the analysis, what would be the operating costs for a business with three employees? b) What would be the revenue for a company with three employees? c) Determine the equation that would model the realized revenue, R, as a function of the number of employees.This question illustrates the argument on p.114 of the book. A and B own neighboring properties. Beneath their properties is a common well that contains 200 units of oil. The cost to A of extracting oil from the well in period t depends on the number of units of oil in the well at the beginning of the period t, ut, and the number of units of oil A extracts in period t, xAt ; specifically, the average cost of extraction for A per unit in period t is xAt /ut. The analogous cost function for B is xBt/ut. The market price of a barrel of oil is 1, there are two periods (t = 1, 2), and the discount rate is zero. The oil is a common property resource. a) (2) Suppose that A and B "unitize" and cooperatively decide how much oil to extract, and split the profit between them. The jointly profit-maximizing policy is that each extracts 50 units of oil from her well in each of the first two periods, after which the well is dry. How much discounted profit will A and B each make? b) (2) Suppose…Q2)Tony Keonte owns a factory that manufactures Eye-Games. His weekly profit (in thousands of dollars) is given by the following function: P(x) = -4x2 + 80x- 300. Where x is the number of Eye-Games sold. a) What is the largest number of Eye-Games that the company can sell and still make profit? (25 points) b) How many Eye-Games will the firm have to produce and sell in order to maximize profit? (25 points)
- Complete all of the following definitionsDoes the output maximization level of input use exist for the following function? If yes, then what is the exact input-use level? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to: d. Assuming a sudden change in trading conditions resulting in a 20% reduction in demand at all price levels, to find the equation of the new demand function and to recommend how the manufacturer should respond.
- I have seen solutions for this question that include solving by matrices and row reduction. Will both these methods give the same answer?The profit function in dollars for a product is given -x^3+76x^2-380x-2800 where x is the number of units produced and sold. If break even occurs when 10 units are produced and sold find a quadratic factor of the profit function and find a number of units other than 10 that gives break even for the product.Consider the following quadratic (potential cost) function
- The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?A company has determined that its prodor for a product can be described by linear function. The profit from the production and sales of the 150 units is $455, and the profit from 250 units is $895 1. What is the average rate of change of the profit for the product when between 150 and 250 units are sold? 2. Write the equation of the profit function for this product? 3. How many units give break-even for this product?For a certain company, the cost function for producing x items is C(x)=30x+200 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050. The maximum capacity of the company is 170 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! 1. Assuming that the company sells all that it produces, what is the profit function? P(x)= ? 2. What is the domain of P(x)? 3. The company can choose to produce either 80 or 90 items. What is their profit for each case, and which level of production should they choose? Profit when producing 80 items=? Profit when producing 90 items=?