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- Suppose that a CEO’s goal is to increase profitability and output from her company by bolstering its sales force and that it is known that profits as a function of output are π = 40q − 2q2(in millions of U.S. dollars). Graph the company’s profit function. Compare and contrast output and profits using the following compensation schemes based on the assumption that sales managers view output and profits as “goods”: (a) the company compensates sales managers solely based on output, (b) the company compensates sales managers solely based on profits, and (c) the compSuppose that a CEO’s goal is to increase profitability and output from her company by bolstering its sales force and that it is known that profits as a function of output are π = 40q − 2q2 (in millions of U.S. dollars). Graph the company’s profit function. Compare and contrast output and profits using the following compensation schemes based on the assumption that sales managers view output and profits as “goods”: (a) the company compensates sales managers solely based on output, (b) the company compensates sales managers solely based on profits, and (c) the company compensates sales managers based on a combination of output and profits.You are the manager of a firm and you are required to optimize the Cobb-Douglas function given the following parameters. The maximum amount of money available to spend is $340 where the price of K=8 and the price of L=4. That is Pk=8 and Pl=4. The function is given as q=K0.4L0.6 . What is the Lagrangian? a. None of the above b. K0.4L0.6−λ(340−8K−4L) c. K0.4L0.6+λ(340−8K−4L) d. K0.4L0.6+λ(340+8K+4L)
- H3. An investor with an initial endowment of $ 16,000 is confronted with the following productivity curve: C1= 240 (16,000 − C0)0.5 where C0 denotes consumption at present, and C1 consumption in the future. Assume the interest rate (for borrowing and lending) is 20%. The investor's utility function, from which it is possible to derive his indifference curves, is defined as: U(C0, C1) =C0C1 . What is the NPV of the investment chosen by the investor? Show proper step by step calculationConstrained Optimization: Cobb-Douglas Production Function A firm operates with a Cobb-Douglas Production function: Q = 12K 0.4L 0.4 where K is units of capital, and L is number of laborers. To produce an output, the firm must pay $40 per unit of capital, and $5 per laborer. However, the firm has a budget of $800 only to spend for labor cost and capital cost. 1. Using your knowledge of the tangency condition in Producer’s theory, find the combination of K and L that the firm should use to produce the maximum possible output. Do not solve the problem using the Lagrangian method. Note: The tangency conditions just states that the slope of the production function must be equal to the slope of the isocost function.Question You are the manager of a firm and you are required to optimize the Cobb Douglas function given the following parameters. The maximum amount of money available is$1600 where the price of K = 12 and the price of L=6. That is PK=12 and PL=6. The function is given as q=K0.4+L0.6. What is the constraint equation? a. none of the above b. 12K - 6L = 1600 c. 12K/6L = 1600 d. 12K+6L=1600
- b) Euler’s theorem states that f(∙) =(∂f/∂x1) ∙ x1 +(∂f/∂x2).x2 for functions that are homogenous ofdegree 1. Show that the function below is homogenous of degree 1 and that it obeys Euler’s theorem f(x1x2) = √(x21+x22)7. 3. Let u(x1, x2) be a regular definite bend-down function (DKAB-RSQC). If μ(x1,x2) = ψ(u(x1,x2)) and dψ/du>0, prove that μ(x1,x2) is also a regular definite downward bending function using the appropriate determinant conditions.You are the manager of a firm and you are required to optimize the Cobb-Douglas function given the following parameters. The maximum amount of money available to spend is $340 where the price of K=8 and the price of L=4. That is Pk=8 and Pl=4. The function is given as q=K0.4L0.6 . What are the optimal values K0 and L0 ? a. None of the above b. K0≈68,L0≈34 c. K0≈72,L0≈18 d. K0≈34,L0≈68
- Assume an individual has a utility function of this form U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2. The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10. a. How much utility does the individual receive if she consumes C = 100 and works h = 7 hours? b. Calculate the rate at which the individual is willing to sacrifice an additional leisure hour when she is already working 4 hours. c. What is this individual’s optimal amount of consumption and leisure?Assume an individual has a utility function of this form U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2. The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10. a. What is this individual’s optimal amount of consumption and leisure? b. Assume a cash grant welfare program is instituted which pays M = 20 dollars for individuals who do not work. Compute the new optimal labour supply for this individual under the welfare program. Assume that prior to the welfare program, p =$1, w =$10, and V =$80 (as in part c). Does the individual accept the welfare program and not work? Show why or why not.11.2 Suppose P(x) represents the profit on the sale of x Blu-ray discs. If P(1,000) = 4,000 and P'(1,000) = −6, what do these values tell you about the profit? P(1,000) represents the profit on the sale of Blu-ray discs. P(1,000) = 4,000, so the profit on the sale of Blu-ray discs is $ . P'(x) represents the as a function of x. P'(1,000) = −6, so the profit is decreasing at the rate of $ per additional Blu-ray disc sold.