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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
a. none of the above
b. 12K - 6L = 1600
c. 12K/6L = 1600
d. 12K+6L=1600
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- 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 constraint equation?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)The Cobb-Douglas function is widely used in Economics to represent the relationship between the inputs and outputs of a firm. It takes the form Y = ALa KB, where Y represents the outputs, L the work and K the capital. This formulation can be applied to utility and takes the form u(x) = xal ...xan, where the exponents are positive and add up to 1. Consider the problem of maximizing utility: max xay1-a S.a p1x+p2y=w x, y≥0 Where p1, p2 > 0 are the prices and w > 0 the budget. A) Write the conditions of KKT and find a solution of them, depending on p1, p2,w and a. B) Can it be said that this solution is optimal for the original problem? Justify. C) Find the multiplier 1, depending on p1, p2, w and a.
- 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≈68A firm has production function F(K, L) = 1/4 (K1/2 + L1/2) . The wage rate is w = 1 and the rental rate of capital is r = 3. (a) How much capital and labor should the firm employ to produce y units of output? (b) Hence find the cost of producing y units of output (the firm’s cost function). (c) Differentiate the cost function to find the marginal cost, and verify that it is equal to the value of the Lagrange multiplierAnswer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.
- State whether the following statements are True, False, or Uncertain. Credits will only be given for answers with explanations. Use graphs when necessary. "In an Edgeworth box, the Pareto Set will be the diagonal line of the box when the goods X and Y are perfect substitutes with the slopes of indifference curves for individual A are of the same slopes of those of individual B"Suppose that a salesperson earns a basic monthly salary of $800 plus a commission rate is 15% and the possible bonuses are lump-sum amount of $1000 if her monthly sales exceed $10,000 and a further lump-sum of $2,500 if her monthly sales exceed $15,000. Find the function that relates sales to earnings for this salesperson and graph it. At which points is the function discontinuous? Interpret the incentives created by this pay scheme?Asap In a perfectly competitive market, the market price of a toy is $100, with labour costs of $5 and capital costs of $8. The Cobb-Douglas function is below, Q = K0.2L0.5 A ) Find the profit-maximizing quantity Q and its associated profit using the Lagrangian multiplier approach. B) To ensure that the firm maximises profit, how would you develop the objective function, constraint, and Lagrangian?
- In the theory of consumer, we argued that the utility is ordinal, that is, utility number does not have any intrinsic meaning other than to give a preference ordering among consumption bundles. In other words, any increasing monotone transformation of a utility function represents the same preference, hence the spacing between indifference curves does not have any significance. Explain why in the theory of producer, the production function and the corresponding isoquant is a cardinal property, that is, the number itself has an intrinsic meaning. And explain the relationship between returns to scale and space between isoquants.Constrained 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.For a subsistence agricultural household, which of the following happen when the price of the staple they are producing increases? [SelectMultiple] Group of answer choices Due to profit effect, their utility as producers increases. The impact on overall welfare of the household is ambiguous since it depends on the relative forces of profit effect and price effect. Their is no effect since subsistence households never sell or buy their staple production. Due to price effect, their utility as consumers decreases.
