Consider one-person one producer economy. Compute the equilibrium prices, consumptions, and profits when the consumer's utility function is given by U(x, y) = Inx + y where y denotes leisure. The production function is given by f(z) = z^2/3 and z denotes labor, total endowment of time is 1. Find consumptions for x and y
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- If a firm's production function is Leontief and the wage rate goes up, the: Multiple Choice firm must use more capital in order to minimize the cost of producing a given level of output. firm must use more labor in order to minimize the cost of producing a given level of output. firm must use less labor in order to minimize the cost of producing a given level of output. cost minimizing combination of capital and labor does not change.Production of Oranges (x) and Pineapples (y) is given by x^2/36+y^2/16=1; Utility for the farmer is U=x*y.1.- What is the Optimal Utility point for the farmer Typed and correct answer please. I ll rateSuppose we have one consumer with a Cobb Douglas utility function for consumption, x, and leisure, R : u(x, R) = a ln a+(1-a) In R. The consumer is endowed with one unit of labor/leisure and there is one firm with a constant-returns to scale technology: a = aL. Determine r(p, w) and R(p, w).
- 6. Consider the following Cobb - Douglas utility function: U = χαγβην *Note, it should be assumed that a, B.y > 0 Show that this production function can exhibit increasing returns to scale globally while maintaining diminishing returns for each individual input.doubt EXERCISE 11.6 Suppose capital and labour are perfect complements in a one- to-one ratio. That is, suppose that Q = min (L, K). Currently, the wage is w=5 and the rental rate is r = 10. What is the minimum cost and method of produc ing Q = 20 units of output? Suppose the wage rises to w' = 20. If we keep total cost the same, what level of output can now be produced and what method of production (input mix) is used? PVERSuppose the production function is given by Q=2K+6L. What is the average product of capital when 4 units of capital and 2 units of labor are employed? Multiple Choice 28 14 N
- A firm face the production function:Q=120L+200K-L2-2K2It can buy L at N5 a unit and K at N8 a unit with a budget of N70. Use any method ofyour choice to find the maximum output the firm can produce.Suppose there are two inputs for production, labor and capital. The firm’s production process isdefined by the following production functiony=f(L,K).Howdoweinterpretthefirm’smarginalrateof technical substitution? a)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same cost level b)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm produces one more unit of output c)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same level of production d)a) and b) are correct e)a) and c) are correctIn a standard consumer optimization problem in microeconomics, a consumer purchases any pair of goods untilU1U2=p1p2(?), at an interior solution, where Ux is the marginal utility of good x for the consumer and px is the price of good x, where x={1,2}. What is the corresponding optimality condition for a worker-consumer in his labour-leisure optimization problem and why is it just a variation on the standard optimality condition (?)?
- Microeconomics 2 - Factor Market - Pareto Optimum Consider an economy in which only 2 factors are capital (K) and labor (L) whose total supply is 100 labor and 100 capital. They are used by only firm that produces only 2 final goods X and Y. The technology describing the production process of each of goods is described by the following production functions: X = 5 Lx + 3 Kx and Y = 1/3 Ly Ky It’s known that the factors have been allocated in such a way that the initial endowment is: Kx = 75; Lx = 85; Ky = 25 and Ly = 15. With these data we ask: Obtain the contract curve corresponding to the production of this economy. Does the starting point constitute a PARETO OPTIMUM? Represent the available information in an Edgeworth Box. Obtain the production possibilities frontier (PFC) curve. Locate the initial endowment THANKS :DIf the production function describing an economy is Y= 20 KL23, then the share of income going to capital: O is about 33 percent. O depends on the state of technology. is about 67 percent. depends on the quantities of labor and capital.Trey works as a waiter for Puff & Stuff catering for a wage of w 11. In addition to his %3D labor income from waiting, Trey makes supplemental income with his household production time by streaming video games on Twitch. He doesn't have any unearned income (V=0). Trey's preferences over consumption and household production are given by the utility function below: u (H, C) = 2\H + VC Assume Trey has 16 hours each day to split between household production and consumption, if he spends 10% of his time at home streaming and earns an hourly rate of P = 7, what will be his optimal allocation of household production? (hint: assume that Trey's utility-max condition remains unchanged and his supplemental income will only impact his budget constraint)