Maria has a utilty function u(x,y) = min{ 2x, 0.5y} and a labor endowment of 120 units. The production functions are x = 4Lx and y = 12Ly. In this case, what is the optimal labor that should be allocated to producing good x?
Answer
The correct answer is (a) 51.4
Maria has a utility function u(x,y) = min{2x, 0.5y}
Whenever we have utility function of the form U = min(ax,by), this means that she considers x and y as perfect complements. For such function in order to maximize Utility(u) a consumer consumes at a point where kink of the indifference curve(IC) will occur. Kink of this function will occur at a point where ax = by.
So kink of the IC of Maria will occur at a point where 2x = 0.5y => y = 4x
It is given that x = 4Lx and y = 12Ly
So, y = 4x => 12Ly = 4(4Lx) => Ly = (4/3)Lx -------------------------(1)
It is given that total labor endowment is 120 => Lx + Ly = 120 => Ly = 120 - Lx ---------------------(2)
From (1) and (2) we have :
(4/3)Lx = 120 - Lx
=> (7/3)Lx = 120
=> Lx = 51.4
Thus, the optimal labor that should be allocated to producing good x is 51.4 units.
Hence, the correct answer is (a) 51.4
Maria has a utilty function u(x,y) = min{ 2x, 0.5y} and a labor endowment of 120...
An economy has a labor endowment of 24 units. Good x has the production function x = 10Lx and good y has the production function y = 2(Ly)0.5, where Lx and Ly are the labor units allocated to sector x and y, respectively. Find output x if a third of labor endowment goes to producing good x. 65 70 72 80
An economy has a labor endowment of 18 units. Good x has the production function x = 10Lx and good y has the production function y = 2(Ly)^0.5, where Lx and Ly are the labor units allocated to sector x and y, respectively. Find the equation for the PPF
Peter has a utility function U(x, y) = min {2x, y}. The price of good x is $5, and the price of good y is $10. If Peter's income is $200, how many units of good x would he consume if he chose the bundle that maximizes his utility subject to his budget constraint?
Peter has a utility function U(x, y) = min {2x, y}. The price of good x is $5, and the price of good y is $10. If Peter's income is $200, how many units of good y would he consume if he chose the bundle that maximizes his utility subject to his budget constraint?
Question 9 Peter has a utility function U(x, y) = min {2x, y}. The price of good x is $5, and the priče of good y is $10. If Peter's income is $200, how many units of good x would he consume if he chose the bundle that maximizes his utility subject to his budget constraint?
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z Problem 4 (a) Derive the demand functions for the utility function (b) Let a = 2, b = 5, px = 1, pz = 3, and Y = 75. Find the...
Consumer A has a utility function u(x,y) = xA + yA and an endowment of (x,y) = (25,5). Consumer B has a utility function u(x,y) = min{xB,yB} and an endowment (x,y) = (25,45). a. Carefully sketch the Edgeworth Box and indicate where the endowment is. b. What is A’s utility and B’s utility if they each simply consumer their endowments? c. Next, add the indifference curve for A and B, through their endowments in your Edgeworth Box. d. Find a...
Suppose that Mia has 10 units of labor and her two production functions are x = 6Lx and y = 10Ly. In another economy, Mr. Fantastic has 14 units of labor and production functions, x = 4Lx & y = 6Ly. In this case, the PPF for Mia is ____ and the PPF for Mr. Fantastic is ____. Group of answer choices 4x + 6y = 280; 3x + 2y = 168 4x + 6y = 280; 2x + 5y...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z
Lucky Luke has 100 units of labor, and faces production functions: x = 10Lx and y = 6Ly, where Lx and Ly are the labor allocations. Luke has the utility function u(x,y) = xy. In this case, what is the optimal basket of goods is ( x, y ) = Answer= (500, 300)