2) Eor each of the production functions below, find the cost function and conditional factor demands...
1) Foreach of the production functions below, draw the isoquant passing througb the point z^(4,1). Label at least two points on the isoquant. Also determine whether the technology exhibits CRS,IRS or DRS. a. f(x)- 2x2 b. f(x)-x1/2+X2 c. f(x)- max(xiX2) d. f(x)-xiX22 2) Eoreach of the production functions below, find the cost function and conditional factor demands if w1-2 and w2-4. What is the amount of x1 and x2 that minimizes the cost of producing 4 units of output? a....
each of the production functions below, calculate the least cost of producing unit of output for the given input prices. (a) 4 - *1 + 2x2; (wi, W2) - (1.4) $ Explain your reasoning. One unit of output can be produced either with 1 unit of input 1 costing $0 , or half of a unit of input 2, costing $ . (b) $ 4 = min{2X1 + X2, X3}; (W1, W2, W3) = (2, 4, 4) 5 Explain your...
1) Eor each of the utility functions below, find the optimal consumption bundle if pi-3 and p2-2 and m-240 a. u(x)-2x2 b. u(x)-xix22 c. d, e. u(x)- 2x1+X2 u(x)-min(x1,2%) u(x)-x1-X22 y(x)-max(x1,x2) X(X1,X2 2) Suppose p1-2, p2-7 for the first 2 units and p2 4 for the rest. a) Ifm-54 and u(x) -X1+3x2, then what is the optimal consumption bundle? b) Ifm-22 and u(x) - min(3xı, 2x2), , thenwhat is the optimal consumption bundle? Erom Workouts: 5.3,5.6,5.7 3)
Question 1: Cost Minimization and Cost Curves Suppose that Jennifer produces good y by using input xi and x2. The production function which Jennifer faces is: y = x} + x] The cost for every unit of xi is wi and the cost for every unit of x2 is w2. There is a fixed cost component F, which also forms a part of her total cost. (a) Write down the cost minimization problem. Solve this problem and express x1/x2 as...
= Question 1: Cost Minimization and Cost Curves Suppose that Jennifer produces goody by using input x and x2. The production function which Jennifer faces is: The cost for every unit of Xi is wi and the cost for every unit of x2 is w2. There is a fixed cost component F, which also forms a part of her total cost. (a) Write down the cost minimization problem. Solve this problem and express X1/X2 as a function of w2/wi. Microeconomics...
Problem 1: A firm has the following production function: min{x1, 2x2) f(x,x2)= A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the optimality condition that determines the firm's optimal level of inputs? C) Suppose the firm wants to produce exactly y units and that input 1 costs $w per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? D) Using the information from part D), write...
Consider a firm which produces a good, y, using two factors of production, xi and x2. The firm's production function is 1/2 1/4 = xi X2. (4) Note that (4) is a special case of the production function in Question 1, in which 1/4 1/2 and B a = Consequently, any properties that the production function in Q1 has been shown to possess, must also be possessed by the production function defined in (4). The firm faces exogenously given factor...
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly y units and that input 1 costs $w1 per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? C) Write down the formula for the firm's total cost function as a function of w1, W2, and y.
Nadine sells user-friendly software. Her firm's production function is f(21,02) = x + 2x2, where x is the amount of unskilled labor and t2 is the amount of skilled labor that she employs. (f) If Nadine faces factor prices (1,3), what is the cheapest way for her to produce 20 units of output? (g) If Nadine faces factor prices (W1,w2), what will be the minimal cost of producing 20 units of output? (h) If Nadine faces factor prices (W1,w2), what...
Homework 9 Use the space below and the back to write out and clearly indicate your answers. Do not use this sheet as scrap paper, but use it to neatly present your work. Suppose a firm has a production function y = f(x1, x2) = x;'x'. The price of factor 1 is w = 4, and the price of factor 2 is W2 = 16. For each part below, show your work. 1) Suppose that in the short run, x1...