Jamie runs an Android app business. She has production function f(x1,x2) = x11/3 x21/4. The price...

Jamie runs an Android app business. She has production function f(x1,x2) =

x₁^1/3 x₂^1/4. The price of factor 1 is w1 = 2, the price of factor 2 is w2 = 3, and the price of the output is 12.

Does this production function exhibit increasing, decreasing, or constant return to scale?
Write out the short-run profit maximization problem with x̄₂ = 81.
Solve the short-run profit maximization problem by showing all the important

steps.
Find the short-run production level that maximizes the profit.
Write out the long-run profit maximization problem.
Solve the long-run profit maximization problem.

Expert Solution

Rahul Sunny answered 7 months ago

Linda sells an android app. Her firm’s production function is f (x1, x2) = x1 +...

Linda sells an android app. Her firm’s production function is f (x1, x2) = x1 + 2x2 where x1 is the amount of unskilled labor and x2 is the amount of skilled labor that she employs. Draw the isoquant at 20 units of output and another at 40 units of output. Does this production function exhibit increasing, decreasing, or constant return to scale? If Linda faces factor prices (w1, w2) = (1, 1), what is the cheapest way to produce...

The production function of a competitive firm is given by f(x1, x2) = x1^1/3 (x2 −...

The production function of a competitive firm is given by f(x1, x2) = x1^1/3 (x2 − 1)^1/3 The prices of inputs are w1 = w2 = 1. (a) Compute the firm’s cost function c(y). (b) Compute the marginal and the average cost functions of the firm. (c) Compute the firm’s supply S(p). What is the smallest price at which the firm will produce? 2 (d) Suppose that in the short run, factor 2 is fixed at ¯x2 = 28. Compute...

Suppose that a firm has the p production function f(x1; x2) = sqrt(x1) + x2^2. (a)...

Suppose that a firm has the p production function f(x1; x2) = sqrt(x1) + x2^2. (a) The marginal product of factor 1 (increases, decreases, stays constant) ------------ as the amount of factor 1 increases. The marginal product of factor 2 (increases, decreases, stays constant) ----------- as the amount of factor 2 increases. (b) This production function does not satisfy the definition of increasing returns to scale, constant returns to scale, or decreasing returns to scale. How can this be? (c)Find...

. Consider a firm that has a production function y = f(x1, x2) = 2x 1/4...

. Consider a firm that has a production function y = f(x1, x2) = 2x 1/4 1 x 1/4 2 facing input prices w1 = 2 and w2 = 4. Assume that the output price p = 8. • What will be the profit maximizing output level? -What will be the profit? • -If this firm is divided up into two equal-size smaller firms, what would happen to its overall profits? Why

An industry has 1000 firms, each with the production function f(x1; x2 ) x1^.5 x2^.5. Theprice...

An industry has 1000 firms, each with the production function f(x1; x2 ) x1^.5 x2^.5. Theprice of factor 1 is 1 and the price of factor 2 is 1. In the long run, both factors are variable, but inthe short run, each firm is stuck with using 100 units of factor 2.The long run industry supply curve:Can somebody explain how to solve?

The production function is f(x1, x2) = x11/2 x21/2 . If the price of factor 1...

The production function is f(x1, x2) = x11/2 x21/2 . If the price of factor 1 is $12 and the price of factor 2 is $24, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?(a) x1 = x2 (b) x1 = 0.50x2 (c) x1 = 2x2 (d) x1 = 24x2 (e) We can't tell without knowing the price of output.

If a firm’s production is f(x1,x2) = 2x11/2 x21/4. If the price of factor 1 is...

If a firm’s production is f(x1,x2) = 2x11/2 x21/4. If the price of factor 1 is $5 and the price of factor 2 is $10, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? Please show all work clearly.

3. Given is the function f : Df → R with F(x1, x2, x3) = x...

3. Given is the function f : Df → R with F(x1, x2, x3) = x 2 1 + 2x 2 2 + x 3 3 + x1 x3 − x2 + x2 √ x3 . (a) Determine the gradient of function F at the point x 0 = (x 0 1 , x0 2 , x0 3 ) = (8, 2, 4). (b) Determine the directional derivative of function F at the point x 0 in the direction given...

A firm has two variable factors and a production function f(x1; x2) = (2x1 + 4x2)^1/2....

A firm has two variable factors and a production function f(x1; x2) = (2x1 + 4x2)^1/2. On a graph, plot three input combinations and draw production isoquants corresponding to an output of 3 and to an output of 4. Also, mention the technical rate of substitution(s) for the isoquants. Show all working.

COST MINIMIZATION - Nadine sells user-friendly software. Her firm’s production function is f(x1, x2) = x1 + 2x2, where x1 is the amount of unskilled labor and x2 is the amount of skilled labor that she employs

Nadine sells user-friendly software. Her firm’s production function is f(x1, x2) = x1 + 2x2, where x1 is the amount of unskilled labor and x2 is the amount of skilled labor that she employs a) If Nadine faces factor prices (1, 1), what is the cheapest way for her to produce 20 units of output? b) If Nadine faces factor prices (1, 3), what is the cheapest way for her to produce 20 units of output? c)...

Question