The production function of a firm is f(x, y) = x + y. The marginal product of input x diminishes with an increase of x. • True • False

Lesson 7- Production Question 1

A firm faces the production function: q=10L^0.32 K^0.56  (a) What kind of returns to scale does this production function feature? Show work. (b) Does this production function exhibit downward-sloping and convex isoquants? Explain.

A firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L^1/2M^1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400and another isocost line showing combinations that cost $200.2. Suppose that the firm wants to produce its output in the cheapest possible way. Find thenumber of machines it would use per worker. (Hint: The firm will produce at a point wherethe slope of the production isoquant equals the slope of the isocost line.)