Exam 17: Technology

The UJava espresso stand needs two inputs, labor and coffee beans, to produce its only output, espresso. Producing an espresso always requires the same amount of coffee beans and the same amount of time. Which of the following production functions would appropriately describe the production process at UJava, where B represents ounces of coffee beans, and L represents hours of labor?

A firm has the production function f(x₁, x₂) = (x^b₁ + x_b²)c, where b > 0 and c > 0. This firm will have

A firm has two variable factors and a production function f(x₁, x₂) = . The technical rate of substitution between x₁ and x₂ is constant.

A firm's production function is f(x₁, x₂) = x₁ + 2x₂. This means that x₂ is twice as expensive as x₁.

A firm has the production function f(x₁, x₂) = x^0.60₁x^0.30₂. The isoquant on which output is has the equation

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 2, its output will be multiplied by

Which of the following production functions exhibit constant returns to scale? In each case y is output and K and L are inputs. (1) y = . (2) y = 3 . (3) y = . (4) y = 2K + 3L.

A firm uses 3 factors to produce its output. Its production function is f(x, y, z) = min{ , y², }. If the amount of each input is multiplied by 3, its output will be multiplied by

The production function Q = 50K^0.25L^0.75 exhibits

If the marginal product of each factor decreases as the amount of that factor used increases, then there must be decreasing returns to scale.

For each of the following production functions, draw a diagram showing the general shape of its corresponding isoquant. Comment on the ease at which labor and capital can be substituted for one another relative to the other two production functions. a. Q = K + L. b. Q = K^0.5L^0.5. c. Q = min(K, L).

The UJava espresso stand needs two inputs, labor and coffee beans, to produce its only output, espresso. Producing an espresso always requires the same amount of coffee beans and the same amount of time. Which of the following production functions would appropriately describe the production process at UJava, where B represents ounces of coffee beans, and L represents hours of labor?