A Leontief production function is given by f(k,l)=min{k/a,l/b). Does it exhibit constant returns to scale, increasing returns to scale, or decreasing returns to scale? A perfect substitutes production function is given by f(k,l)=al+bk. Does it exhibit constant returns to scale, increasing returns to scale, or decreasing returns to scale?

If a firm has the production function q = f(L, K) = L + 2K, then its technology exhibits:   constant returns to scale   increasing returns to scale   None of the above.   decreasing returns to scale   increasing marginal product

1/2 Consider a firm with the production function ƒ(x₁, x₂) = x¹/²x₂. The price of the two inputs is ₁ = 2 and w₂ = 1. If x₁ = x₂ = 16, the marginal product of input 1 is When ₁ is increasing and 2 stays the same, the marginal product of input 1 is Constant Decreasing Increasing This production function has Constant returns to scale Decreasing returns to scale O Increasing returns to scale None of the other answers is correct Does the production function have a diminishing technical rate of substitution? No Yes

Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost function, as a function of y. .e. Write down the formula and draw the graph of the marginal cost function, as a function of y.