1. Explain if each of the following statements is true or not:
i. If average product is increasing, marginal product must be less than
ii. If marginal product is negative, average product must be negative.
iii. If average product is positive, total product must be increasing.
2. Suppose that a firm has the production function given by f(x1,x2)=4√(x1x2).
Let w1 = $64 and w2 = $1. What is the total cost of producing 20 units of
output in the long-run?
3. Consider the same firm as in question 2, who is facing the same input prices
w1 and w2 as above. Suppose that we are now in the short-run and the
firm has to use x2 = 4. What is the short-run cost of producing 72 units of
4. A firm produces an output using capital and labor using the production
technology described by f(xL,xK) = xLxK. Let w denote the price of labor
and r denote the price of capital. Assume that w = $2 and r = $1. Derive
the equations for the total, average and the marginal cost functions of this