problem 1: Crew Brew generates a popular brand of beer in its mini-brewery situated on a small river in Wisconsin. It utilizes a special formula, combined with the fresh water from the local stream, to make a drink popular with local folks and tourists who visit throughout the summer fishing season and autumn deer hunting season. The production function of Crew follows the formula:
Q = 50K + 50L, where Q = barrels of beer, K = units of capital and L = units of labor.
The marginal products for the inputs are: MPK = ∂Q/∂K = 50 and MPL = ∂Q/∂L = 50.
i) Assume that the capital can be purchased for $8 per unit and labor costs $6 per unit. Determine the optimal combination of inputs for the firm to employ?
As the marginal products are identical and labor is the cheaper input, Crew Brew must employ only labor to produce its product.
Note that MPL/PL is always more than MPK/PK.
ii) Assume that the cost of inputs changes to $7 for a unit of capital and $9 for a unit of labor. Determine the new optimal combination of inputs?
iii) Describe the context in which a firm might use inputs in the combination describeed above.
problem 2: A firm’s total cost function is: C = 50 + 6Q + 2Q^{2}.
Marginal cost [MC] = 6 + 4Q
i) find out the level of output that minimizes average total cost [AC].
ii) At what level of output does the marginal cost equal average variable cost [AVC]?