problem 1: Are each of the following assedions TRUE, FALSE, or UNCERTAIN? describe your answers with the broadest possible exception (if any), using graphs if possible.
a) If a firm is operating with constant marginal cost, it will also have constant average cost.
b) If marginal cost is increasing, average cost will also be increasing.
c) If a product requires two inputs for its production, and if the prices of the two inputs are equal, profit maximization requires that these inputs be used in equal amounts.
d) If a firm is operating at minimum short-run average cost, it is also operating at a point on its long-run average cost curve.
e) Long-run average cost can never exceed short-run average cost.
f) Long-run marginal cost can never exceed shoft-run marginal cost.
problem 2: A firm has the given production function: Q = K^{1/2}L^{1/2}
It pays wages @ $5/hour, rents capital @ $l0/hour, has 25 units ofcapital, and can sell any amount of output $4/unit. How much output should the firm produce, with what combination of inputs, and how much profit will the firm earn?
problem 3: A firm has a short-run production function defined by: Q = -.02L^{2} + 8L.
What is the short run demand curve for labor (L) in terms of the market wage rate (w), if the firm can sell all its output at $5 per unit?
problem 4: A firm's technology is defined by the production function: Q = 9K^{2/3}L^{1/3}.
It pays wages @ $18,hour (w) and rents capital @ $36/hour (r).
The demand for its goods is given by the demand function: Q = 240 - 10P.
a) What is the firm's marginal rate of technical substitution (MRTSKL), optimal condition in the product market, optimal inputs in terms of its optimal output, cost constraint in terms of its optimal output (TC), and marginal cost function (MC)? What is its demand function in terms of Q, its total revenue (TR) and marginal revenue (MR) functions?
b) What is the firm's profit-maximizing levels of price (P*), output (Q*), capital (K*), labor (L*), and profit (t*)?
c) What is the firm's revenue-maximizing levels of price (P), output (Q), and profit (r)? Which of (b) or (c) is better?
problem 5: A firm's production function is: Q = K^{1/2}L^{1/2} and the demand for its oulput is: Q = 300 - 10P.
a) lf the firm's wage rate is $10/hour and capital rental rate is $2.50 per hour, what are its optimal output, inputs, price and profit?
b) If now the wage rate rises to $22.50, what will be its output, inputs, price and profit?
c) describe this change in terms of output and factor substitution effects.
d) Are these normal or inferior inputs?
problem 6: A firm in a perfectly competitive industry has this cost function: TC : 2700 + 3q^{2}
a) If market demand is Q_{D}: 1500 - 5P, what is an individual firm's optimal price, output, and profit? What is the industry's total price and output? How many firms are there in the industry?
b) Now, if demand increases to Q_{D}= 2400 - 5P, what is the short-run optimal pdce, output and profit per firm, total industry output and number of firms in the industry?
c) What happens in the long-run?