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1 A firm has a short run production function defin

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1. A firm has a short-run production function defined by: Q = -.02L2 + 8L. 

What is the firm’s optimization principle stated in terms of input choice?

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? When does this equation not hold?

 

 

2. A firm has a short-run production function defined by: Q = -.02L2 + 8L. 

What is the firm’s optimization principle stated in terms of input choice?

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? When does this equation not hold?

 

 

3. A firm’s technology is defined by the production function: Q = 9K2/3L1/3.

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 (p*)?

c) What is the firm’s revenue-maximizing levels of price (P), output (Q), and profit (p)? 

Which of (b) or (c) is better?

 

 

4. A firm’s technology is defined by the production function: Q = 9K2/3L1/3.

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 (p*)?

c) What is the firm’s revenue-maximizing levels of price (P), output (Q), and profit (p)? 

Which of (b) or (c) is better?

 

 

5. A firm’s technology is defined by the production function: Q = 9K2/3L1/3.

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 (p*)?

c) What is the firm’s revenue-maximizing levels of price (P), output (Q), and profit (p)? 

Which of (b) or (c) is better?

 

 

6. Are each of the following assertions TRUE, FALSE, or UNCERTAIN? 

Explain 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 short-run marginal cost.

 

(Guidelines for TRUE / FALSE / UNCERTAIN questions:

These are mutually exclusive options, so choose only 1 based on the following:

• TRUE: The economic theory as presented in this course shows that there are no exceptions

to this statement. Prove or explain why or this is so and support it with a graph.

• FALSE: The economic theory in this course shows that there is at least one exception to this 

statement. Describe this exception clearly, supported by a graph or an example. Try to 

explain the economic fallacy that the statement captures; do not just give an example.

• UNCERTAIN: The economic theory as presented in this course does not address this idea 

well enough for you to pick either True or False. Beware of this answer: most statements 

will have a definite answer; if the statement is False it is not Uncertain.

 

 

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