Question

In: Advanced Math

Maximize or minimize the following functions. Be sure to check your second-order conditions. (a) maxQ Π...

Maximize or minimize the following functions. Be sure to check your second-order conditions.

(a) maxQ Π = (20 − Q)Q − 4Q

(b) maxQ Π = (12 − Q)Q − 2Q2

(c) maxL Π = AL1/2 − 4L

(d) maxL Π = ALα − wL (where A and α are exogenous parameters and w is the wage rate on labor, L)

Expert Solution

(a) Given: . Differentiating we get:

As the second derivative is negative, maximum occurs at Q=8, and maximum value is 64.

(b) Given: . Differentiating we get:

As the second derivative is negative, maximum occurs at Q=2, and maximum value is 12.

(c) Given: . Differentiating we get:

As the second derivative is negative, maximum occurs at L=A²/64, and maximum value is A²/16.

(d) Given: . Differentiating we get:

If , then the second derivative is negative, and maximum occurs at , and maximum value is

.

However, if , then the second derivative is positive, and minimum occurs at , and minimum value is

Colby Messinger answered 2 years ago

2) Show that second-order conditions for cost minimization are weaker than second-order conditions for profit maximization.

Find the first-order and second-order partial derivatives of the following functions: (x,y) =x2y3

Select the correct economic criterion (maximize profit, minimize cost, maximize benefit) for each of the following...

Select the correct economic criterion (maximize profit, minimize cost, maximize benefit) for each of the following scenarios: A services contractor received a fixed price contract to install and maintain IT equipment for the city of San Diego. What is the economic criteria for the services contractor? A couple has budgeted $15,000 for their wedding. What is the economic criterion for the couple planning their wedding? A sandwich shop has found that decreasing the price of a sandwich increases sales but...

Why should sunk costs be ignored when making economic decisions in order to maximize or minimize...

Why should sunk costs be ignored when making economic decisions in order to maximize or minimize things such as utility, profits, total cost, time, etc? Does the law of diminishing marginal utility hold true in every situation? Is it possible to think of any goods for which consuming additional units, at least initially, will result in increasing marginal utility? Why or why not? Explain why the marginal cost curve intersects the average total cost curve at the level of output...

Let f and g be two functions whose ﬁrst and second order derivative functions are continuous,...

Let f and g be two functions whose ﬁrst and second order derivative functions are continuous, all deﬁned on R. What assumptions on f and g guarantee that the composite function f ◦g is concave?

28. The goal of utility maximization is to allocate your _ in order to maximize your _

28. The goal of utility maximization is to allocate your _______ in order to maximize your _______ 29. The additional utility gained from consuming an additional unit from a good is called _______ 30 If marginal utility is positive, then as consumption increases _______ 31. The tendency of marginal utility to decline as consumption increases beyond some point is called _______

Directions: Complete each of the following problems. Be sure to show your work in order to...

Directions: Complete each of the following problems. Be sure to show your work in order to receive full or partial credit. Calculators are allowed along with 1 page (1 side) of notes any any necessary statistical tables. 1. (True / False) Estimating parameters and testing hypotheses are two important aspects of descriptive statistics. 2. (True / False) A statistic is calculated from a population and a parameter is calculated from a sample. 3. (True / False) Descriptive statistics include visual...

The timing and the amount of the second stimulus check are still undetermined. In your opinion,...

The timing and the amount of the second stimulus check are still undetermined. In your opinion, is the stimulus check a must to bail out the economy from the current downturn by COVID-19 pandemic? What will be the impact of the stimulus checks on the unemployment rate? Please state your answer in the language of economics and indicate which macroeconomic model (classical, Keynesian, monetarist, or rational expectation) to support your answer.

What are the 4 major macromolecules and how to they support life.Be sure to check your...

What are the 4 major macromolecules and how to they support life.Be sure to check your spelling. Minimum response should be 10 sentences.

Answer the following questions in order to approximate the value of sin(0.8). Note that π/ 4...

Answer the following questions in order to approximate the value of sin(0.8). Note that π/ 4 ≈ 0.785 radians. (a) Do you have enough information to use right triangles to estimate sin(0.8)? Why? (b) Estimate sin(0.8) using values of sin(x) that you know from part (2). (c) Estimate sin(0.8) using the graph of y = sin(x) from part (3). (d) Estimate sin(0.8) using the 5th degree Taylor polynomial for sin(x) at a = 0 (I will accept either the Taylor...