Question: Julia has a Cobb-Douglas utility function, Use the Lagrangian method to find her optimal values of q and q2 in terms of her income

Julia has a Cobb-Douglas utility function, Use the Lagrangian method to find her optimal values of q and q2 in terms of her income and the prices. Let Y be Julia's income, p be the price of q, P2 be the price of 92, and be the Lagrangian multiplier. First, Julia's Lagrangian as a function of q1, 92 a, Y, P1, P2, and is U(91.92)=992-2 L=q2+(Y-P191-P292) Show Julia's Lagrangian function and her first-order conditions. The first-order conditions for Julia to maximize her utility subject to the constraint as functions of 9, 92 a, Y, P, P2, and are L 291 L 292 L d = = 0, = 0, and = 0.

Step by Step Solution

★★★★★

3.41 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Q Foc 80 u L 2CY 1292 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Finance Questions!

A monopoly has a Cobb Douglas production function per hour Q (K, L) = K^1/3 L^1/3. The cost of capital (rent) is $27 per hour and the cost of labor (wage) is $8 per hour. Moreover, this firm has a...

Jay's Jewelry Store entered into the transaction listed below. The company uses the perpetual inventory system. July 6 Purchased $1,800 of merchandise on credit, terms 3/15. July 8 Returned $300 of...

In Problems 1-3, prices p1 and p2 are in dollars and q1 and q2 are numbers of units. 1. The demand functions for two products are given by q1 = 300 - 8p1 - 4p2 q2 = 400 - 5p1 - 10p2 Find the demand...

Consider the game having the following payoff table: (a) Use the approach described in Sec. 15.5 to formulate the problem of finding optimal mixed strategies according to the minimax criterion as a...

Follow the instructions of Prob. 15.5-3 for the game having the following payoff table: (a) Use the approach described in Sec. 15.5 to formulate the problem of finding optimal mixed strategies...

Let X1, . . . , Xn be a random sample from the Poisson distribution with mean . Let Y = a. Prove that there is no unbiased estimator of 1/. (Write the equation that is equivalent to E (r(X)) = 1/....

"This is your lucky day. You have just won a $20,000 prize. You are setting aside $8,000 for taxes and partying expenses, but you have decided to invest the other $12,000. Upon hearing this news, two...

Knowing that the pump of Prob. 11.35 has BEP at Q = 8000 gal/min, use the similarity rules to find the appropriate (a) Impeller diameter, (b) Rotation speed, and (c) Head produced for a pump of the...

An LTI system has impulse response h[n] = 5 (1/2) n u[n]. Use the Fourier transform to find the output of this system when the input is x[n] = (1/3) n u[n].

Li Ming Yuan and Tiffany Shaden are the department heads for the accounting department and human resources department, respectively, at a large textile firm in the southern United States. They have...

Suponga que la elasticidad de la demanda para "steaks" es -2.5 cuando hay una disminucin en precio de 30%. Podemos concluir que la cantidad demandada aumento es

A restaurant manager who arranges to have all of the restaurants leftovers, plus 50 prepared meals, donated to a food bank each week probably exhibited ________ power to coordinate the extra work...

How would you express "Juan needs to take an Economics class" in Spanish? Juan tiene tomar una clase de economa. Juan tener estudia una clase de economa. Juan tiene que tomar una clase de economa....

Balance sheet 1: 1. If Total Assets are $3,600 and Total Equity is $2,800 then what is the value of Total Liabilities? 2. Fill in the missing information from the balance sheet. Gulf Shipping Company...

The Texas Bill of Rights, Section 24 states that the "Military shall _______ to the civil authority." Question 99 options: at all times be subordinate. at times of peace be subordinate. at no time be

Question 5 of 21. A significant downfall of the Milestone chart is that it does not effectively portray the relationships, dependencies, and constraints among the project activities and events. Which...

Show how the MVDs Ename - > - > and Ename - > - > Dname in Figure 1 4 . 1 5 ( a ) may arise during normalization into 1 NF of a relation, where the attributes Pname and Dname are multivalued.

Which task is performed by a book-keeper? A. Analysing the trading results B. Entering transactions in the ledger C. Preparing year-end financial statements D. Providing information for...

Dr. Isobel Stevens is supervising physician at the Westbury HMO, a New York City-based medical facility serving the poor and indigent. Stevens is evaluating the cost effectiveness of a preventive...

Characterize each of the following statements as true or false, and explain your answer. A. If marginal revenue is less than average revenue, the demand curve will be downward sloping. B. Profits...

The Denver Athlete's Club (DAC) is a private, notforprofit athletic club located in Denver, Colorado. DAC currently has 3,500 members but is planning on a membership drive to increase this number...

A high-end skiwear producer makes parkas for men, women, juniors, and preschoolers. For each gender, there are tens of styles, and for each style approximately five colours and four sizes. This...

A flower shop uses 250 clay pots a month. The pots are purchased for $2 each. Annua1 holding cost is estimated to be 30 percent of purchase cost, and ordering cost is $20 per order. The manager has...

A food processor uses approximately 27,000 non-returnable glass jars a month for its fruit juice product. Because of storage limitations, a lot size of 4,000 jars has been used. Monthly holding cost...