Please explain steps to formulate the equation in (i) a) A planner in a small, open economy has a utility functionU = x1X2and production takes place according to the production functionsY1 =10L, – 0.5L?Y2 = 10L2 – LThe world prices of the goods are p1 = 10 and p2 = 5. The total amount of labouravailable in the economy is 5 units.(i)Formulate the Lagrange equation.(ii)Write down the Karush-Khun-Tucker conditions.(iii)Determine a possible solution.

In economics, a utility function is a term that expresses how satisfied or happy a person is after…

Answered: A planner in a small, open economy has…

A planner in a small, open economy has a utility function U = X1X2 and production takes place according to the production functions

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: Find P(A) is P(A') is 0.05

A: Given: P(A') is 0.05

Q: 1. Assume the cost of making 30 belts is $800, the cost of making 35 $910, and the cost equation is…

A: Marginal cost measures the change in total cost due to a change in quantity produced. Marginal cost…

Q: Which is NOT a quantifiable measurement (business metric)? Easy to calculate Repeatable…

A: There are generally two kinds of market metrics: quantitative and qualitative measures. It is…

Q: 2-7 Heinrich is a manufacturing engineer with the Miller Company. He has determined the costs of…

A: The cost of equipment = 288,000 overhead cost per year = 48,300. The variable cost is $14.55 per…

Q: Define the term engineering economic decisions?

A: Engineering economics is the Application of economic principle in the analysis of decision making in…

Q: When the production volume (Q)is 50 units the total costs (TC)is (1500)omani RIyals and fixed costs…

A: Variable cost = Total cost- Fixed cost Average variable cost = Variable cost / Quanity produced

Q: 3. Convert the following intrinsically functions into linear equations. (a) Y₁ = eB₁+B₂X₁+U₂ (b) Y =…

A: We have 3 equations which we have to convert in linear equations. With parameter beta's.

Q: A soda bottling plant uses are capital (K), electricity (E) and raw materials (R) in production. Its…

A: We are going to solve for marginal rate of technical substitution to answer this question.

Q: If TVC is $1000 and output is 20 units Calculate AVC

A: The information being given is:- Total variable cost = $1000 Output = 20 units We need to calculate…

Q: (b) Explain why the graph in the figure is not the graph of the function f. What must be done to the…

A: A vertical line test states that a line perpendicular to x axis must cut the curve at most once for…

Q: How can the calculation of the Unit-Cost be done?

A: Fixed cost refers to those costs that remain the same regardless of the level of production.…

Q: solve and show steps please (3) A mobile phone provider charges $3.75 plus $0.15 per minute for…

A: We are going to solve step by step to let student understand the process of forming linear model…

Q: PLS HELP ASAP ON BOTH

A: 2. The correct answer is c) bevel gauge.A bevel gauge is a tool used to measure and transfer angles,…

Q: Don't use chatgpt, I will 5 upvotes What is the total cost of two units?…

A: Since, AFC of 2 Units = 120 (Given)We can find, Fixed Cost (FC) = 2 *120 = 240Now, It is given that…

Q: 13. (Section 4.4) The weekly revenue, R(r), in thousands of dollars, t weeks after January 1st, for…

A: Revenue refers to the money that is generated from a specific business operation, that is calculated…

Q: what is meant by Optimum expansion path. Explain using illustrations

A: Optimal expansion path refers to the combination of factors of production that enable the firm to…

Q: 7. lim √x-2 X-4 X-4

Q: Suppose the price of a bottle of water is $5. Use the black line (plus symbol) to draw a price line…

A: Supply in economics refers to the quantity of a good or service that producers are willing and able…

Q: Complete the following table by deriving the marginal tax rates in the income ranges of $20,000 to…

A: Marginal tax rate and average tax rate formula can be written as follows:

Q: Mathematically determine Combined Budget Equation

A: Budget Equation shows that how much consumer can spend on two different goods with the given level…

Q: Define the term incremental costs?

A: Incremental costs include the total cost for producing one more unit of the output.It is the extra…

Q: Month and Cleaned April May June July August September October Miles Mowed Labor Costs 240 $6,800…

A: High-volume month (June):Units produced = 325Labor cost = $8,310Low-volume month (October):Units…

Q: help please answer in text form with proper workings and explanation for each and every part and…

A: bk=L2∫0Lf(x)sin(Lkπx) dx=62[∫030sin(6kπx) dx+∫36−(x−3)sin(6kπx) dx]=−31∫36(x−3)sin(6kπx)…

Q: How is the Handling Geometric Gradient Series process performed by economic engineers?

A: Geometric gradient series is a series of cash flows that will be either increase or decrease at the…

Q: (a-) Given the function , y = 4x2 + 9 - Eind the derivative dy/dx.

A: y=4x2+9 dydx=d(4x2+9)dx=d(4x2)dx+d(9)dx Since, the derivative of a constant term is equal to 0,…

Q: For this you will need to submit 2 documents. A word document with your answers typed out and an…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: hedule detailing the weekly total production of per week, and the cost of each unit of capital is tz…

A: The objective of this question is to calculate the value marginal product (VMPL) of the 7th worker.…

Q: 1. Prepare the scatter diagram and insert the trendline or line of best-fit. Use a scale of 2 cm to…

A: Introduction: The phrase "production costs" refers to all of the direct and indirect costs…

Q: The technically officient combination of two products a business cản produce in the current period…

A: For production of the output a combination of inputs are required. To maximize the production of…

Q: GOOD AFTERNOON, I JUST WOULD LIKE TO KNOW HOW YOU GOT 0 AND 81 ON QUESTION B, HOW DID YOU SOLVE THE…

A: Solution to sub part b with proper steps is given below:

Q: A small company of science writers found that its rate of profit (in thousands of dollars) after t…

A: dPdt=(3t+6)(t2+4t+6)14

Q: In the implicit function exy² + x² = 1, y is a function of x. Find an explicit formula for y' and…

A: Whenever a function is expressed in terms of both dependent and independent variables, it is said to…

Q: Given that Q = Q(K, L) = (aK" + (1– a)L")F represents a production function, where Q is output, and…

A: Since, parts a and b are solved in the question. We know: dK/dL = (α-1)/α (L/K)r-1 This is the…

Q: If total cost is $320 and output is 4 units Calculate AC

A: Average cost (AC), also known as average total cost (ATC), is the average cost per unit of output.

Q: typing fast i will give 5 upvotes

A: Estimating the flow rate of SAE 50W oil from one tank to another through a tube. Here are the steps…

Q: It costs a company $58 to produce 6 units of a product and $78 to produce 10 units. Assuming that…

Question

Please explain steps to formulate the equation in (i)

a) A planner in a small, open economy has a utility function
U = x1X2
and production takes place according to the production functions
Y1 =
10L, – 0.5L?
Y2 = 10L2 – L
The world prices of the goods are p1 = 10 and p2 = 5. The total amount of labour
available in the economy is 5 units.
(i)
Formulate the Lagrange equation.
(ii)
Write down the Karush-Khun-Tucker conditions.
(iii)
Determine a possible solution.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Define utility function and production function:

VIEW

Step 2: Calculate Lagrange function:

VIEW

Step 3: Determine Karush-Khun-Tucker condition:

VIEW

Step 4: Determine possible solution:

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

The slope of an isoquant is A. ΔLTC / ΔQ B.-ΔK / ΔL. C.ΔTVC / ΔQ D. None of the Above
Activity Rob Otics Ltd, a small business that specializes in manufacturing electronic- control equipment produces units as follows: No. of Units 100 Units 200 Units 300 Units You are required to calculate: (a) Find the variable cost per unit. (b) Find the Total Fixed cost. (c) Estimate the total cost if output is 250 units. (d) Estimate the total cost if output is 500 units. Total Costs (In Omani Rial) 5000 6000 7000
t FI Search (Alt+Q) Draw Design View Help Table Design Layout Design Layout References Mailings Review As the manager of Lewis Inc., a company that produces lamps, you conducted a study of the production process. The study was based on 8 units of capital currently used by your firm. (This is the short run in which capital is fixed.) 1 Week 7 Assignment Compatibility Mode Saved to this PC Text Predictions: On @ 2 W 3 Per unit capital costs are $20 and the price of lamps is $12 each (this is a competitive market). Workers at Lewis Inc. are paid $60 per labor unit. (You can think of one unit of labor as one worker, and each worker is paid $60.) Fill in the blanks in the following table. Hint: Please follow Table 1 on page 364 of the textbook. Please note that a competitive, profit-maximizing firm hi 1 7 Labor (L) E 0 1 2 8 9 10 Accessibility: Unavailable $ 4 3 4 5 6 7 FI . R Q C Capital (K) F5 % 8 8 8 8 8 8 8 8 8 8 8 L T i F6 Output (Q) 6 0 10 30 60 80 90 95 95 90 80 60 Marginal Product…
A car wheel making company has the following data related to cost: Total Cost = $ 15000 + 1000X and Total Revenue = 2500X, where X is the number of wheel. Plot the Total Cost and Total Revenue on the graph.
Calculate and complete columns (3), (4), (5), (6) and (7) as instructed by quiz question # 8. (1) (2) (3) (4) (5) (6) (7) Quantity of Total Labor Product 10 50 11 54 12 60 13 64 14 66 15 67 Use this area for calculations if needed and to answer Q10
24
The cost, in millions of dollars, of building a three-story high school in NewYork State was estimated to be:   2C x x x x      1.7 0.14 0.0001 20 400where x is the number of thousands of square feet. Suppose that you arecontemplating building a for-profit three-story high school and estimate thatyour total revenue will be $0.2 million dollars per thousand square feet.(a) What is minimum area for a three-story high school in New YorkState, that this model covers? (b) What is the variable cost of building a three-story high school in NewYork State? (c) What is the fixed cost of building a three-story high school in NewYork State? (d) Determine the profit function,P x( ), for building a three-story highschool in New York State? . (e) Determine,P(250) , for building a three-story high school in New YorkState, and interpret the result. (f) How many thousands of square feet should a three-story high schoolbuilding in New York State be in order to break even?
ook The table below shows some of the expenditure amounts in the economy of Arkinia. The MPC, the MTR, and the MPM are all constant, as are the values of the three injections. a. Complete the table below. Mc Graw Hill 10 Y 0 108 200 300 400 500 600 700 800 S T 800 201 40 60 80 100 120 140 160 180 YD 60 20 140 220 300 380 460 540 620 C 65 130 195 260 325 390 455 520 S The Economy of Arkinia -20 -5 10 40 25 55 70 100 85 I 50 50 50 50 50 50 50 50 50 Tools O Search G < Prev 180 180 180 180 180 180 180 180 180 X 50 50 50 50 50 50 10 of 10 50 50 50 AT IM www 40 50 60 10 20 30 70 Next 80 90 XN 38 30 -40 Draw a 45° line (labelled Y) and the aggregate expenditure function, labelled AE₁. Identify expenditure equilibrium with the letter e₁. Use the tool "el" to show the expenditure equilibrium. Plot only the endpoints of Y and AE. Once all points have been plotted, click on the line (not individual points) and a tool icon will pop up. You can use this to enter exact co-ordinates for your points…
Urmilaben
Describe the various efficiencies that can be applied when we select an analysis period?
I need the answer as soon as possible
please graph!