Explain the concept of a maximum - value function. Explain the Envelope Theorem for unconstrained and constrained optimization. Give an economic example of these concepts.
Q: Problem 1: Winter melons A farmer is using land and fertilizer to produce winter melons. The…
A: In short run, only one factor is variable In long run, both factors are variable
Q: A firm manufactures outputs y₁ and y using two inputs ₁ and 72. The production function is (y₁, y2)…
A: The firm maximizes its profit function and chooses the quantity of input to be used at given prices…
Q: A local entrepreneur has built a successful business which is still growing. He is aware that the…
A: A local entrepreneur has built a successful business which is still growing. He is aware that the…
Q: Since MC(y) is the derivative of c(y), c(y) must be the integral of MC(y) . Select one: True False
A: Total Cost refers to the total cost of producing goods and services. Marginal Cost refers to the…
Q: What is an example of an Economic function in which we have more than one independent variable? (an…
A: DefinitionAn economic function that involves more than one independent variable is often referred to…
Q: Q#1: Explain the first order condition, second order conditions and Nth order conditions for…
A: Comparative statics analysis makes up the majority of economic theory. The determination of changes…
Q: what are the two distinct input bundles (P, W) in the diagram which give q = 48?
A: The diagram that consists of the optimum bundle is given as follows
Q: 1)A firm’s cost curve is C = F + 10q - bq2 + q3, where b> 0. a.At what output levels does the MC…
A: Economic costs involve not just the accounting costs but also the opportunity cost of making one…
Q: Consider the following production function with inputs L and K: Q = (L 0.5 + K0.5)2. The input…
A: Firm wish to produce certain amount of output and it wishes to produce that output at lowest…
Q: In a factory an article is produced whose production function is: z = 15 – 2x2 + 12x – 3y? + 6y for…
A: Production function is given as: z = 15 -2x2+ 12x-3y2+6yPrice of input x = 6Price of input y =…
Q: GIVE ME AN EXAMPLE OF MARGINAL ANALYSIS WITH MARGINAL R AND MARGINAL C IN A TABLE.
A: Marginal Analysis is a statistical model used by corporations to maximize their potential profits.…
Q: As a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500,…
A: The optimal level of labor and capital is given by the point where the marginal rate of technical…
Q: Constrained Optimization: Cobb-Douglas Production Function A firm operates with a Cobb-Douglas…
A: The objective of the question is to find the optimal combination of capital (K) and labor (L) that…
Q: Which of the following is an example of economies of scope? A) A mountain resort begins running…
A: Economies of scope, refer to the cost savings and efficiencies that can be achieved when a firm is…
Q: Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its…
A: The cost of production in economics means the total expenses incurred by a firm in the process of…
Q: Given the total cost function TC = 0.5q³ - 10q² + 80q • Find the average cost AC and the marginal…
A: The functional relationship that is between cost and output is referred to as the "cost function."…
Q: A manufacturer's production is modelled by the function f(x, y ) = 100x 34 y 14 where x у represents…
A: The objective of the question is to find the maximum production level given the cost constraints for…
Q: A linear programming problem has two constraints 2X + 4Y ≥ 100 and 1X + 8Y ≤ 100, plus…
A:
Q: There is a firm making custom stuffed animals. The demand function for custom stuffed animals is: P…
A: Profit maximization is a fundamental concept in economics and business management that refers to the…
Q: Kusho Industries produces and sells computer chips. Its (hourly) production function is Q=4K 0.4L…
A: The money spent to purchase the factor of production to produce final goods and services is termed…
Q: Set up and solve the following nonlinear optimization problem using Excel and the Solver add-in.…
A: Nonlinear optimization deals with the optimization of a nonlinear objective function subject to…
Q: Part 1 of 2 40%, 2 of 5 points Points: 0 of 1 Save The marginal cost of a product can be thought of…
A: To minimize the marginal cost of producing digital cameras, we need to find the minimum point of the…
Q: A manufacturer's production is modelled by the function f(x, y ) = 100x 34 y 14 where x у represents…
A: The objective of the question is to find the maximum production level given the cost constraints for…
Q: Constrained Optimization A firm wants to minimize the cost of producing 100 units of output given…
A:
Q: 3. A manager has estimated the average variable cost (AVC) function for his firm to be: AVC= 60 -…
A: Answer; Level of output at which production is most efficient is 6.
Q: T = - Q² + 17Q – 60 Find Q that maximizes the function:
A: Interest rate effect the consumption decision of whether to consume today and tomorrow.
Q: A T-shirt screener can screen t-shirts (q) in two different ways. He can either use a fast screening…
A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…
Q: Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are…
A:
Q: If Maria spends Q hours on her evening run, her Marginal Benefit from the Qth hour, expressed in…
A: Now it's 2th hour instead of Q, so apply ot in the equation.
Q: Engineers in your company have determined that the cost of production of good X follows the function…
A: The company is operating in an industry that has many competitors, making similar products and each…
Q: equations of the TVC, AVC, and MC functions. b. The level of output at which AVC and MC are minimum,…
A: Average variable cost (AVC) is a firm's variable costs (labour, electricity, etc.) divided by the…
Q: suppose now that the firm must pay a fixed cost of c > 0 in order to produce (e.g., this could be…
A: Profit: It refers to the amount that is extra or that a firm can use to explore more opportunities.…
Q: In optimization we convert a problem to which calculus problem? Group of answer choices a. Find an…
A: The issue is one of mathematical optimization, particularly as it pertains to calculus. It entails…
Q: F(x)=2-3p and C(x) = 3x^2 calculate the formula for the optimal output and its price
A: We are going to solve this question using marginal approach.
Step by step
Solved in 2 steps
- Given the following data on input and output levels. Suppose the output price is $5 and input price is $10. Find the values of AVP and MVP when X = 4: X 0 2 4 6 8 10 12 Y 0 100 250 450 600 700 750 $312.50 and $375 $20 and $375 $265.50 and $475 $20 and $750Need urgent answer and correct. Will upvoteSuppose that the Travnikar Corporation manufactures widgets. Analysts that work for the company have found a function C(x) which reports the cost to produce x widgets and a function R(x) which reports the total revenue from selling x widgets. Currently, the company is producing 500 widgets, but the analysts find that R'(500)=85 and C'(500)=79. In order to maximize profits, should the analysts recommend increasing or decreasing production?
- ***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?…G.189.Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (æ), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non- mathematical introductory) economics as the cost of producing one additional item. If the current production level is æ items with cost C (z), then the cost of computing h additionial (C(z+h)-C(z)) items is C (z + h). The average cost of those h items is . As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (z). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (z) = 0.02a3 – 10z + 450. (a) Find the marginal cost function. MC (z) (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50…
- 1. Inputs K, L, R and M cost £10, £6, £15 and £3 respectively per unit. What is the cheapest way of producing an output of 900 units if a firm operates with the production function Q = 20K0.4L0.3R0.2M0.25? 2. Make up your own constrained optimization problem for an objective function with three variables and solve it. 3. A firm faces the production function Q = 50K0.5L0.2R0.25 and is required to produce an output level of 1,913 units. What is the cheapest way of doing this if the per-unit costs of inputs K, L and R are £80, £24 and £45 respectively?Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output if it the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?Consider the following graph of y = f(x). E D A Which of the following statements about the function f is true? Select one: O f has an endpoint at E and a y-intercept at B. O f has a global maximum at A and a global minimum at C. O f has a critical point at C and a global minimum at D. O f has a global minimum at A and a y-intercept at D.
- In your city , each police officer has a budgetary cost of $40000 per year. The property loss for each burglary is $4000. The first offecer hired will reduce crime by 40 burglaries and each additional officer will reduce crime by half as much as the previous one. How many officers should the city hire ? Illistrate with a graph with a marginal benifit curve and a marginal cost curve Can someone answer this correctly with an MC and MB graph? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Increasing returns and imperfect competition: (a) The production function for the word processor is Y = X – 100 million if X is larger than 100 million, and zero otherwise. By spending $100 million, you create the first copy, and then $1 must be spent distributing it (say for the DVD it comes on). For each dollar spent over this amount, you can create another copy of the software. (b) The production function is plotted in Figure 6.5. Output is zero whenever X is less than 100 million. Does this production function exhibit increasing returns? Yes. We spend $100 million (plus $1) to get the first copy, but doubling our spending will lead to 100 million copies (plus 2). So there is a huge degree of increasing returns here. Graphically, this can be seen by noting that the production function “curves up” starting from an input of zero, a common characteristic of production functions exhibiting increasing returns. (Constant returns would be a straight line starting…Let y = f(x1, x2)=x11/2 + x1x2 be a firm’s production function, where x1≥0, x2≥0. Write down the firm’s production possibility set, and its input requirement set. Is this production function concave, quasi-concave? Is this production function homogenous? Find its returns to scale when x1=1, and x2=1.