Consider the following cost minimization problem: Minimization CT = wL + rK Hold it: q= L1/2 K1/2 a) Obtain the long-run cost function b) If K = 9 and w = 1, obtain the long-run cost function
Q: Consider the following short run cost function: TC = 4Q3 - 24Q² + 16Q + 100 Derive the expressions…
A: Given Total cost TC= 4Q3-24Q2+16Q+100 We have to find the marginal cost and average total cost of…
Q: For the cost function C(x) 125x + 375 x+7 where C is in dollars and x is the number produced in…
A:
Q: Consider the following production function: Q=KªLB a) Derive the cost function b) Draw the AC and MC…
A: * ANSWER :- * A) at eqm, MRTS = w/r MRTS = MPL / MPK
Q: The average cost for a firm is given as a function as follows:- AC 3Q²-6Q + 20 = Calculate the Total…
A: WE Know that the average cost simply defined as the total cost per unit of output. That is :- AC =…
Q: What are “Adam Smith’s laws of the market” What does Adam Smith think is behind the economy/market?…
A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…
Q: The total cost of producing one unit is $100 The total cost of producing two units is $150 At a…
A: It is given that, the total cost of production of 1st unit = $100. The total cost of production when…
Q: Ing fong TC = 8Q³ - 96Q² + 32Q Derive the expressions for marginal cost and average cost. What is…
A: Average cost: ‘average cost’ is the ‘total cost’ divided by the number of units of the good. It…
Q: Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a)…
A: TPL = 180L2 - 3L3 APL = TP/L = 180L - 3L2 MPL = CHANGE IN TP/CHANGE IN L = 360L - 9L2
Q: If you have the data of Total cost (TC)= 15, 25, 30, 40, 55, 75, 100 against units of output (Q) =…
A: Marginal cost is the cost which incurred by producer when they produce one or more additional unit .…
Q: For a production function at a given level of output in the short run, the marginal product of labor…
A: Marginal product of labor refers to the extra unit of output produced when an additional unit of…
Q: Suppose that in the short-run (Labor is the only variable input) when output equals 50, (1) the firm…
A: Cost refers to the value or expenditure incurred in the production, acquisition, or consumption of…
Q: Given the following costs functions C1=5q C2=5q+5 C3=5q-5 1. Calculate the marginal costs functions.
A: Marginal cost is the change in the total cost of a firm that arises when the firm produces one more…
Q: You are given the following long-run cost function: TC = 150Q - 20Q2 + 1.8Q3 What level of Q will…
A: Economies of scale is where slope of long run average cost <0, while disceconomies of scale comes…
Q: 39) If the marginal cost curve is below the average variable cost curve, then A) average variable…
A: Economics is a branch of social science that describes and analyzes the behaviors and decisions…
Q: i)derive the Total Cost Function, TC(q) ii) draw the Isoquant for the given level of output iii)…
A: Production function : q = 4L + 5K Input prices : w =2 , r = 4 Output level,, r = 4
Q: Does a relationship exist between increasing returns to scale and long-run average cost? Ex with the…
A: Economies of scale or increasing returns to scale are utilized conversely; both implies to a fall in…
Q: (a) Suppose we have the following production function: Q = K²/³12/3. Does the technology have…
A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…
Q: Which cost concept includes both explicit and implicit costs? a) Total cost b) Variable cost c)…
A: In financial matters, understanding various sorts of costs is significant for dissecting business…
Q: (a) Find the number of hours for which each cost function will give the same cost. hours (b) !f the…
A: Fron the provided data, Acme (x); 140+10x Bell (x);200+4x
Q: The average cost function for skateboards. AC = (q^3 - 30q^2 + 350q) / q AC = q^2 - 30q + 350 Draw…
A: The graph of the average cost function AC=q2−30q+350, along with labeled critical points and the…
Q: (4) w = 3. firm's production function is F(K, L) = 2√/K + L. Factor prices are r = 2 and (a) Find an…
A: The marginal product of labor represents the increase in output as a result of an increase in labor…
Q: Given the following production cost function: TC=5+29 R1 R² +0.5 R³ TC: total cost in '00 (hundreds)…
A: Production costs are the costs a company incurs while creating a something or providing a service…
Q: eturns to scale
A: Option (A). Q = 5L2 + 4K3/2L When both inputs are doubled, new production function is Q* = 5 x (2L)2…
Q: 1. Find the cost minimizing input demand functions (x₂ (w, q)) and the cost function (c(w, q)) for…
A: The production function estimates the required inputs to produce the target output level. It defines…
Q: 7. Given the Average Coat function: AC = x2 + 2y² - 2y- 6x + 207 – 2x %3D 7.1 Find the quantities of…
A: In a market, an optmial level of output, at which average cost is minimized, is the one at which…
Q: A firm can manufacture a product according to the production function Q = F(K, L) = KO.50LO.50. (a)…
A: The production function refers to the functional relationship between the given input and the…
Q: I need help with this homework question For the problem in the picture: i)derive the Total Cost…
A: ISO-Quant: Iso -Quant shows different combinations of capital and labour such that each combination…
Q: A firm's short-run cost function is C(a) = 240q – 69° + 0.6q° + 600. Determine fixed cost, F;…
A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…
Q: (e) Let P = $600. Find optimal output where r = $200 and w= $300. You can do this in a table or…
A: Break even price is that price level where total profits = 0 => Total Revenue - Total Cost = 0…
Q: For Questions 24 to 28, consider the following total cost function: TC = 0.2q° + 6q + 50 where TC is…
A: In a market, average total cost, marginal cost and other types of cost can be determined with the…
Q: I need help with this homework problem. For the problem in the picture: i)derive the Total Cost…
A: The production function Input price: wage for labor (w)= $8, rent r = $24 Output q=12The cost…
Q: Introduction to Calculus in Economics: Calculus is a powerful tool used in economics. One of the…
A: The Average Cost is the per unit cost of production acquired by separating the total cost (TC) by…
Q: Consider the following cost function: C(Q) = 1000+0.1Q I| Calculate total costs when Q=100 O 1,001…
A: Total cost function shows the relationship between cost and output produced. To determine cost at a…
Q: (a) Suppose we have the following production function: Q= Suppose K is fixed in the short- run at…
A: DISCLAIMER “Since you have asked multiple questions, we will solve the first three questions for…
Q: QUESTION 12: Let the production function be as follows Q = K2/3L¹/3 Find the cost-minimizing level…
A: Cost minimization problem of the producer: For the given output level of the firm and per unit cost…
Q: The production function is f (L, M ) = 5L1/2M 1/2, where L is the number of units of labor and M…
A: The production function is given as L is the number of labor units.M is the number of machines. The…
Q: Give the formulas for and plat average fixed cest, AFC, marginal cast, MC, average variable cost,…
A: Cost curves are graphical representations of the relationship between the quantity of goods or…
Q: Mr. Ali decided to buy some sandwich and burger for his family. As he found the price of sandwich is…
A: Demand is the willingness and ability of consumers for consuming and buying goods and services at…
Q: For the cost function 125x + 375 C(x) = x+7 where C is in dollars and x is the number produced in…
A: Here we are given the cost function. A cost function is the function of output, and it gives the…
Q: Compute the average variable cost, average cost, and marginal cost for each function.
A: Total cost is the cost that is incurred in production of a hiven level of output.Variable cost is…
Q: a= min[x,y]^(1/2) a)Draw isoquants for a = 1, a = 4 and a = 9. b)What kind of returns to scale does…
A: Production refers to the process of using inputs to make useful output. The functional relationship…
Consider the following cost minimization problem:
Minimization CT = wL + rK
Hold it: q= L1/2 K1/2
a) Obtain the long-run cost function
b) If K = 9 and w = 1, obtain the long-run cost function
Step by step
Solved in 3 steps
- 86. Average and marginal costs. The total daily cost (in dollars) of producing x city bikes is given by C(x) = 500 + 2x + 0.2x² (A) Sketch the graphs of the average cost function and the marginal cost function on the same set of coordinate axes. Include any oblique asymptotes. (B) Find the minimum average cost.2. Find the total cost function given, the fixed costs are $200 and the variable cost per unit is a quadratic function with vertex (50,100) and v-intercept (0,110).Which of the following is an example of an implicit cost? A) the cost of fuel and materials. B) the cost of fertilizer for a farmer C) wages paid to workers D) the economic depreciation of capital equipment the business owns
- Assume that C(x) is in dollars and x is the number of units produced and sold. For the total-cost function C(x)=0.01x² +0.4x + 50, find AC and C'(x) when x = 60 and Ax = 1. AC $ (Simplify your answer. Type an integer or decimal rounded to two decimal places as needed) C'(x) when x= 60 is $ (Type an integer or a decimal) per unit(a) For the cost function C(w1, w2, y) = 2y²w} w, calculate the Allen elasticity of substitution between the two inputs at the cost-minimizing input point (xf(w1, w2, y), a(w1, w2, y)). (b) Consider the production function f(r, y, z) = Vry + rz+ yz. Find the scale elasticity SE at (x, y, z) = (1,2, 3), (5, 1,6), (6, 6, 6) and determine if the pro- duction function is IRTS, CRTS, or DRTS locally at each point. (c) A profit maximizing firm in the market operates where the production exhibits decreasing return to scale (DRTS). Is this market in its long-run equilibrium? Justify your answer. (d) Suppose that there are the infinite number of potential firms that produce the identical output good y under the cost function C(y) = + 3. Assume free entry and exit. Find the long-run equilibrium output price p, the amount of the output that each firm in the market produces in the long-run equilibrium, and the value of profit that each firm earns in the equilibrium.Suppose a firm has the following production function Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8 = (16/Q)+ 4√? (b) Draw the SRAC curve(c) By solving the first order conditions that the global minimum of production is 4(d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path(e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.
- Assume the following total cost function: Total Cost $75 1 105 128 What is the average fixed cost of producing 2 units? What is the marginal cost of producing 2 units?Introduction to Calculus in Economics: Calculus is a powerful tool used in economics. One of the initial applications areas is the study of a firm, a topic in microeconomics. An important function is the cost function function C (z), the cost of producing z items (of whatever they are selling). This question deals with just the cost function C (z). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (z) = 5z – 8/I – 3. Find the production level that minimizes the average cost per unit. The number of units that minimizes the average cost is NumberSuppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph TPL, APL, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (iii) the maximum value of MPL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…
- Consider the following cost function: 3 C=0.2q³-6q² + 80q + 150. (Enter a numeric response using a real number rounded to two decimal places.) When output is 19 units, average cost is $ When output is 19 units, marginal cost is $ The output level where average variable cost equals marginal cost is units.Fill in the blanks with: (a: rising) (b: at a minimum) (c: at a maximum) (d: falling) (e: constant) 1: When marginal cost is less than average variable cost, average variable cost is: 2 When marginal product is greater than average product, average variable cost is: 3: When marginal product is negative, total product is: 4: As total output increases average fixed cost is: 5: When marginal cost is at a minimum average product is:2) The cost price of a Saturn is $13 000. When the dealer sells each car for $25 000, he sells 21 cars per month. For each reduction of $1000 in the selling price, the dealer sells 3 more cars each month. a) Determine the Profit equation for this function. b) Explain how the profit function was determined. Explain each variable. c) Determine the selling price of a car for maximum monthly profit.
