Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?
Q: What combination of goods x and y should a firm produce to minimize costs when the cost function is…
A: Minimize C (x,y) = 6x2 + 10y2 - xy +30 Subject to: x+ y = 34 The Lagrange equation will be: L = 6x2…
Q: f(x1, 12) = (x1 - 1)0.25x9-5.
A: We are going to use the relationship between upward sloping marginal cost curve and supply curve to…
Q: Given the production function f(x,x2) = x,ax, calculate the profit maximizing demand and supply…
A: The optimal degree of utilisation of a firm's inputs might help it reach the point of profit…
Q: (b) If the average cost function of a good is 16 4· AC = 12x + 4 + find an expression for marginal…
A: The total cost incurred by a firm operating in a market includes fixed costs and variable costs.…
Q: Given the following cost function, determine the underlying production function. 1 2C(m, w, y) =…
A: The cost function shows the functional relationships between factors payments and outputs. It shows…
Q: A firm produces output y from inputs x1 and x2 whose prices are given as w1 = 1 and w2 = 1…
A: Answer- Given in the question- The production function = y = x11/2 x21/2 Inputs x1 and x2 Prices w1…
Q: Consider a firm with a production function given by y = a ln x1 + ß lIn x2 with a, ß E (0,1) which…
A: The production function shows the technical relationship between input factors and output. It can be…
Q: Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its…
A: The marginal revenue (MR) measures the addition to the total revenue when one more output unit gets…
Q: A company can sell x units of a product when the price is p = D(x) = 5.00 – 0.006x dollars. The…
A: Marginal profit is the profit earned by a firm after the production and sale of an additional unit.
Q: Find the marginal cost function. C(x) = 174 + 1.7x The marginal cost function is C'(x) = ||.
A: The cost function is: C(x) = 174+1.7x
Q: The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) in a very…
A: Given wage rate of labor (w) = 2 capital rent (r) = 5 Price of Product (P) = 0.75 Total Cost (TC) =…
Q: Consider a firm with the production function ƒ(x1, x2) = x₁/²x2. The price of the two inputs is w₁ =…
A: Given information Production function q=X10.5X2 W1=2--- price of factor X1 W2=1---- price of factor…
Q: Suppose that production for good X is characterized by the following production function, Q =…
A: In the short run, all factor of production are not variable. The at least one factor is fixed and…
Q: Suppose the production is characterized by the function Q(K,L) = 50K05L05. The price of labor is $5…
A: Cost is minimized at the bundle of inputs where marginal rate of technical substitution is equal to…
Q: If the average cost function of a good is 13 AC = 2Q + 6 + 6 Find an expression for MC. If the…
A: MC, marginal cost is the additional cost incurred with an additional unit of output produced.
Q: Consider a beekeeper. The beekeeper has the following production function where the input is the…
A: Hi Student, Thanks for posting the question. As per the guideline, we are providing answer for the…
Q: A firm uses two inputs to produce a single product. If its production function is Q = x¹/4y¹/4 and…
A: Here, production function:- Q=x14y14 it sells at the price=$1 each input=$4
Q: If the production function is given by f(x1, x2) = min{x1, x2} + min{x3, x4}, what is the minimum…
A: A production function in economics describes the technological relationship between the quantities…
Q: Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its…
A: Hi, thanks for the question. Since there is multiple subparts, I will answer for the first question.…
Q: Let the production function be Q = 4* K1/4 L1/4 assume that both factors are variable. (a) Derive…
A: a.Given,Production function
Q: Given the input-output matrix below, find the output matrix if final demand changes to 500 for…
A: We are going to find the Leontief matrix and output matrix to answer this question.
Q: Find the marginal cost function. C(x) = 174 + 1.7x The marginal cost function is C'(x) = ||:
A: The total cost function is: Cx=174+1.7x
Q: A firm faces the production function Q = 6K0 L0.5. If it can buy input K at £32 a unit and input L…
A: Cost is minimized when marginal rate of technical substitution equals price ratio of inputs.…
Q: A firm can manufacture a product according to the production function Q=3K1/2L1/2, and capital is…
A: When capital is fixed at 4, the production function in terms of labor(L) is;…
Q: A company can manufacture a product according to the production function Q=3K1/2L1/2, and capital is…
A: The cost of production is delineated in social science because the expenses spent to urge the…
Q: firm has the following production function: q = 8KL, where q is the weekly output, K is the number…
A: Firm's production function: q = 8KL K=10 machines Every machine rents for $50,000 per week and every…
Q: Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm…
A: Disclaimer:- as you posted multipart questions we are supposed to solve only the first 3 questions.…
Q: The prices of inputs x1; x2; x3; x4 are p1 = 2; p2 = 2; p3 = 5; and p4 = 2. If the production…
A: The prices of inputs x1; x2; x3; x4 are p1 = 2 p2 = 2 p3 = 5 p4 = 2. If the production function is…
Q: Let the production function of a firm is given as q=(x0.5 +y0.5)2 Where x and y are inputs and wx is…
A: a .) Demand condition for the factors of production is achieved at the point where the production is…
Q: Consider a firm that has the following production function: Y = min{x₁, ½x2}. The inputs' prices are…
A: Both inputs are used in the fixed proportion. This is a case of complementary inputs.
Q: Consider a beekeeper. The beekeeper has the following production function where the input is the…
A: Table shows the quantity of honey and quantity of apples manufactured at each number of beehives –…
Q: Production Function: q=32n+2nl+16l n is the size of net l is the hours of labor employed Total…
A: Given Production function: q=32n+2nl+16l ... (1) Total cost function: C=14+2n2+4l2 ...…
Q: A firm has the following production function: q=L1/2⋅K1/2 Assume the firm must pay each unit of…
A: In the short run, capital is fixed at 4 units and in the long run both inputs are allowed to vary.…
Q: Q.No.3. Consider the production function:…
A: Q.NO.3. Given The production function: Y = 0.75X + 0.0042X² – 0.000023X³ (a) dY/dX = 0.75 +…
Q: The prices of inputs x1; x2; x3; x4 are p1 = 2; p2 = 2; p3 = 5; and p4 = 2. If the production…
A: Let us say, A = min {x1, x2} and B = min{x3, x4}. Then, the production function looks like A + B.…
Q: The cost minimizing equilibrium condition is a. MPL/PL = MPK/PK. b. PL = PK. c. MPL = MPK.
A: Marginal rate of technical substitution refers to the rate at which the firm can replace inputs to…
Q: Suppose the production of airframes is characterized by a CobbDouglas production function: Q =LK.…
A: The Cobb-Douglas (CD) production function is an economic production function that describes the…
Q: Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm…
A: Dear student, you have asked multiple sub-part questions in a single post.In such a case, I will be…
Q: Let the production function of a firm is given as q=(x0.5 +y0.5)2 Where x and y are inputs and wx…
A: a .) Demand condition for the factors of production is achieved at the point where the production is…
Q: For a unit demand function p=24-8x where x is the number of units and p is the price in tk,finds tge…
A: Sales function is demand function itself. Profit function is π = TR - TC
Q: According to the information below, which of the following is (are) true? Units of variable input…
A: The total cost of production is the summation of all the fixed cost as well as the variable costs in…
Q: f the average cost function of a good is AC = 2Q + 6 + 13 Find an expression for MC. If the current…
A: AC(average cost) is the TC(total cost) divided by Q(quantity). MC(marginal cost) is the change in TC…
Q: The prices of input (x1,X2,X3,X4) are (4, 1, 3, 2) a. If the production function is given by…
A: When the production function is of perfect complement, then all the inputs are required to be…
Q: Consider a beekeeper. The beekeeper has the following production function where the input is the…
A: Hi Student, Thanks for posting the question. As per the guideline, we are providing answer for the…
Consider the production function:
Y = 0.75X + 0.0042X2 – 0.000023X3
If input
Step by step
Solved in 2 steps
- If the production function of a firm is P = 60kl, where the price per unit of input k is $10 and I is $5, 1. Count the units of each input so that the total cost incurred is minimum. 2. If the firm wants to produce 120 units of output, what is the minimum total cost?Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x)=7000+6x+0.01x^2+0.0002x^3. (a) Find the marginal cost function. (b) Find the marginal cost at x=100 (c) Find the cost at x=100Consider a production function Q = (K1/2) + (L1/2) + (M1/2) where L, K, M represent labor, capital, and material. Input prices for L, K, M are 1, 1, and 1. The firm wants to produce 12 units of output. a) What is the total cost if K = 4? b) What is the total cost if K = 4 and L = 9?
- Find the supply function and the input demand functions for the CES production function: f(x1,x2)=A(αxρ1 +(1−α)xρ2)β/ρ, where A > 0, β > 0, 0 < α < 1, and 0 ̸= ρ < 1.1. 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?The unit price of a product is given by P(X) = 200 - 0,01X and the total cost function C(x) = 50X + 20.000 How many items should be sold to maximize profit?
- Suppose a firm with a production function given by Q = 30K0.5L0.5 produces 1,800 units of output. The firm pays a wage of $50 per unit and pays a rental rate of capital of $120 per unit. MPL = 15K0.5/L0.5 ; MPK = 15L0.5/K0.5 . How many units of labor and capital should the firm employ minimize the cost of producing 1,800 units of output, and what would be the total cost?Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?For the cost function C(Q) = 75 + 4Q + 2Q2, the marginal cost of producing 5 units of output is:
- Suppose that production for good X is characterized by the following production function, Q = K0.5L0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $15 and the per-unit wage, w, is $25, then the average fixed cost of using 9 units of capital and 81 units of labor is $75. incalculable since there is insufficient information to determine the average fixed costs. $80. $5.Suppose the cost function is C(Q) = 50 + Q − 10Q2 + 2Q3. What is the marginal cost of producing 10 units?The weekly marginal cost of producing x pairs of tennis shoes is given by the following function, where C(x) is cost in dollars. C′(x)=15+500x+1 If the fixed costs are $4,000 per week, find the cost function. What is the average cost per pair of shoes if 1,000 pairs of shoes are produced each week?