A manufacturer has modeled its yearly production function P (the monetary value of its entire production) as a Cobb-Douglas function P(L, K) = 1.46L0.65K0.45 where L is the number of labor hours, in thousands, and K is the invested capital, in millions of dollars. (a) Calculate  PL  and  PK. PL =        PK =        (b) Find the marginal productivity of labor and the marginal productivity of capital when  L = 140  and  K = 40.  (Round your answers to two decimal places.) marginal productivity of labor        marginal productivity of capital

Q: At a certain factory, the marginal cost (MC) is MC = 3(q – 4)2 dollars per unit when the level of…

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Q: Suppose that the demand for a product is given by q2p=6,000, where q represents the number of units…

A: Suppose that the demand for a product is given by q2p=6,000, where q represents the number of units…

Q: Consider a competitive market in which price adjusts to excess demand or supply a enter and exit the…

A: (i) Given,                                   dpdt=0.5(qD-qs)                    (1)Where,…

Q: Determine the AV at time 9 of $100 invested at time 4 given the accumulation function a(t)=0.05t2+1.

A: Consider the function: Accumulation function,at=0.05t2+1at=0.05t2+1For time 4;…

Q: The manufacturer of a product finds that the marginal revenue is MR(q) = 767 - 67q - 58q². Find the…

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Q: b) If the marginal revenue function for a manufacturer's product is dr = 2000 – 204 – 3q² dq Find…

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Q: Suppose that in a simplified model with proportional taxation consumer’s utility is represented by a…

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Q: The total cost of producing 1 unit of a product is ху C(x, y) = 32 + 6x + 2y + 52 dollars where x Is…

A: We have to find- if labor costs are held constant, find the function that describes the rate at…

Q: Suppose that the marginal propensity to consume is de - 0.7 -.-2y dy (in billions of dollars) and…

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Q: A firm's marginal cost function is C'(x) = x² + 4x + 100 with x representing the number of units per…

A: We will find out the required cost of producing 5 to 9 units per day.

Q: The total cost of producing 1 unit of a product is C(x, y) = 26 + 8x + 6y + AY 56 dollars where x is…

A: Let x be the cost per pound of raw materials and y be the cost per hour of the labor. Part (a)…

Q: Given the utility function, U=∂x+ßy, determine the marginal rate of substitution

A: The given utility function U = ∂x+βy

Q: Find the demand function p, given the marginal revenue function dr/dq below.  dr/dq = 277 - 3q -…

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Q: Find the elasticity of the demand function pq = 18 at p = 3.

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Q: Suppose that the price p of a product and its demand x are related through the price-demand equation…

A: To find the region for which the demand function is elastic.

Q: Find the marginal demand D'(p).

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Q: A division of Vandelay Industries manufactures a deluxe toaster oven. Man- agement has determined…

A: Marginal cost function is given by C'(x) = 0.0003x2-0.12x+20 We have to find total cost so we will…

Q: The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1100 + 13x − 0.1x2 +…

A: Given: The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1100+13x− 0.1x2+…

Q: A manufacturer has determined that m employees will produce a total of q units of product per day,…

A: the marginal-revenue product is given by dR/dm where R is the revenue. Using the chain rule of…

Q: Assume that it costs a company approximately C(x) =716,807+412x+0.019r? dollars to manufacture x…

A: Find the derivative of the cost function to estimate the marginal cost function and then substitute…

Q: Find the production level at which the marginal cost function starts to increase. C(q) = 0.0008q3 –…

A: We want to find when the marginal cost of the function start to increase.

Q: Consider the Cobb-Douglas production function f(x, y) = 200x0.7y0.3. When x = 1000 and y = 500, find…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: The total cost of producing 1 unit of a product is C(x, y) = 36 + 8x + 4y + ху dollars where x is…

A: Given the total cost of producing 1 unit of a product is Cx,y=36+8x+4y+xy44

Q: A manufacturer of mountain bikes has the following marginal cost function: 700 C'(q) 0.8q + 5 where…

A: Here we solve the given problem.

Q: For demand function Qd = a-bP and supply function Qs = dP-c, using Cramer’s rule determine…

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Q: A manufacturer of aluminum doors currently is able to sell 500 doors per week at a price of $75…

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Q: The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1100 + 11x – 0.1x? +…

A: a) Given that C(x)=1100+11x-0.1x2+0.0005x3Differentiating both sides with respect to…

Q: A manufacturer has determined the marginal-cost function dc/dq below, where q is the number of units…

A: To find the average cost of producing 500 units.

Q: A company has determined that its price-demand function for its sale of its product is given by…

A: Price - demand function :  p + 0.05 x = 85  x =  ( 85 - p ) / 0.05

Q: Find the demand function p, given the marginal-revenue function dr/dq below. dr = 269 – 9q - 1.29 dq…

A: Here, the given marginal revenue function is: drdq=269-9q-1.2q2...(1) where r is the revenue…

Q: The total cost of producing 1 unit of a product is C(x, y) = 36 + 8x + 4y + XY 44 dollars where x is…

A: The function is Cx,y=36+8x+4y+xy44.   Partially differentiate the function with respect to x.…

Q: In the manufacture of a product, fixed costs per week are $4000. Fixed costs are costs, such as rent…

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Q: A firm faces a demand function of the form P = 90 – 2Q? (a) Plot the graph for their total revenue…

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Q: 15 Find the marginal-revenue function if the demand function is p = In (q + 3) dr %3D dq

A: TO FIND MARGINAL REVENUE FUNCTION 1.REVENUE r(q) = pq 2.substitute values and solve 3.MARGINAL…

Q: 14. Show that the demand function D(p) =alp', where a and b are positive real numbers, has a…

A: Solution is given below:

Q: Given a cost function C(x) as C(x)=120+2x, calculate the marginal average cost when x=5, and use…

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Q: Given a cost function C(x) as C(x)=10,000+20x. Calculate the marginal average cost when x=500, and…

A: To estimate the average cost using differentiation.

Q: A company determined that the price-demand and cost functions for selling x units of a certain…

A:

Q: Find the consumer surplus for the demand curve P = 420 – 10q when g * = 20 items are sold at the…

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Q: A smaller theater has a seatine caracity of,000 nhen ta Ticket price is$20 attendenceis ,500 Aftera…

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Q: Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.002x° +0.07x + 18x+600,…

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Q: Suppose that the marginal propensity to save is ds In(y + 1) dy - 0.93 - (In billons of dollars) y…

A: This is Separable differential equation

Q: Particular values of the marginal cost function of Kuddly Kites, a company that sells kites shaped…

A: Basic:  -------------------------------------------------------------------------- Given:  n   =…

Q: Given cost and price (demand) functions C(q) = 120q + 43,100 and p(q) = - 1.8q + 860, what is the…

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Q: Find the PV of an income stream that pays out continuously at a rate R(t) = $5000e0.1t /year for 7…

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Q: Assume that it costs a company approximately C(x)=760,744+435x+0.019x^2 dollars to manufacture x…

A: differeniate w.r.t x

Q: Assume that it costs a company approximately C(x) =664,641+580x+0.019 x² dollars to manufacture x…

A: The cost function is c(x)=664641+580x+0.019x2

Q: A liquid form of antibiotic manufactured by a pharmaceutical firm is sold in bulk with a total…

A: Let's find.

Q: A software entertainment company recently ran a holiday sale on its popular software program Using…

A: Let's find.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.