A firm has a total cost function C(Q) = 100 + 8Q - 8Q 2 + Q 3 and demand function is Qx d = 33 – 2px Required: %3D (i) Calculate the firm's marginal cost when Q = 5
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![A firm has a total cost function C(Q) = 100 + 8Q – 8Q 2 + Q 3 and demand function is Qx d = 33 – 2px
Required:
(i) Calculate the firm's marginal cost when Q = 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1718efe-92d0-4ded-b90d-a27e96ca5142%2Fbd2a01da-8fa0-438a-ad4f-c0311e6c163a%2Fslcopxc_processed.jpeg&w=3840&q=75)
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- A firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q +0.25Q 2 . Use these two functions to form the firm's profit function and then determine the level ofoutput that yields the profit maximum. What is the level of profit at the optimum?A firm has a linear demand function for it's product.When the price of the product is sh.20,the quantity demanded is 40 units.When the price increases to sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is giving by: Mc = 40q- 2q^2+2 Fixed cost = 5 million Where q= quantity demanded,Mc = marginal cost(sh.million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at the maximum profitSANUMARC produces fingerlings for sell. The quantity x (kg) of these fingerlings demanded each week is related to the wholesale unit price p by the equation P = − 0.006x + 180 The weekly total cost incurred by SANUMARC for producing x kgs of fingerlings is C(x) = 0.000002x3 – 0.02x2 + 120x + 60,00 a. Find the marginal cost function C, b. Find the marginal revenue function R’ and the marginal profit function P’ c. Compute P’(2000) and interpret the results.
- A noncompetitive firm has the following total cost function: TC = 3Q³ – 40Q² + 250Q + 900 If the demand function for the firm's product is P = 2000 – 40Q. Find the firm's profit maximizing level of output and profit.A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (b) Find a function for the average cost of this company?Эшestion 1 A computer retailing company specializes in the sale of jump drives to community college tudents. The demand function for jump drives is p=2x+10x+1000 dollars For the samne company the average cost function is given as: ē = 2x +36x-1600- 20 * dollars Where p is the price in dollars and x represents units of output. 1) i1) Find the price and output that will maximize profit. Find the maximum profit
- A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 Find the marginal cost analytically, and draw its graph Find the marginal revenue analytically, and draw its graph Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. Write the profit function and draw its graph Is the profit function concave up or concave down?The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 37x - 0.07x2. (a) Find the marginal cost function C'(x). C'(x) = (b) How fast is the cost going up at a production level of 100 teddy bears? When they produce 100 teddy bears, the production costs are increasing at a rate of x dollars per teddy bear In other words, the cost to produce the 101st teddy bear is approximately dollars (c) Find the average cost function C, and evaluate C(100). C(x) = C(100) = So when they produce 100 teddy bears, the average cost per teddy bear is x dollars. (d) Fill in the blanks: Since the marginal cost is less than the average cost per unit, increasing production from 100 teddy bears will cause the average cost per unit to decrease.Suppose that the total cost function of a firm is TC = 1000 + 10Q2c) At the minimum output, what is the value of total cost d) Find the marginal cost (MC) function
- A firm has a linear demand function for it's product.When the price for the product is Sh.220,the quantity demanded is 40 units.When the price increases to Sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is given by; MC = 40Q-2Q^2+2 Fixed cost = Sh. 5 million Where Q= quantity demanded, Mc= marginal cost(cost in Sh. Million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at a maximum profitThe “Sad Student” Company finds that it costs a total of C(q) = 9720 + 500q -1.5q2 + 0.005q3 Dollars to produce q lots of its latest board game named “Calculus Teacher Shooter”, each lot consisting of 100 games. A)Analyze the behavior of cost function B) Interpret the constant term in the expression of C(q) c)Analyze the behavior of the marginal cost as a function of the output q D)Interpret the effect of the constant term in the expression of total cost function on marginal cost function E)Analyze the behavior average cost function F)Analyze interaction of marginal cost and average cost numerically and derive the formula of this relationship with respect to relevant mathematical economics theory and interpret your formulaThe cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula Cx) - 100 + 40x - 0.08. (a) Find the marginal cost function C(x). Cx) = 40 - 0.16x Use it to determine how fast the cost is going up (in s) at a production level of 100 teddy bears $ 24 per teddy bear Compare this with the exact cost of produong the 101" teddy bear (in ). The cost is increasing at a rate of s 24 per teddy bear. The exact cost of producing the 101" teddy bear is s Thus, there is a diference of (b) Find the average cost function C, and evaluate č100) (in s). C100) -s x per teddy bear What does the answer tell you? per teddy bear. The average cost of producing the first hundred teddy bears is s Eter an tuber