Consider with the cost function producing a single good with the cost function {.. 5, If A = 0 C(A) = 10 + 10A, if A > 0 a) the Firm's Sunk Cost and Fixed Cost. b) Find the elasticity of substitution if Function is given as F(x,y) = CX"y")
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- Suppose that the cost function for a commodity is C(x) = 40 + x2 dollars. (a) Find the marginal cost at x = 4 units. MC(4) = Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 5th unit is predicted to be $ (b) Calculate C(5) – C(4) to find the actual cost of producing 1 additional unit. Need Help? Read It Watch ItA factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"(a) Find the marginal cost function C'(x). C'(x) Use it to estimate how fast the cost is increasing when x = 60,000. | per game system Compare this with the exact cost of producing the 60,001st game system. The cost is increasing at the rate of $ | game system is $| the estimated cost of producing the 60,001st game system found using the marginal cost function. | per game system. The exact cost of producing the 60,001st J. The actual cost of producing the 60,001st game system is --Select-- (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (Round your answer to the nearest cent.) C(x) C(60,000) - $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.
- b) A firm has an average cost functionA(q) =125 +q^2 - 4 q 16where q is the firm′s output. (iv) Write an equation for the total cost function.(v) Hence calculate the level of output for which total costs are minimum.A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?The total cost (in dollars) of producing x food processors is C(x) = 1600 + 40x-0.1x². (A) Find the exact cost of producing the 61st food processor. (B) Use the marginal cost to approximate the cost of producing the 61st food processor. CHEO (A) The exact cost of producing the 61st food processor is $ (B) Using the marginal cost, the approximate cost of producing the 61st food processor is $
- The total revenue function for a product is given by R=655x dollars, and the total cost function for this same product is given by C=19,250+70x+x2, where C is measured in dollars. For both functions, the input x is the number of units produced and sold. a. Form the profit function for this product from the two given functions. b. What is the profit when 25 units are produced and sold?It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake issold for $4.90 each.(i) Make a table showing the total cost and the revenue obtained from producing 20,40,60,80 and 100 cupcakes.(ii) Write algebraic expressions representing the cost C and the revenue R as functions of the number of cupcakes X produced and number of cupcakes X sold respectively.(iii) Graph both functions on the same coordinate axes and from your graph determine the cordinate at which cost equals revenue.If you were a taxi driver, the daily revenue and cost are as the following: Revenue: $250 Variable cost (gas, your labor…): $190 Mortgage payment for car: $70 License Fee: $30 For profit maximization, will you operate your taxi business today? What is the minimum daily revenue to keep the operation in the short run? What is the minimum daily revenue to keep the operation in the long run? Please show calculation formula and/or equation.
- E. A firm has the production function f(T1, 12) = 1750 , 50 What is the marginal rate of technical substitution (M RTS)? (a) MRTS =-1 2.5x, (b) MRTS = -x2/x1 (c) MRTS = -5x2/01 (d) MRTS =-0.5x2/21 (e) MRTS = -0.2x2/21 %3D %3DC(x) = 0.01x-0.3x + 10x gives the cost, in thousands of dollars, to produce x thousand items. (a) Find a formula for the marginal cost. (b) Find C'(0). Give units. (c) Graph the marginal cost function. Use your graph to find the minimum marginal cost, the production level for which the marginal cost is the smallest. (d) For what value of x does the marginal cost return to C'(0)? (a) Find a formula for the marginal cost. c'(x) =D (b) Find C'(0). Give units. c'(0) = (c) Use the derivative of the marginal cost function to find the minimum marginal cost, the production level for which the marginal cost is the smallest. The minimum marginal cost of additional dollars per item produced occurs when thousand items are produced. d) Recall your answer to part b. For what value of x does the marginal cost return to C'(0)? Marginal cost returns to this value of C (x) when x = items are produced.The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given by the following function. )= 4x (x² +27,000) 4x R'(x) = 2 (a) Find the total revenue function if the revenue from 130 devices is $21,660. (b) How many devices must be sold for a revenue of at least $38,000? BECED (a) The total revenue function is R(x)=, given that the revenue from 130 devices is $21,660. (Round to the nearest integer as needed.) (b) devices must be sold to generate a revenue of at least $38,000. (Type a whole number.)