Find the marginal revenue function for the total revenue function given by 1 TR(Q) = 500Q- Find the marginal cost function for the total cost function given by TC(Q) = Q³ – 90Q² + 7,500Q
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- A firm has the following information on production and costs from past data: Output (Y) 6 12 18 Total Cost (TC) 2775 5361 8199 If the total cost function is known to be TC = aY'+ bY² + kY + ƒ , and the demand for the product of the firm is Y = 320- (1/2). P answer the following: • Determine the coefficients of the cubic cost function. • Derive all cost and revenue curves and the profit function. • Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all points. • Calculate the break even and profit maximizing levels of output and price. • What is the relationship between price, marginal revenue and own price elasticity of demand at the profit maximization point.A firm has the following information on production and costs from past data: Output (Y) 0 12 18 6 Total Cost (TC) 9 2775 5361 8199 If the total cost function is known to be TC = aY' + bY ² + kY + ƒ , and the demand for the product of the firm is Y = 320-(1/2). P answer the following: • Determine the coefficients of the cubic cost function. • Derive all cost and revenue curves and the profit function. Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all points. Calculate the break even and profit maximizing levels of output and price. • What is the relationship between price, marginal revenue and own price elasticity of demand at the profit maximization point.10) Find the marginal and average functions for the following total functions and graph the results. Total – cost function: C = 3Q² + 7Q + 12 Total – revenue function: R = 10Q – Q² %3D Total – product function: q = aL + bL² – cL³
- = Suppose that the marginal revenue for firefighting protective clothes is MR marginal cost is MC = 3.5x + 15 with a fixed cost of $295. Assume R(0) = 0. a) How many units will result in a maximum profit? x = b) Find the revenue function. R(x) c) Find the cost function. C(x) 337.5 4x and the d) What is the maximum profit (to the nearest dollar)? The maximum profit isdefine total fixed costs1. Find the cost minimizing input demand functions (x¿(w,q)) and the cost function (c(w,q)) for the following production functions: 1/3 21382 a. f(x) = x₁
- (a) Find the conditional input demand function for inputs 1 and 2, as well as the cost function for this firm. (b) What is the firm's marginal cost when it is producing y units of output?The total cost functionbof a firm is define by TC=35+5Q-2Q+2Q,fine the marginal cost of the firm when it's output level are at 3and 5 units respectively10) Find the marginal and average functions for the following total functions and graph the results. Total – cost function: C = 3Q2 + 7Q + 12 Total – revenue function: R = 10Q – Q? Total – product function: q = aL +bL² – cL³
- Given a firm's cost function C = F(x) = ax² +bx + d: Find the firm's Average cost funetion (A(x) and Marginal cost function M(x). O Is C(x) more appropriatc as a long-run or short-run cost function? Explain. Determine whether the Marginal cost function is strictly monotonic for a> 0, b>0, and d> 0. Does this finction have an inverse for economically meaningful values of x? If yes, find dx/dM. If not, show/explain what restriction would be necessary for inverse to exist. a. b. c. d.14. The research department of Acme, Inc. has determined the marginal cost function for one particular item to be m(x) = 0.12e0.04x dollars per item, where x is the number of items produced. If Acme's fixed costs amount to $3,000, find the cost function, C(x), for the company.The “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 formula