Benefit function: B(R) = 500R - 15R²Cost function: C(R) = 10R2Control variable: Ra. Take derivatives to obtain the Marginal Benefit function (MB) and the MarginalCost function (MC).b. Solve for the value of the control variable R that maximizes Net Benefits N(R).c. Calculate the value of maximum Net Benefits using the value of R obtained in partb (i.e., N(R*)).

Given:Benefit function: B(R) = 500R - 15R2 Cost function: C(R) = 10R2 a. MB = 500 - 30RMC = 20RTo…

Answered: Benefit function: B(R) = 500R - 15R²…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 8E

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Exercise 1 A consumer's utility function is u(x, y) = x²y³ and the budget constraint is prx +Pyy ≤ w, where the parameters pr, Py and we are all strictly positive. (a) Solve the consumer's utility maximization problem. (b) Use the envelope theorem to estimate the change in the indirect utility function (i.e., the problem's value function) when the price py is changed to py + e, with e > 0.
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How did you arrive at -0.15 here? MB = (1/3)(90 - 0.6(9,588 + g)½- 0.3g½)To find Susan's optimal contribution, we need to calculate her marginal benefit, which is the derivative of MB with respect to g:MB' = (1/3)(-0.15(9,588 + g)(-1/2) - 0.15g(-1/2))
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Please solve the screenshot and explain each step clearly using typefont. Thank you!
Please help me to solve the question (d) (e) below.
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Philip sells homegrown heirloom tomatoes at a local farmer's market. Suppose for the past several weeks, Philip has been selling his tomatoes for $2.25 per pound and he has been selling 90 pounds of tomatoes each week. Suppose this week he drops the price of the tomatoes to $1.75 per pound and as a result of the price drop, he is stilling 110 pounds of tomatoes. (a) Using the midpoint rule, what is the percentage change in the quantity of tomatoes sold from the drop in price? % (Enter your answer as a percentage with no decimals rounded to the nearest whole percent (i.e. 33% or -10%)) 4 (b) Using he midpoint rule, what is the percentage change in the price of Philip's tomatoes? % (Enter your answer as a percentage with no decimals rounded to the nearest whole percent (i.e. 33% or -10%)) (c) Using the midpoint rule, what is the price elasticity of demand for Philips, tomatoes? (Enter your

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