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Your firm's research department has estimated your total revenues to be
and your total costs to be
.
What level of Q maximizes net benefits?
(Note that the marginal functions are MR(Q) = 30,000 - 160Q and MC(Q) = 40Q)
Step by step
Solved in 2 steps
- Your firm's research department has estimated your total revenues to be R(Q) = 30,000Q - 80Q^2 and your total costs to be C(Q) = 1,000 + 20Q^2 (a) What level of Q maximizes net benefits? (Note that the marginal functions are MR(Q) = 30,000 - 160Q and MC(Q) = 40Q) (b) what is the marginal benefit for the level of Q you computed? (c) what is the maximum level of net benefits?You are the manager of a firm that specializes in small single-board widgets. Your goal is to determine the number of units (Z) that must be produced and sold by your firm each month in order to maximize profits. The total benefits (revenues) and costs to your firm of producing various quantities are given in the first three columns of the following table. Based on this scenario, complete the table and answer the accompanying questions: Control Variable Z Total Benefits B(Z) Total Cost C(Z)0 0 01 200 102 380 303 540 604 680 1005 800 1506 900 2107 980 2808…For a certain company, the cost function for producing x items is C(x)=30x+200 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050. The maximum capacity of the company is 170 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! 1. Assuming that the company sells all that it produces, what is the profit function? P(x)= ? 2. What is the domain of P(x)? 3. The company can choose to produce either 80 or 90 items. What is their profit for each case, and which level of production should they choose? Profit when producing 80 items=? Profit when producing 90 items=?
- Suppose that you can purchase satellite TV service for a fixed monthly fee of $79, no matter how many hours of TV you watch. Assuming that the principle of diminishing marginal benefit applies to watching TV, the optimal (efficient) number of hours of TV to watch per month is: Group of answer choices Zero The number of hours where marginal benefits are zero. The number of hours where marginal cost is lowest. The number of hours where marginal benefits are maximized.For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−90)^2+4,050. The maximum capacity of the company is 130 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! 1. Assuming that the company sells all that it produces, what is the profit function? P(x)= 2. What is the domain of P(x)? 3. The company can choose to produce either 50 or 60 items. What is their profit for each case, and which level of production should they choose? 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?Your firm’s research department has estimated your total revenues to be R(Q) = 30, 000Q − 80Q2 and your total costs to be C(Q) = 1, 000 + 20Q2. (Note that the marginal functions are MR(Q) = 30, 000 − 160Q and MC(Q) = 40Q). What level of Q maximizes net benefits? What is the marginal benefit and marginal cost at this level of Q? What is the maximum level of net benefits? What is another word for net benefits in this example?
- Your firm's research department has estimated your total revenues to be R left parenthesis Q right parenthesis equals 30 comma 000 Q minus 80 Q squared and your total costs to be C left parenthesis Q right parenthesis equals 1 comma 000 plus 20 Q squared. What level of Q maximizes net benefits?You are the manager of a firm that specializes in small single-board widgets.Your goal is to determine the number of units (Z) that must be produced and sold by your firm each month in order to maximize profits. The total benefits (revenues) and costs to your firm of producing various quantities are given in the first three columns of the following table. Based on this scenario, complete the table and answer the accompanying questions: Control Variable (Z) Total Benefits B(Z) Total Cost C(Z) Net Benefits N(Z) Marginal Benefit MB(Z) Marginal Cost MC(Z) Marginal Net Benefit MNB(Z) 0 0 0 1 200 10 2 380 30 3 540 60 4 680 100 5 800 150 6 900 210 7 980 280 8 1040 360 9 1080 450 10 1100 550 A. Graph the total cost and total benefit curves.B. On another graph, plot the points for the marginal cost, marginal benefit, and marginal net benefit.C. Show how the two…You are the manager of a firm that specializes in small single-board widgets.Your goal is to determine the number of units (Z) that must be produced and sold by your firm each month in order to maximize profits. The total benefits (revenues) and costs to your firm of producing various quantities are given in the first three columns of the following table. Based on this scenario, complete the table and answer the accompanying questions: Control Variable (Z) Total Benefits B(Z) Total Cost C(Z) Net Benefits N(Z) Marginal Benefit MB(Z) Marginal Cost MC(Z) Marginal Net Benefit MNB(Z) 0 0 0 1 200 10 2 380 30 3 540 60 4 680 100 5 800 150 6 900 210 7 980 280 8 1040 360 9 1080 450 10 1100 550 a. How many units (Z) maximize net benefits?b. What is the relationship between marginal benefits and marginal costs at the level of Z you determined above?c. Graph the total…
- A firm’s total cost C is given by the function: C = 4X2 Where X is the level of output and C is the cost. The firm can sell any number of units of output at a price of 64. However, production inflicts damage on the firm’s neighbours. The total damage D inflicted depends on the firm’s output: D = 4X + X2. Assume that the neighbours have the property rights: In the absence of an agreement between the firm and its neighbours, what would the level of output be? If an agreement between the firm and its neighbours is negotiated, what are the smallest and largest payments that the firm would have to make?Next Friday, you plan to sell cakes at a bake sale to raise money for your school. You plan to charge $30 per cake, and you anticipate that you will sell 10 cakes. You can either purchase cakes to sell or bake them yourself. If you purchase the cakes, they will cost $25 each. If you bake your own cakes, your cost depends upon the number of cakes you bake, as shown in the table below. Number of cakes you bake Total cost of baked cakes ($) 0 0 1 10 2 22 3 36 4 52 5 70 6 90 7 112 8 136 9 162 10 190 a) How many cakes should you bake? How many cakes should you purchase? Bake ___ cake(s) and purchase ___ cake(s). b) Given your answer to part a, how much in total will the 10 cakes cost you? $ c) How much would it have cost you to bake all 10 cakes? $ d) How much would it have cost you to purchase all 10 cakes? $According to the marginal decision rule, if marginal benefit: Group of answer choices A. exceeds marginal cost, an activity should be increased. B. is less than marginal cost, an activity should be increased. C. exceeds marginal cost, net benefit is maximized. D. is already equal to marginal cost, an activity should be increased.