Suppose the following describe the marginal cost of extraction of a raw resource, the marginal cost of the recycled resource, and the demand for the resource (raw and recycled forms are perfect substitutes). MC1 = 150 + 2q1 MC 2 = 200+ 192 WTP = 400 -1(q1+q2) a) Draw a graph (clearly label the lines: Demand, MC1, MC2) b) Determine the optimal amount of q1 and q2 (show your work). c) If consumer preferences changed such that demand became: WTP = 225 4(q1 q2) what would be the optimal amount of q1 and q2? d) Also include a graph of the situation with the new demand.

Suppose the following describe the marginal cost of extraction of a raw resource, the marginal cost of the recycled resource, and the demand for the resource (raw and recycled forms are perfect substitutes). MC1 = 150 + 2q1 MC 2 = 200+ 192 WTP = 400 -1(q1+q2) a) Draw a graph (clearly label the lines: Demand, MC1, MC2) b) Determine the optimal amount of q1 and q2 (show your work). c) If consumer preferences changed such that demand became: WTP = 225 4(q1 q2) what would be the optimal amount of q1 and q2? d) Also include a graph of the situation with the new demand.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.6P

See similar textbooks

Similar questions

Suppose the relationship between your study time and your grade on a History midterm is given by the following table: If you study for Your grade will be 4 hours 80 5 hours 90 6 hours 93 a) What is the "marginal grade improvement (MGI)" of the 5th hour of studying? b) What is the "marginal grade improvement (MGI)" of the 6th hour of studying? c) Why might the MGI be diminishing?
The marginal profit for a certain company is MP₁(x) = -x² + 18x-45. The company expects the daily production level to rise from x = 3 to x = 5 units. The management is considering a plan that would have the effect of changing the marginal profit to MP₂(x)= -x² +14x-33. Should the company adopt the plan? Determine the area between the graphs of the two marginal profit functions from x = 3 to x = 5. Interpret this area in economic terms. C Should the company adopt the plan that would make the marginal profit be MP₂? O A. Yes, because the company will make a larger profit under the new plan. B. No, because the company's profit will be smaller under the new plan. O C. It is impossible to tell using the given information. The area between the graphs of the two marginal profit functions from x = 3 to x = 5 is sq. units.
Bounds Inc. determined through regression analysis that its sales (S) are a function of the amount of advertising (measured in units) in two different media. This relationship is given by the following equation (X = newspapers, Y = magazines): S (X, Y) = 200X+100Y− 10X2− 20Y2 + 20XY Find the level of newspaper and magazine advertising that maximizes the firm’s sales. Calculate the firm’s sales at the optimal values of newspaper and magazine advertising determined in part (a).
You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for its hamburgers in order to maximize its weekly revenue. To make life as simple as possible, you assume that the demand equation for Johannesburg hamburgers is linear. (a) Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 5000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero. Use these data to find the linear demand function q(p), where p is the price per hamburger and q is the number of hamburgers they sell at that price per week. q(p) = (b) Find the price elasticity of demand. E(p) = (c) When you raise the price by 1% from $2 per hamburger, the demand decreases by %. Demand is of unit elasticity. v
You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for its hamburgers in order to maximize its weekly revenue. To make life as simple as possible, you assume that the demand equation for Johannesburg hamburgers is linear. (a) Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 2000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero. Use these data to find the linear demand function q(p), where p is the price per hamburger and q is the number of hamburgers they sell at that price per week. q(p) = X (b) Find the price elasticity of demand. E(p) X (c) When you raise the price by 1% from $2 per hamburger, the demand decreases Demand is of unit elasticity. V by 1 %.
You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for its hamburgers in order to maximize its weekly revenue. To make life as simple as possible, you assume that the demand equation for Johannesburg hamburgers is linear. (a) Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 6000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero. Use these data to find the linear demand function q(p), where p is the price per hamburger and q is the number of hamburgers they sell at that price per week. q(p) = (b) Find the price elasticity of demand. E(p) = (c) When you raise the price by 1% from $2 per hamburger, the demand decreases Demand is of unit elasticity. v by X %.
Green et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)
The cost of controlling carbon dioxide emissions [C(E)] at a firm goes up rapidly as the amount of emissions (E) increase. Let's assume the relationship is defined by the function below. C(E)= 5000+ 40E +2E² E20 where E is measured in tonnes per year and C is measured in dollars per year. a) Determine the Marginal Cost function for controlling carbon dioxide emissions and find the marginal cost at 50 tonnes of emissions: b) Determine the Average Cost Function for controlling carbon dioxide emissions and find the tonnes of emissions at minimum average cost. c) The government is charging a tax of $270 for every tonne of carbon dioxide emitted. At, 50 tonnes of emissions, is it profitable for the firm to control emissions on its own or pay the carbon tax?
A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 24 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 3 sales per week. (a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.) P(x) = (b) What price should the society charge for each feeder to maximize profits? $ What is the maximum weekly profit? $
Consider an input-output model with 3 sectors. Sector 1 is heavy industry, sector 2 is light industry, and sector 3 is agriculture. Suppose the input requirements are given by the following table: Agriculture Heavy Industry 0.1 Units of Heavy Industry Goods Units of Light Industry Goods Units of Agriculture Industry Goods a. Suppose the final demands for the three goods are 85, 95 and 20 units respectively. If x1, x2 and x3 denote the number of units that have to be produced in the three sectors, write down the Leontief system for the problem b. Verify that x1 = 150, x2 = 200 and x3 = 100 is the solution 0.3 Light Industry 0.2 0.2 0.2 0.2 15 0.1 0.2 0.1
The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?
In 2016 Longwood University hosted the only Vice Presidential Debate. It was an expensive endeavor that, along with the significant educational benefits to our campus, was also meant to encourage interest and, ultimately, increase the number of applicants to Longwood. Suppose we have the following application data: Year 2015 2016 2017 2018 2019 Number of Applicants 5000 5100 6000 6800 7800 Administration points to this post-debate increase in number of applicants as clear evidence that the debate expenses were well worth it - applications increased because of the debate. Why is this conclusion problematic, and why would multiple regression analysis address the problem you identified and, hence, lead to better evidence of a potential impact of the debate on number of applicants?