Problems (Please show all work and remember to label all graphs!)
1) Marginal Analysis
You are the manager of GetMoney Inc. and you produce cardboard boxes. Suppose that you hired a consultant for your company to estimate the demand for your cardboard boxes. You collect data on the price and quantity of boxes sold and send it to your consultant, who then estimates the inverse demand equation as P = 11 – (2.5)*Q. Please also assume that you have a fixed cost of $1 and that the variable cost as estimated by your consultant is V(Q) = 5Q + (0.5) ∗ 𝑄2.
- a) What is the quantity that maximizes profits based upon the above information? What are the corresponding maximum profits that you can earn? (Please use graphs to support your answer.)
- b) At the quantity that maximizes net benefit, are marginal benefits positive, negative, or zero? At this quantity, would you recommend increasing production in order to increase net benefits? Why or why not. (Please use graphs to support your answer).
- c) Are marginal benefits equal to zero at this quantity? Why or why not?
2) Supply and Demand/Demand Analysis
Suppose that your analyst estimates the demand equation for good X as given below:
𝑄𝑥 =12−𝑃 −𝑃 −2𝑃 +2𝑀 𝑑𝑥𝑦𝑧
Good X sells for $2 per unit, good Y sells for $1 per unit, good Z sells for $1 per unit, and consumer income is $5.
- Please indicate whether good Y and Z are complements or substitutes and include in your response whether you think it is possible for a single good to have multiple complements or substitutes. If you answer yes to this question, please provide a real- world scenario in which this situation would hold.
- Using the information provided by your analyst, please determine the demand equation. (Please use graphs to support your answer).
- Please calculate the own price elasticity of demand for good X. Is the demand for good X elastic, inelastic, or unit elastic? (Please use graphs to support your answer and indicate the region of the demand equation on the graph from part b in which your calculation of own-price elasticity lies.)
3) Supply and Demand
For this question, please find an article from a mainstream news source that discusses the effect of supply and demand shocks on prices in the market for the product. Please also discuss whether you think that the graphs and noted shocks are consistent with the zoom lecture on supply and demand regarding price effects. (please use graphs to support your answer).
4) Elasticity of demand
For this question, please find an article from a mainstream news source that covers the topic of elasticity of demand, which highlights the importance of elasticity of demand, prices, and revenues and discuss how these three concepts are related within the context of the article. (please use graphs to support your answer).