Microeconomics

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4. (15 points) Suppose we have the market for frozen pizzas. Below is the supply and demand schedule.


6. (5 points) Jane has $20 to spend on breakfast for the next few days. Bagels cost $5 and cups of coffee cost $4. Draw Jane's budget constraint in the space below with bagels on the X- axis.


Two MSU fraternities, Phi Kappa Sigma and Phi Kappa Tau, are accustomed to each having 6 parties a month. Phi Kappa Sigma and Phi Kappa Tau are located close to each other on Bogue Street. These parties impose a negative externality on their other neighbors on Bogue Street. Suppose President Stanley decides that the socially optimal total number of parties on Bogue Street is 8 parties a month. The total benefits each fraternity derives from having a certain number of parties a month are given in the table below.


[1] What are the "choice variables and what are the "parameters' in this problem? What is the difference between them? [2] How do we know this problem has a solution? [3] Explain the relevant Lagrangian function. [4] Explain the conditions that will characterize a KT-point. [5] Use the conditions in part [4] to find the optimal consumption bundle (r*, y), and the associated Lagrange multiplier X*. [6] Explain why z* and y* can be interpreted as "functions". [7] Find the partial derivative of z* with respect to each "parameter of the problem". [8] Explain the interpretation of each partial derivate you find in part [7]. [9] Find the "indirect utility function' V = u(x, y), and explain its interpretation. [10] Find the partial derivative of V with respect to M, and explain its interpretation.


Question One Jane and John are a new couple trying to make a future production plan together. Assume there exist two types of production they can conduct: Household Production (HP) and Market Production (MP). If Jane does household production, her production value is $20 per hour; if she does market production, her production value is $10 per hour. If John does household production, his production value is $10 per hour; if he does market production, his production value is $20 per hour. Both Jane and John can work 8 hours on workdays. a) Calculate Jane and John's possible production frontiers (PPFs) on a workday and draw them in two diagrams. b) Combine Jane and John's PPFs in the same diagram. If both of them conduct market production, only, what would be their combined PPF? Show it in the diagram. If they do wish to keep some household production, who should do it? Show this new PPF in the diagram. Is there a limitation on this new PPF? c) On the other hand, if both Jane and John conduct household production, only, what would be their combined PPF? Show it in a diagram. If they do wish to keep some market production, who should do it? Show this new PPF in the diagram. Is there a limitation on this new PPF? d) If Jane and John "pool" their production possibilities together and split these possibilities equally between household production and market production, what would be their new PPFs? Show them in a diagram. e) Is there a gain for Jane and John to collaborate? If so, show it in a diagram.


1. Hessah spends a total of a 100 KD each month on two desserts: chocolate chip cookies and vanilla ice cream. Let C and Pc denote the quantity and price of chocolate chip cookies she consumes, respectively. Let V and Py denote the quantity and price of vanilla ice cream cups she consumes, respectively. The table below shows Hessah's optimal baskets as the price of vanilla ice cream changes. a. Sketch Hessha's price-consumption curve for vanilla ice cream on any of the attached graph papers. Label her optimal baskets. Place the quantity of vanilla ice cream cups on the horizontal axis and the quantity of chocolate chip cookies on the vertical axis. b. Sketch Hessha's demand curve for vanilla ice cream on any of the attached graph papers. C. Sketch the Engel curve for vanilla ice cream on any of the attached graph papers. d. Comment on whether vanilla ice cream is a normal or an inferior good. Explain your answer. e. Sketch the Engel curve for cookies on any of the attached graph papers. f. Comment on whether cookies are normal or inferior goods. Explain your answer.


Question 2: At the end of February 2022 and thereafter, the Russian invasion of Ukraine had a significant impact on energy markets. As a result, natural gas prices increased across most of the world. Higher natural gas prices had increased the cost of producing electricity since natural gas is used as fuel by many power plants. Analyze what happened to the market for electricity in New England in late February 2022. Assume that the heating season temperatures in the region, which influence the use of electricity by consumers, had not changed between December 2021 and late February 2022. • Using your graph from Question 1, depict the changes that have taken place in the electricity market. Clearly show any shifts in demand and/or supply curve(s). Label any curves that have shifted as D₁ and/or S₁; and show the direction of the shift graphically with an arrow. • Clearly show the new market equilibrium if it has changed from your answer to Question 1. Label the new equilibrium price as P, and equilibrium quantity as Q₁.


5. 10. The Surgeon General announces that eating carrots improves and promotes healthy vision. As a result, the equilibrium price of carrots a increases, and producer surplus decreases. b increases, and producer surplus increases. C decreases, and producer surplus increases. d decreases, and producer surplus decreases.


Question 1 1. (From previous semester's final exam) Consider the market for solar power. Assume the market is perfectly competitive and initially in long-run equilibrium; solar power sells for $.25 per kwh (kilowatt hour, a unit of power). a. Draw 2 graphs, one to represent the market (supply and demand), and one to represent a single firm (demand, marginal cost, and average cost curves). Assume a u-shaped average cost curve. Show the equilibrium price and the quantity produced by the market (Q) and by each individual firm (q). b. Next, to encourage conservation, Congress taxes all forms of energy EXCEPT solar power, causing an increase in the demand for solar power. Show what happens to the market and the firm in the short run; indicate clearly what happens to price, quantity, and profit. c. What happens to the market and the firm in the long run? Indicate clearly what happens to price, quantity, and profit, for each the market and the firm.


More rabbits Suppose that you have the utlity function u(c)= In(c). Suppose that you can choose between taking c = 2 for sure or a rabbit that is worth either c = 1 or c = 8 with probability 2/3 and 1/3, respectively. Which would you prefer?


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