QUESTION: Use the sheet 1( picture below) utility function and parameter values to find the optimal solution via analytical methods (calculus/lagrangean/algebra). Show your work. Note that x1
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QUESTION: Use the sheet 1( picture below) utility function and parameter values to find the optimal solution via analytical methods (calculus/lagrangean/algebra). Show your work. Note that x1<a/b, so we will use the first utility function given in the yellow box in the sheet.
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- Suppose that Marissa is interested in buying some beers and hamburgers. Her budget constraint for these two goods is given below: If beers cost $6/beer, how much income does she have to spend on beer and hamburgers? Group of answer choices $24 $18 $12 not enough information to answer the questionPisa Pizza, a seller of frozen pizza, is considering introducting a healthier version of its pizza that will be low in cholesterol and contain no trans fats. The firm expects that sales of new pizza will be $20 million per year. While many of these sales will be to new customers, Pisa Pizza estimaes that 40% will come from customers who switch to the new, healthier pizzai nstead of buying the original version. a) Assume cusotmer will spend the same amount on either version. What level of incremental sales is associated with introducing the new pizza? b) Suppose that 50% of hte cusomters who will switch from Pisa Pizza's orignial pizza to its healthier pizza will switch to another brand if Pisa PIzza does not introduce a healthier pizza. What level of incremental sales is associated with introducing the new pizza in this case?Suppose the consumer's utility function is given by U(x,y) = X3/5y2/5, and the exogenous variables are given by M = 500, Px = 5, and Py = 4. Price of y changes to Py = 2. What is the income effect ony?O A.-14.53O B. +14.53O C. +24.21O D. +25.79O E. None of the above
- Suppose the consumer's utility function is given by U(x,y) = X3/5y2/5, and the exogenous variables are given by M = 500, Px = 5, and Py = 4. Price of y changes to Py = 2. What is the income effect ony?O A.-14.53O B. +14.53O C. +24.21O D. +25.79O E. None of the above Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.Consider the system of equations: pi = β0 + β0qi + β2ti + β3zi + ui qi = α0 + α1pi + α2ki + ԑi where p and q are endogenous variables.t, z and k are exogenous variables.u and ԑ are disturbance terms. And i is cross section. Explain how you would go about estimating the stated system of equations.Mr. Dogan has 4000 TL to spend. He considers buying meat whose price is 400 TL per kg. and cheese whose price is 160 TL /kg. Given this a) What condition (equality) leads him to a utility maximization. State the condition numerically and tell clearly what each of the variables mean in that equation b) Now suppose that income of Mr. Dogan and price of meat does not change but price of cheese is down to 130 TL/kg. Do the equality and optimal basket found in a still maximize the utility? If not; what is the new condition for utility maximization (write the condition as a numerical equation defining the variables in the equation)
- You have k20per week to spend and two possible uses for this money,:telephoning friends back home and drinking coffee. Each hour of phoning costs k2 and each cup of coffee costs k1. Your utility functions U(X,Y)=XY,where X is the hours of phoning you do and Y the number of cups of coffee you drink. How much income per week will enable you to achieve the same quantities at the new process the ones you chose before? What income will enable you to attain the same utility as you did before.? Comment on your answer in the context of equivalent variation and compensation variationConsider a consumer with the utility function U (x1, x2 ) = 10x12/3x21/3 −50. Suppose the prices of x1 and x2 are 10 and 2 respectively and the consumer has an income of 150. (a) Write out the consumer’s constrained optimization problem. Specifically, write out the objective function and constraint for the problem (e.g. max _?_ subject to _?__). (b) Write the Lagrangian equation corresponding to the constrained optimization problem. Derive the Necessary First Order Conditions. (c) Use the NFOCs to solve for the consumer’s optimal bundle. (d) Show that at the solution you found in (c), the tangency condition is satisfied: MRS = p1 / p2. (e) How did the ‘50’ in the utility function influence the optimal con- sumption bundle? How did the ‘10’ in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle change if the utility function was x12x2? Lastly, how would…1. Gorgeousleny with an income of P150 would like to buy two goods. Let us say juice and bread. Price of juice is P12 and price of bread is P6. If gorgeousleny will buy the ist 5 juices she is entitled to a 50% off. Draw the graph. After a week gorgeousleny went back to the store and will still buy her two favorite goods with the same income of P150 and price of bread and juice is constant. but this time the promo of 50% off is applied after the ist 5 juices. Draw the graph. . a. ) Measure the qty. of bread on the vertical axis and the qty. of juice on the horizontal axis. Label both graph with its corresponding points, pt. A for bread and point B for juice. the combination of bread and juice label it as point C. b.) For both graph, What is the slope from point C to point B? ; What is the slope from from point A to point C?
- Rank the three economic variables from most important to least important.Provide one relevant reason to justify your selection for each of the threepositions. (i.e. a reason why each variable is placed at position 1, 2 and 3.) Rank Variable Justifications 1 2 3Ten years ago, the town of Easton decided to increase its annual spending on education so that its high school graduates would be able to earn higher wages. Now Easton has asked you to evaluate the effectiveness of the spending increase. Their data show that before the spending increase, the average annual salary of recent high school graduates was $25,000 and that now that average salary has risen to $28,500. Fortunately for your analysis, a neighboring community (Allentown) did not change its annual spending on education. Ten years ago, recent Allentown high school graduates earned an average of $22,500, and now that average is $23,750. (a) Use a difference-in-differences estimator to determine whether Easton’s spending increase caused the wages of their high school graduates to increase. (b) What underlying assumption do you have to make in order for your estimate to be valid? What might cause your underlying assumption to be invalid? (c) This data set contains only two…4. Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows : Kate's net worth is $ 4.5 million ( decreased from $ 5.5 to $ 4.5 million ) Mary's net worth $ 3.2 million ( increased from $ 3 to $ 3.2 million ) ( First determine the reference point ( use a parameter ) and then derive reference utility function for each ) .