In our basic model of utility maximization, identify the graphical representations of the following concepts: (a) Preferences (b) Resource scarcity
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In our basic model of utility maximization, identify the graphical representations of the following concepts:
(a) Preferences
(b) Resource scarcity
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- Apples (pounds per week) 0 A> B B> D b d Butter (pounds per week) he graph above indicates that a consumer's preference combination. Which one of the following is correct based on the graph? C> B C E>F E F BTotal Utility derived from the consumption of a product to a consumer is given by U = (20-0.50)'Q where Q is the number of units consumed Using a graphical representation, show what is the nature of variation in the utility with the increasing consumption of the product? Is it in line with the law of diminishing marginal utility? Explain.Graphical and Intuitive Optimization Consider a consumer who must allocate their available income between the consumption of two goods, Beer and Pizza. Their preferences over Beer and Pizza adhere to the usual assumptions we have made about preferences. The indifference curve map below reflects their preferences and the budget constraint reflects current income and prices. In the simplest terms possible, define or explain the term "Marginal Utility of Beer" (MUB). In the simplest terms possible, define or explain the term "Marginal Rate of Substitution of beer for pizza" (MRSBP). In the simplest terms possible, intuitively explain the meaning of MUB/PB, where PB represents the price of one unit of Beer.
- Define conversation analysis (CA)A utility function is given by the equation U = 20xe¬0.1x, where x is the number of glasses of wine consumed. (a) Show that this utility function has a maximum value and calculate the maximum utility. (b) Describe how marginal utility changes for glasses of wine consumed after the maximum utility is reached. Do you consider this reasonable? Give an explanation.Ice cream and cakes are perfect substitutes for a child, and 2 units of ice cream is always worth 3 units of cakes (however many ice creams or cakes she might have, she would be willing to give up 2 ice creams to get 3 more cakes to keep the same utility level) . (a) Write down a utility function u(x,y) that represents the child's preferences, where x is the number of ice creams and y is the number of cakes she has. (b) If the prices are px= 8 and py =5, and she has $140 to spend on the two goods this summer, what is her optimal bundle? (c) If the price of ice creams decreases slightly, down to px = 7, what happens to her optimal bundle in this case? Did it change "slightly" compared to (b)?
- a) You need to take a trip by a car to another town that you never visited before. Therefore, you are studying a map to determine the shortest route to your destination. Depending on which route you choose, there are five other towns (call them A, B, C, D, E) through which you might pass on the way. The map shows the mileage along each road that directly connects two towns without any intervening towns. These numbers are summarized in the following table, where a dash indicates that there is no road directly connecting these two towns without going through any other towns. Table 3: Miles between Adjusted Towns Town A B C D E Destination Origin 40 60 50 A 10 70 B 20 55 40 с 50 D 10 60 E 80 i) Formulate a network model for his problem as a shortest path problem by drawing a network where nodes represent towns, links represents roads, and numbers indicate the length of each link in miles. ii) Use the network form in i) to find the shortest path from origin to the destination.Question3 a) Suppose a household is faced with the choice between consuming gasoline (G) and all other goods (OG). Today the household consumes 800 liter of gasoline a year.Suppose then that a gasoline price increase is perfectly compensated by a wage increase. If the family followed the utility maximization model, how would this affect their consumption of gasoline? Explain by using a figure. b) Explain by using an example why an MRS (Marginal Rate of Substitution) between two goods must equal the ratio of the price of the goods for the consumer to achieve maximum satisfaction?Suppose Ed's utility from the consumption of martinis (m) is proportional to the number he drinks: U(m) = m. Further, Ed is particular about his martinis: He enjoys them in exactly three parts of gin (g) to one part vermouth (v). So we can write the utility as: U(m) = U (g, v) = min (g, 3v). (a) Provide a sketch of Ed's indifference curve in the (g, v)-space for various level of utility. (a) Let the prices be p, and p, and Ed's income be I. Find the demand functions for 9 and v [Hint: Use the proportional rule and budget constraint. No need for differential calculus] (b) Using the results in (b), what is Ed's indirect utility function? (c) Find the expenditure function; given a level of utility U, and prices pg and Pv.
- According to the equation, sales (Y, measured in $1,000 per month) and advertising (X, measured in $1,000 per month) are related as follows: Y=40+3X Suppose you are told that the sales committee has set an ambitious goal of $64,000 for next month’s sales. The treasurer needs to know how much to budget for advertising, and you have to come up with the answer.What is a good or service that has become expensive/cheap due to (a) natural scarcity/abundance of supply or naturally high/low demand, and (b) artificial mean (e.g., government policy, competition restricting practices)?U.S. food markets consumers viewed beef as a normal good from 1960-1976, but viewed it as an inferior good after that point. This type of change is not abnormal, in that as average household incomes rise, preferences might change. For instance, as households move from poor to middle-class, their consumption of beef might increase. However, as households move from middle- class to upper-middle-class, they might choose to purchase more exotic foods products. Assuming you are a beef producer in 1983, what will happen if incomes continue to increase? a. The marginal cost of beef will increase. b. The marginal cost of beef will decrease. c. The demand for beef will increase. d. The demand for beef will decrease.