How can I analyze and find the Marshallian Demands of the following Utility function? u(x)=min{x1,x2}x3 I understand that goods x1 and x2 are perfect complements with each other, but what is the relation with x3?
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- If consumers buy less of a commodity when their incomes rise, this commodity is ( an inferior good , or a normal good ) ? . When the price of this commodity rises, the substitution effect is ( negative or postive) and the income effect is ( negative or postive) ? . So the net result for consumption of this commodity ( depends on which effect dominates , is an increase , is a decrease) ? .2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2Y/X and MUy = 2\X/Y ) a) Suppose Y=3. Calculate John's utility for X=4,9,16, and 25. For a given level of Y, does good X display diminishing marginal utility?What is the law of diminishing marginal utility why or how is this relevant for our discussion of the demand curve?
- Harry consumes 2 goods, X and Y and he spends N$60 per month. The price of good X is N$4 and the price of good Y is N$10. Harry's utility function is U(X, Y) = XY. (i) What is Harry's marginal rate of substitution? (5) (ii) What is the expression for Harry's budget constraint? (3) (iii) What is the slope of Harry's budget constraint? (2) (iv)Find the values of good X and Y maximizes Harry's utility. Show all your work. (6) (v) Illustrate Harry's utility maximizing combination on a clearly labelled graph. (4) (vi) Suppose the price of good X increased to N$6. Illustrate Harry's income and substitution effects on a well labelled graph. Show your work. (10) (vii) Suppose Genie is consuming two goods, coffee and beer. She spends all her income on a combination of coffee and beer where MUcoffee/Peoffee is 5 and MUbeer/Pbeer is 3. Explain why this combination is not maximizing her satisfaction. What should she do to maximize her utility? (5)Jerry spends his entire budget on bread and gasoline. His preferences are complete, transitive, monotonic, and convex. For Jerry, bread is an inferior good that follows the law of demand. Moreover, his cross-price elasticity of demand for gasoline with respect to the price of bread is negative. Suppose the price of bread increases, all else constant. a. Create a chart to show the total, income, and substitution effects on bread and gasoline of the increase in the price of bread. b. Use budget lines and indifference curves to graphically illustrate the three effects. Be sure to label each effect on your graph (or through the chart from part a) and plot bread on the x-axis and gasoline on the y-axisI. You only consume two goods and your preferences are represented by utility function U(x₁, x₂) = (x0.5 + x2.5)² for x₁ > 2 and x₂ > 0. 1. Find your marginal utility for each good. Simplify your answers. Based on your answers, are your preferences strictly monotonic? Why or why not? 2. Do your preferences obey the law of diminishing marginal utility for each good? Why or why not? If not, what is the behavior of your marginal utility for each good? Use calculus and words to answer this question.
- 2 Debbie consumes only D (Donuts) and E (Eggs). Furthermore, it is known that she considers D and E to be "perfect complements" at a 2:1 ratio (i.e. 2 donuts has to go with 1 egg). Based on this, answer the following: a) Derive Debbie's demand for Eggs (you should get E as a function of M, PD and PE). b) Suppose Debbie's income is $100, while PD = $3 and PE = $4. How much D and E would Debbie be consuming? What is the elasticity of demand for E? What is the income elasticity of demand for E? What is the cross-price elasticity of demand for E? c) Suppose PE rose to $7. Graphically show the effect. Be sure to decompose into a substitution effect and an income effect. How much income is needed to compensate Debbie for the effect of the price increase? d) Derive her Hicksian Demand.2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences over these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where x represents the number of cans of soda and y represents the number of juice boxes. a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y). b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda and juice. Write Ping's demand curve for juice (y). Illustrate his demand curve. c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and $30, resp.). Use your demand functions to find his best bundle. In an indifference curve diagram illustrate his best bundle at these prices. For the remainder of the question assume that Ping's allowance (income) rises to $36 per week and the prices of the two goods are unchanged at Px= $1.5 and Py= $1. d) Use your demand functions to find his new best bundle. e)…c) From the following budget line and the utility function, calculate the amount of two commodities that maximizes satisfaction. What is the maximum amount of satisfaction? 2500= 20X + 30Y U = 300 X0.6Y0.7
- Economics Consider the following utility function: U=100X^0.75 Y^0.10. A consumer faces prices of Px = $5 and Py =$10. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 12 units of good X and 15 units of good Y. Then the marginal rate of substitution LOADING... is equal to: MRS= The consumer should consume maximize utility toWhich of the following utility functions represent preferences which do not satisfy monotonicity? 1 U= - x+y 1 U= - 5ху Ou=xy O u= yWould you expect total utility to rise or fall with additional consumption of a good? Why?
