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I need assistance in working this through, step by step. I understand the MRS concept, but need help in the algebra to solve it
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- A consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $2Economics 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 toWhen do we differentiate between using the formula MU(x) = TU(x) – TU(x – 1) and Marginal Utility = Change in Total Utility (ΔTU) / Change in No. of Units Consumed (ΔQ) when calculating marginal utility. This is confusing to me. On that note, which formula should we use for the below scenario? Part 1 Given the quantity of total movie tickets and total concession stand items consumed in a month and the total utility derived at Ruby Red Movie Theater for each, calculate the marginal utility and the marginal utility per dollar for movie tickets and average concession stand items. Step 1: Calculate marginal utility and marginal utility per dollar for movie tickets. Quantity of Tickets Consumed Total Utility Marginal Utility Movie Ticket Price Marginal Utility Per Dollar for Movie Tickets 0 0 --- --- --- 200 150 $10.00 400 275…
- Suppose Susan has to choose between purchasing high-definition televisions and milk. Which of the following is the utility-maximizing rule that Susan should follow while choosing the optimal quantities of these two goods? (Note: In the answer options that follow, MU stands for "marginal utility.") O MU of Milk = MU of HDTVS O (MU of Milk) × (Price of Milk) = (MU of HDTVS) × (Price of HDTVS) MU of Milk MU of HDTVS Price of HDTVS Price of Milk MU of Milk MU of HDTVS Price of Milk Price of HDTVS Since milk costs little and high-definition televisions are expensive, it must follow that when people choose their optimal quantities of milk and high- definition televisions to purchase, the marginal utility they receive from the last high-definition television they buy is v than the marginal utility they receive from the last gallon of milk they buy.Mariah consumes music downloads (M) and concert tickets (C). Her utility function is giveh by U = 0.5M? + 2C². a. Using calculus, what is the marginal utility of music downloads? b. Using calculus, what is the marginal utility of concert tickets? Write the equation for the MRSMC (i.e., the MRS of C for M; M is increasing, C is С. decreasing). d. Would the bundles of (M = 4 and C = 1) and (M = 2 and C = 2) be on the same %3D %3D %3D %3D indifference curve? How would you know? e. Calculate the MRSMC when M = 4 and C =1 and when M = 2 and C = 2. Explain why the %3D %3D values of MRSMC differ across these two bundles. f. Based on your answers above, are Mariah's indifference curves convex? Explain using the values calculated. er thisWhat is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? Explain why, if this rule does not hold, the choice cannot be utility-maximizing.
- 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) ? .Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…Demonstrate how a consumer’s equilibrium changes if the price of a product changesaccording to marginal utility theory. Include in your answer a discussion of the derivation of the demand curve according to marginal utility theory. Please provide a detailed answer with a graph if possible.
- Carol has very weird preferences. She only cares about quantity. When evaluating a bundle, Carol only looks at the highest amount of a good she can consume in each bundle, regardless of whether it is of eggs or dumplings. She is indifferent between two bundles only when the largest consumption of a good within each bundle is the same across bundles. So, for instance, if a bundle offers 5 eggs and 1 dumpling she finds that bundle indifferent to a bundle offering 4 eggs and 5 dumplings. These preferences are transitive. But are they monotone? And convex?0.8 A consumer's utility function is given by the expression: U = (0.6X0.5 +0.4Y0.5) ². Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.You are choosing between two goods, X and Y, and your marginal utility from each is as shown in the table below. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase to maximize utility? What total utility will you realize? Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? Using the two prices and quantities for X, derive a demand schedule (price–quantity-demanded table) for X.