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however, option e mentions upward sloping straight line, did you simply mean upward sloping curve or you meant upward sloping straight line. Please also let me know if option F is correct
- 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 this13. Shawn likes to consume pineapple smoothies and hotdogs. His preferences are represented by the utility function U(x,y) = 34x - x²/2 + y where x is his consumption of pineapple smoothies and y is his consumption of hotdogs. The price of pineapple smoothies is $2 and the price of hotdogs is $1. If the price of pineapple smoothies increases to $6, the change in Shawn's consumer surplus is: A) -144 B) -128 C) -120 D) -112 E) -90A consumer consumes two agricultural products: Red Meat, and Tomatoes according to the following utility function: U = RT That is, the total utility is the multiplication of the quantity consumed of the two products. Given that consumer's income is 210, price of R is 10, and the price of Tis 2, a)Write down the budget constraint (budget line equation) for this consumer. b)Determine the quantities that the consumer should consume of each of the two products c)Calculate the value of the lagrangian multiplier and derive the demand function for Red Meat and for tomatoes.
- Which of the following utility functions represent preferences which do not satisfy monotonicity? 1 U= - x+y 1 U= - 5ху Ou=xy O u= yTom consumes only beer (B) and whisky (W). His utility function is U(B,W) = 2B + 5W, where B is the quantity of beer and W is the quantity of whisky. The price of beer is PB = 2, the price of whisky is PW = 5, and Tom’s income is M = 20 dollars. (a) Obtain the equation of Tom’s indifference curve for the utility U > 0 with beer in the horizontal axis and whisky in the vertical axis. What is the magnitude of the slope of Tom’s indifference curves? Explain the economic meaning of this magnitude. Are Tom’s indifference curves vertically parallel? Explain. (b) Obtain the equation of Tom’s budget line. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? Does Tom consume beer at the current prices (indicated above)? Explain in detail. (c) Are Tom’s preferences quasi-linear? Are they homothetic? Justify each of your answers. (d) Tom’s brother, Jerry, has a utility function given byTom consumes only beer (B) and whisky (W). His utility function is U(B,W) = 2B + 5W, where B is the quantity of beer and W is the quantity of whisky. The price of beer is PB = 2, the price of whisky is PW = 5, and Tom’s income is M = 20 dollars. (a) Obtain the equation of Tom’s indifference curve for the utility U > 0 with beer in the horizontal axis and whisky in the vertical axis. What is the magnitude of the slope of Tom’s indifference curves? Explain the economic meaning of this magnitude. Are Tom’s indifference curves vertically parallel? Explain. (b) Obtain the equation of Tom’s budget line. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? Does Tom consume beer at the current prices (indicated above)? Explain in detail. (c) Are Tom’s preferences quasi-linear? Are they homothetic? Justify each of your answers. (d) Tom’s brother, Jerry, has a utility function given by V (B, W ) = max{B, W }. (d.1) Are Jerry’s…
- 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= $2I. 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.Shanise has the following utility function: UX.Y) = X +Y where X is her consumption of candy bars, with price Px = $2.25, and Y is her consumption of espressos, with Py = $6.50. Derive Shanise's demand for candy bars and espresso. Shanise's demand of candy bars and espressos is O A. X= 1.0021 and Y = 0.5231. O B. X=0.330l and Y = 0.040I. O C. X=0.2461 and Y = 0.040I. O D. X= 0.8331 and Y = 0.6831. O E. X=0.0611 and Y =0.5231. Assume that Shanise's income is I = $75. How many candy bars and how many espressos will Shanise consume? Shanise will consume |candy bars and espressos. (Enter your responses rounded to two decimal places.) What is the marginal utility of income? The marginal utility of income is- (Enter your response rounded to two decimal places.)
- Reid has the following utility function. U = 24m1/3d1/2 where U is Reid's total utility, m is the quantity of muffin consumed, and d is the quantity of doughnuts consumed. Reid has a budget of $25.00, the price of a muffin is $1.00 and the price of doughnut is $0.60. a. What is the equation for the marginal utility Reid receives from muffins? What is the equation for the marginal utility Reid receives from doughnuts? b. What is the equation for the marginal rate of substitution, MRSm,d? Is Reid's utility function subject to the law of the diminishing marginal rate of substitution? c. Reid has a $15.00 gift card that can only be used to buy doughnuts and $10.00 cash to spend on either of the two goods. The price of a doughnut is $0.60 and the price of a muffin is $1.00. Using equations, determine, determine Reid's optimal combination of muffins and doughnuts given the cash and gift card.You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.Suppose that Dale consumes only coffee and cheese, both of which have diminishing marginal utility. For each of the following cases, determine whether Dale should 1Consume more coffee and less cheese, or2Consume less coffee and more cheese: 1.The marginal rate of substitution of cheese for coffee is 3 (i.e., the marginal utility of cheese is three times the marginal utility of coffee), while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 2.The marginal rate of substitution of cheese for coffee is 1 (i.e., the marginal utility of cheese is equal to the marginal utility of coffee) while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 3.The marginal rate of substitution is initially equal to the price ratio, but the price of coffee increases. 4.The marginal rate of substitution is initially equal to the price ratio, but the price of cheese decreases. 5.The marginal rate of substitution is initially equal to the price ratio, but Dale enters exam…