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- Suppose the consumer’s utility function is given by U(x,y) = x2/4y3/4where The equation for this consumer’s demand curve for isDefine the Marginal Rate of Substitution between two goods (X and Y).If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginalrate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen toconsumer 12 units of X and 30 units of Y.Please get correct
- 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.Consider the following utility function. U=U(X,Y)=X0.2Y0.8 Find the marginal utilities. Determine their signs. Provide the economic interpretation of the signs of these marginal utilities. Determine whether the law of diminishing marginal utility holds for both goods.For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +Xb
- Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2A consumer with I dollars budget has the utility u(x,y) = x(y+1) over amounts of cake (x) and ice cream (y) she consumes. The prices are px , py respectively. (a) Derive her demand for cake (x), as a function of prices px , py and her budget I. (b) Looking at the demand function in (a), is cake a normal good or an inferior good? Are cake and ice cream complements or substitutes? (c) Calculate the (i) (own) price, (ii) income, (iii) cross- price elasticity of demand for cake at the point where I = 80, px =10, py = 20.Karen has perfect complement preferences over toothbrushes B and toothpaste P, with the associated utility function U(B,P) = min (3B, 2P). Suppose the price of a toothbrush is $6, the price of toothpaste is $4 a tube, and she has $72 to buy her entire year's supply of toothbrushes and toothpaste. How many toothbrushes and tubes of toothpaste will she buy?
- A utility function is given as U = √MB where B represents the quantity of books consumed and M represents magazines. This uülity is shown via indifference curves in the diagram to the right. Holding the number of magazines constant at 20 units, as we increase our consumption of books from 5 units to 10 to 15 and to 20 units, marginal utility with respect to books. is CIES Magazines (Y) 50- 45 40 35 30 25- 20- 15- 10- 5 0- 10 15 RSTV a quie 10 15 20 25 30 35 40 Books (X) 45 5 eboo SCOR scor scor score scoreAbigail, Bernard, Cornwallis, and Douglas each derive a distinct amount of utility from consuming apples and bananas. Initially, apples cost $2, bananas cost $1, and each person receives a weekly allowance of $20 to spend. For each of the four sets of preferences described below, calculate the compensating variation if the price of apples rises to $5. (a) (4) Abigail: U(a,b) = a + 2b (b) (4) Bernard: U(a,b) = 2a + b (c) (4) Cornwallis: U(a,b) = b −a (d) (4) Douglas: U(a,b) = min(a,3b)Please get correct
