Consider a consumer who consumes two goods and has utility function u(x1, x2) = x2 + √√√₁. The price of good 2 is 1, the price of good 1 is p, and income is m. Start with m = 10 and p = 1.5, and suppose that the price of good 1 increases by 25%. Compute the substitution and the income effect.
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- Exercise 2 Utility 1. Muhammad derives utility from only two goods, curry (Qc) and drinks (Qd). Muhammad has an income of RM240 and the price of curry (Pc) and drinks (Pd) are both RM3 Derived Muhammad budget constraint?Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.
- Question 7 A consumer has a utility function 100-(x₁-4)4 -(x2-3)4 and a budget constraint of 9x1+3x2 <200. How much of good 2 do they consume?Peter consumes only chocolate ice cream and vanilla ice cream. He is spending all of his income. His marginal utility of chocolate is 200 and his marginal utility of vanilla is 200, and the price of chocolate is $1.00 per scoop and the price of vanilla is $2.00 per scoop. To maximize his utility, Peter shouldEXERCISE 4 Milo spends £27 on stamps (S) and maple candy (C). His preferences for these goods are given by the following utility function: U(S, C) = min {S, 3C). Suppose that price per unit of S is £1.1 and the price per unit of C is £2.1. a) Write down Milo's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. In your graph, indicate the consumption bundle of 12 stamps and 6 maple candies. Can Milo afford this bundle? Explain. b) Find Milo's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. c) If the price of a stamp increases to £1.4, how should Milo's income change for him to be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Milo's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Milo's demand for stamps and/or…
- Brian spends his entire monthly income of $1200 on shoes (S) and pizzas (P). The price of a pair of shoes is $60, and the price of a pizza is $20. If he consumes 10 pairs of shoes and 30 pizzas, his MRS is 2P/1S. (A quantity of shoes is measured along the x-axis, and a quantity of pizza is measured along the y-axis.) His choice is optimal. True FalseEXERCISE 4 Milo spends £27 on stamps (S) and maple candy (C). His preferences for these goods are given by the following utility function: . Suppose that price per unit of S is £1.1 and the price per unit of C is £2.1. Write down Milo’s budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. In your graph, indicate the consumption bundle of 12 stamps and 6 maple candies. Can Milo afford this bundle? Explain. Find Milo’s optimal consumption bundle, both algebraically and graphically. Explain your reasoning. If the price of a stamp increases to £1.4, how should Milo’s income change for him to be as well off as before this change in prices? Discuss the implications of the price change from c) on Milo’s optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Milo’s demand for stamps and/or maple candy.Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.
- Exercise Suppose the utility function of a person consuming two commodities X and Ywith income Birr 600 is given by U = 2 X 06Y 04 If the per unit price of X is Birr 20 and per unit price of Y is Birr 40 a) What is the utility maximizing level of consumption of X & Y ? b) Find the MRSyy at the optimum ?Mario consumes two goods: cars and motorbikes. An increase in the price of cars while holding income and the price of motorbikes constant will: (A) increase the marginal utility provided by cars. B) decrease the marginal utility per dollar spent on cars. (C) reduce the individual's preference for cars. D increase the marginal utility per dollar spent on motorbikes6. A consumer has an expenditure function given by E = Ū(P+). When the consumer has an income of 100, it can reach a maximum utility of 20. The price of x increases by 3 and the consumer's income increases by 25. Are they better off or worse off than before the changes? Explain how you know. Full solution please