(a)lf we allow for the possibility of satiation, the consumer's budget constraint takes the form pxs pw, Walrus' law then becomes pz(p) so for all p2 0. Show that the standard textbook proof of the existence of Walrasian equilibrium still applies for this generalized form of Walrus' law.
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- 45. (a) If we allow for the possibility of satiation, consumer's budget constraint takes the form px S pwị. Walras' Law then becomes pz(p) S 0 for all p S0. Show that the standard proof of the existence of general equilibrium still applies for this generalized form of Walras' Law.On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?
- Consider an economy with two goods, consumption c and leisure 1, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of 7 percent. The con- sumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h) = c-3h¹+, where 3 > 0 and p > 0 are parameters. 1+pfonsumer's demand xy for two different and the consumer's in come is $72. different Consumer's demand xy for chosen to maximize two the శ్రిందికి goods are x² lefility function The per respectively unit of , and the Consumer's in come is $7 x and y are $3and $4. 22,2 © telrite out the fagrangean for the Constrained maximization problem © Find the utility maximizing demands for both goods and he Larange multiplier, 2 o What is the change in consumer's ufility if income Changes from $72 to $752 3) For each utility function, determine the marginal utility with respect to x, marginal utility with respect to y, and the MRS. (3pts each) a) U(x, y)-3x+2y b) U(x, y) 10x¹/5 y c) U(x, y)=x+ y²
- 2. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility.goods, XandY per of good X is N$4 and the price of good Vis No10 Harrys unlity funchon is UCX,)==XY. Harry consumes 2 and he spend's Npbo month The price Find The values of gocal X and Y maximizes Harcys unly illustruate Hary's utlty maximizing.combinason clearly labelled on a graph. Suppose llustrate Harrys price & spod X increased to Ngb effects income and substitution ef the anel laballed graph.ayesha derives utility from travelling and outdoor dinning o weekends as given utility function U(t,d)=TD.the price of a day spent travelling is $160{Pt=160} and price of dining outdoor $200{Pd=200}.ayesha annual budget for this is $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphically
- 3. [In class, we noted that the consumer will spend all their money if they have in- creasing preferences. Here, we give a calculus-based condition for the consumer to spend all their money, that doesn't assume more is always better. The con- dition is a stronger version of what is sometimes called "local non-satiation".] Let E X, and let MU, denote the marginal utility for good i € {1,2} at r. (a) Suppose some good i has MU, #0 (it could be positive or negative), and suppose the consumer is not spending all her money at bundle x (that is pr 0 if MU; <0. Argue that the consumer would not optimally choose r. x (b) Suppose MU₁(x) = MU₂(x) = 0, the good is affordable (p ≤ m), and u is concave. Explain why r is optimal.Law of equi marginal utility is an important law of cardinal utility analysis. Explain this law with the help of its assumptions. Also explain the mechanism that how the total utility will be maximum at a point when the marginal utilities of both the goods become equal. Furthermore, there is a relationship between total and marginal utilities where they both pass through different stages when the consumer continues his or her consumption regularly. Describe this case brieflyWhich among the following is not true?Select one:a. None of the answers are correctb. When marginal utility declines, a higher price is needed to induce the consumer tobuy more of a particular productc. When marginal utility declines, a lower price is needed to induce the consumer tobuy more of a particular productd. All the answers are correcte. Utility maximizing rule and the demand curve are logically consistent
