A consumer with the following utility function U = xy2 faces two constraints. The first is the normal budget constraint where he has GH¢150 and the price of x and y are both GH¢1. Also, the consumer has been issued 200 ration coupons by the government which he must use whenever he buys either x or y. It takes 2 coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x it would require GH¢3 or 6 coupons) (i) Write down the Lagrangian for this problem. (ii) Applying the steps of Kuhn-Tucker, find the optimal x and y. Identify which constraints, if any, are binding.

A consumer with the following utility function U = xy2 faces two constraints. The first is the normal budget constraint where he has GH¢150 and the price of x and y are both GH¢1. Also, the consumer has been issued 200 ration coupons by the government which he must use whenever he buys either x or y. It takes 2 coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x it would require GH¢3 or 6 coupons) (i) Write down the Lagrangian for this problem. (ii) Applying the steps of Kuhn-Tucker, find the optimal x and y. Identify which constraints, if any, are binding.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

abby is a single mom with a weekly budget of $100. She can spend her weeklyincome on food and diapers for her son. Price of food is $1 and price of a diaperis 50 cents. Her son needs at least 5 diapers a day, therefore she must purchaseat least 35 diapers weekly. Jennifer’s utility function is U (f, d) = f 0.9d0.1,where f and d represent quantity of food and diapers, respectively.Question 1 Part aFind abbys optimal consumption bundle. Make sure to draw her budgetconstraint and indifference curves and clearly demonstrate your solution.
Please help
3
Maya is doing her undergrad at Queen's University. She loves donuts and chocolate chip cookies (CCC). Her utility function is given by u(x, y) = √8x +5 + 2y, where x denotes her consumption of donuts and y denotes her consumption of CCC. Her budget is $10/day. The price of a donut is $1. (a) When the price of CCC is $1, what is Maya's optimal choice of donuts and CCC? (b) When the price of CCC is $8, what is Maya's optimal choice of donuts and CCC? (c) When the price of CCC increases from $1 to $8, calculate Maya's substitution effect and income effect. (d) According to your calculation in part (c), is CCC a normal good or an inferior good? Explain. Is CCC an ordinary good or a Giffen good? Explain.
For the below questions, consider a consumer that consumes two goods, x and z with the following utility function. ū=x0.75 0.25 Suppose initial values for income and the prices of goods x and z are y = 100, Px = 5, and Pz= 15 respectively, then the price of good x increases to Px = 10. What is the magnitude of the Total Effect? TE = -9 TE = 7.5 TE = -7.5 TE = 9
Joe Bob from Workout Problem 4.12 has a cousin Don who consumes goods 1 and 2. Don thinks that 3 units of good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is the only one that would not represent Don's preferences? U(x1, x2) = min{2x1, 3x2}. Ux1, x2) = 20x1 + 30x2 - 10,000. Ux1, x2) = 2x1 + 3x2 + 1000. Ux1, x2) = 4x²2₁ + 12x₁x2 + 9x²₂. More than one of the above does not represent Don's preferences.
Please get correct, I keep getting wrong. Thank you so much.
Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.
Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6 Now suppose that instead both goods are priced as follows: There is a discount of 50% on the price of good 1 on each additional unit in excess of 3 units, and there is a discount of 50% on the price of good 2 on each additional unit in excess of 3 units. Draw the new budget constraint and derive it analytically.
Robin consumes two goods X and Y. His utility function is given by U(x, y) = x*y. The price of Good X used to be $10 per unit but has recently increased to $20 per unit due to the good being taxed. The price of Good Y has remained unchanged at $20 per unit. Robin has $2000 to spend. Suppose the government wants to give Robin enough money so that he can still consume the amount of X and Y that he was consuming before the price change. Which of the following statements is CORRECT? O At the earlier prices, Robin would consume 75 units of X and 100 units of Y. This bundle now costs $2750. But if the government gave Robin an additional $750 then Robin would prefer to consume 80 units each of X and Y. At the earlier prices, Robin would consume 50 units of X and 100 units of Y. This bundle now costs $2500. So, the government needs to give Robin an additional $500 to afford the original bundle. But if the government gave Robin an additional $200 then Alex would prefer to consume 100 units each…
For the utility function U = Qx0.28Q (1-0.28) and the budget 137 = 11Qx+6Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.6. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y.a) Determine this consumer’s current utility level. b) Compute the consumer’s marginal utilities of goods X and Y. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X.d) Determine this consumer’s optimal consumption of both goods. e) By how much does the consumer’s utility increase when she consumes the optimal bundle?