ralph has a utility function u(x,y) = 0.5x + y and an income of $M. Let the price of x be $4 and the price of y be $10. In this case, the consumer's optimal demand for good x* = M/16 2M M/4
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- 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? 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. It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. If the price of pizza is 12 and the price of beer is 4, then we can't determine how much pizza relative to beer Bob purchases. Pizza and beer are perfect substitutes.21:45 Sat 7 Aug 26% O Screenshot_20210807-213016_Office.jpg 21:30 a) Choose X, and X, to max the utility fxn, U(X,X) =ahX;+(l-a)\n X, st: M = P, X 1 + P,X , a) Consider a price decrease for good 1 from P, toP . Write down the Demand functions for good 1 when prices are P, and when prices drop from PtoP b) What is the compensating income, M° associated with the price change? C) Obtain the SE and IE associated with the price change IIyour answer. 2. The utility function of a consumer over two goods x and y is given by u(x,y) = 20 ln x + 2y The price of y is 1. Let p denote the price of x. The consumer has an income of M> 10. The consumer's price elasticity of demand for x has a lower absolute value compared to the income elasticity of demand for y. Is this true or false? Explain by calculating both elasticities.
- Suppose we have a market with 200 individuals with preferences over two goods, x and y. 1. Consider that all 200 individuals have the utility function U = x²/3y¹/3 and that each individual has the same income and is subject to the same prices. Calculate the market demand for x as a function of income and prices. 2. Find the own price elasticity of demand for good x. Is the elasticity constant or is it changing at different values of P? 3. Suppose now that we know m = 135, P = 3, 4. What is the market demand for x? This should be a number. and Py 4. Consider now that 100 individuals (type A) have the utility function U = x²/³y¹/³ and the other 100 (type B) have the utility function U = x¹/3y2/3. Each individual still has the same 'y income and is subject to the same prices. Calculate the market demand for x as a function of income and prices. 5. Suppose now that we know m = 250, P = 5, and Py 3. What is the market demand for x? This should be a number. = =Jane has the utility function U(x,y) = x(y+3). The price of x is 2₺ and the price of y is 1₺. Income is 15₺. a) How much x does Jane demand? How much y? b) If his income doubes and prices stay unchanged, will Jane's demand for both goods double? c) The prices change, so that x now costs 1 and y now costs 4. What is the new ordinary demand?10:55 Sun 8 Aug 30% Screenshot_20210808-073803_Office.jpg a) Choose X, and X, to max the utility fxn, UX,X)=chX;+(l-a)hX, st: M = P, X, + P¿X ; a) Consider a price decrease for good 1 from P toP" . Write down the Demand functions for good 1 when prices are P, and when prices drop from R toP" b) Obtain the SE and IE associated with the price change
- Ravi's utility function for various combinations of X and Y satisfy all the axioms of choice. Given his budget constraint, it has also been observed that the cross-price elasticity of demand between X and Y is zero as the price of X falls. Given this scenario, comment with an appropriate diagram, what kind of commodity is Y?Moe's income is $320 per week and he spends it on two goods, X and Y. Good X costs $8 and good Y costs $4 per unit. His utility function is U = 4.5XY. (a) Calculate Moe's utility-maximizing purchases of X and Y. (b) Calculate Moe's constrained utility- maximum if his income decreases by $2.00? (c) If the price of Y doubles, with no change in the price of X, by how much would his income have to increase to enable him to maintain his initial level of utility (as in part (a) above)?I need help with my homework assignment that i dont undertsand. Suppose a consumer has a utility function given by U(X,Y) = MIN(X, 2Y). The consumer has $90 to spend (M = $90). The Price of good Y is PY = $1. Using a graph, sketch the consumer’s demand curve for Good X. Make sure to identify three points on the demand curve. Make sure your graph is neat, accurate, and scaled properly.
- 19:32 Fri 6 Aug 91% Screenshot_20210806-193021_Office.jpg a) Choose X, and X, to max the utility fxn, UX,„X,)=chX;+(l-a}hX; st: M - P, X + P,X ; a) Write down the demand functions for goods 1 and 2 b) Consider a price decrease for good 1 from P, toP" . Write down the demand functions for good 1 when prices are P, and when prices drop from R toP c) What is the compensating income, M associated with the price change? Obtain the SE and IE associated with the price change 24To maximize total utility, consumers will always choose the marginal unit of the good that yields the most marginal utility per price. True FalseShanise 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.)