Ricky has utility function u=x?y. This implies that MUx=2xy. MUy=x². His income is 100. The price of y is 10. (a) Find his demand for x at price 20. (b) Find his demand for x at price 30. (c) Write down his demand function for x: that is, write down his demand for x as a function of the price of x.

Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = lnx + 2lny (MUx = 1/x, MUy = 2/y). a. Derive his demand functions for x and y. Are they homogeneous in income and prices? b. Assuming I = $60 and px = $1, graph his demand curve for y. c. Repeat part (b) for the case in which px = $2.

Greg has the following utility function: u=x10.75x20.25. He has an income of $68.00, and he faces these prices: (p1,p2)=(8.00,4.00). Suppose that the price of x1 increases by $1.00. Calculate the equivalent variation for this price change. $

Given the following utility function: U(Q,Q2) = 100LN(4Q1/2 + 2Q,/2) %3D a. Show that the function is cardinal. b. Show that the function is ordinal. c. Derive the demand functions for the two goods. d. For Q1 show that the law of demand holds. e. Show that Q1 is normal. f. What is the relationship between the two goods.

Let U(x, y) = 3x + y be the utility function of a consumer, whohas a budget of I. As a function of I, find the consumer’s Walrasian demand when the prices are px = py = 1. The price of good x increases to 2, find the new Walrasian demand for the new prices    px= 2 and py = 1. Decompose this change into an income and a substitution effect.

Marvin has a Cobb-Douglas utility function, 0.5. 0.5 42 U =q1 his income is Y = $900, and initially he faces prices of p, = $2 and p2 = $1. If p, increases from $2 to $5, what are his compensating variation (CV), change in consumer surplus (ACS), and equivalent variation (EV)? Marvin's compensating variation (CV) is $. (Enter your response rounded to two decimal places and include a minus sign if necessary.)

use the demand function below to answer the questions that follows Qdx = 3/4 - 1/3Px - 5Py + 2Pz - 2/10M given that Py = 2; Pz = 10 and M is 5: e. find the demand function f. plot the demand function g. using the information in (e), calculate the quantity if Px = 3

(A) Suppose an individual who derives utility u(x, y) from consuming a units of the good X and y units of the good Y. Prices of goods X and Y are respectively p = 1 and Py = p. Furthermore, the individual has a budget m. What is the demand for Y if the utility function is: u(x, y) = min{x, ay}. (a) y(p, m) = am (b) y(p, m) = = (c) y(p, m)= (d) y(p, m) = = am a+p m a+p m 1+p (B) Same setup as (A) with u(x, y) = ax + y and ap Pr. The quantity demanded of good X is q. Which of the following is true ? (a) The substitution effect increases q but the income effect decreases q and over- come the substitution effect. Overall q decreases. (b) The substitution effect decreases q but the income effect increases q come the substitution effect. Overall q increases. and over- (c) Both the income and substitution effects increase q. Overall q increases. (d) Both the income and substitution effects decrease q. Overall q decreases. (D) Suppose an inferior good X (not Giffen). Its price increases from…

ECONOMICS LECTURE NOTE 5.1.3 Example Use the table below to answer the questions that follows Commodity x Quantity Commodity y Quantity Marginal utility 60 Average utility 1 30 2 50 2 27 3 35 3. 22 4 15 4. 18 5 5 15 6. 6. 12 iii. Which of the commodities would he pay higher price when 4 units are consumed? Suppose the price of X is 5 and that of Y is 4. How many of the quantity of X and Y should be consumed in order for the consumer to be in iv. equilibrium. If price of X increase to 10 whiles that of Y remains the same, explain how the equilibrium conditions will behave.

Consumer 1 has the utility function xy U = x+y_subject to PxX + pyY = m Derive the generalized demand function for good x and good y.