Şeyma has the following utility function: U(x,y) = x'/²y+/2 and faces the budget constraint: M = P,x + P,y. Suppose M = 120, P, = 1 and P = 4. Find the optimal x and y.
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- For the utility function U = Qx0.15Qy(1-0.15) find the trade-off rate between good X and good Y at Qx= 9 and Qy=13Consider the following infinite-horizon utility maximization problemMarina decides to purchase a ring made from an alloy composed exclusively of gold (G) and titanium (T). The price of gold is $60 per gram, and the price of titanium is $30 per gram. Her total budget for the ring is $600. Her utility function is given by U(G,T) =GT. Suppose the price of titanium falls to $20 per gram. At the final basket, the optimal amount of titanium is（）grams.
- Ken has a utility function for tennis rackets (X) and tennis balls (Y) of the form U(X,Y)=min(4X,2Y). His Hicksian demand for X is given by :Suppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the quantity of pizza demanded, P is the price of a pizza, and Pb is the price of a burrito. What is the slope of this demand function, and what information does the slope provide?..Two grad students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by ui(fi, xi) = φi(fi)+xi, where φi(·) is strictly concave, fi is the amount of food consumed by student i, and xi is a composite numeraire good. Each student has a fixed budget of mi. EVALUATE THIS CLAIM: Both students eat too much!
- Consider the utility function u(x) =√x1+ √x2 ; and a standard budget constraint: p1x1+p2x2=I. a.Are the preferences convex? b. Are the preferences represented by this function homothetic? c. Verify that the demand function is homogeneous of degree 0 in prices and income.Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F) = 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $4000. Suppose F is on the horizontal axis and D is on the vertical axis. Jane's marginal rate of substitution between F and D is equal to 10 1 F/D D/F. Ceja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. Find out the combination of Apples and Bananas that maximize Ceja’ satisfaction
- Casper consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only one supplier, and the more cocoa you buy from him, the lower the price you have to pay per unit. In fact, x2x2 units of cocoa will cost Casper √x2x2 dollars. Cheese is sold in the usual way at a price of $2 per unit. Casper's income is $10 and his utility function is u(x1,x2)=x21x2u(x1,x2)=x12x2, where x1x1 is his consumption of cheese and x2x2 is his consumption of cocoa. (1) Sketch Casper's budget set. (2) Sketch some of his indifference curves. (3) Calculate the amount of cheese and the amount of cocoa that Casper demands at these prices and this income. Do not forget to check the corners. (Hint: Write down the Lagrangean for this problem and solve the maximization programAn individual utility function is given by U(x,y) = x·y. This individual demand (optimal purchase) equation for x is a factor a of I/px: x* = a (I/px). In this specific case, factor a is equal to?Bob enjoys cookies (x) according to the utility function U(x)=20x- 2 tx , where t is a parameter that reflects how hungry he is. Cookies are costless in Bob’s world and so there is no income constraint. Using the envelope theorem, calculate how Bob’s maximum utility from eating cookies varies with t.
