1) Ambrose has the utility function U(x,x:) = 4x: + xX:. (X:: nuts, x:: berries). a) If Ambrose is initially consuming 25 units of nuts and 17 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additonal 39 units of nuts? b) If Ambrose has an income of 30 liras, the price of nuts is 2 and the price of berries is 1 liras, what is the ordinary demand of Ambrose? What is the corresponding utility level?
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- Marina 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.Roman loves corn bread. He buys corn meal and wheat flour in order to make corn bread. His recipe calls for two cups of corn meal and one cup of flour for each batch that he bakes. More corn bread is better for Roman. He can bake fractions of a batch, but has no use for corn meal or flour that is left over. What of the following is Roman’s utility function on cups of corn meal, denoted by c, and cups of flour, denoted by f?Suppose Mia's utility function on lemon soda (X) and chips (Y) is given by U(X,Y) = X0.5Y0.5 She has $80 per month to spend on lemon soda (X) and chips (Y). The prices of lemon soda (PX) and chips (PY) are $2 and $4 respectively.a. Solve for her optimal consumption bundle of lemon soda (X*) and chips (Y*)? i. Optimal Consumption in lemon soda (X*) : ii. Optimal Consumption in chips (Y*) : b. Suppose the price of lemon soda (X) increases to $8, what is the new optimal bundle? i. Optimal Consumption in lemon soda (X*) : ii. Optimal Consumption in chips (Y*) :
- Assume a consumer has a utility function U(x1, x2) = x1x2 where x1, x2 represents the amount of two goods 1 and 2 consumed in a given time period, find the utility-maximizing consumption function subject to the budget constraint5x1 + 4x2 <= 50What kind of preferences are represented by a utility function of theform u(x1, x2) = √x1 + x2? What about the utility function v(x1, x2) =13x1 + 13x2?Michael does not like to mix peanut butter and jelly in the same sandwich. However, he will consume them separately; for him, a sandwich with 1 spoon of peanut butter is exactly the same as a sandwich with 2 spoons of jelly. Michael has an income of m = 50, and the prices per spoonful of peanut butter and jelly are pPB=5 and pJ=11. Please write down Michael’s utility function over peanut butter (PB) and jelly (J). 2. Please determine Michael’s Marshallian demands PB*m and J*m3. Please determine Michael’s new Marshallian demands PB*m and J*m, when the price of peanut butter falls to pPB = 1.4. What are the (Hicks) SE and IE? Draw a diagram to show your analysis, with peanut butter on thehorizontal axis, and jelly on the vertical axis. 5. Recall that there are two different types of substitution effects. For example, in Q2 we have used theHicks SE. Does your answer to the last part change if we use the Slutsky SE? Justify. 6. Nam likes his peanut butter and jelly sandwiches with exactly…
- what is the derivative of the utility function UU = log (100-2PPii) + log(PPjj+PPdd) with respect to PPjj. Budget constaint XXii = 100 - 2PPiiConsider 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?A consumer utility function is U=(x1,x2) Where X1 is the quantity of good 1 that is bought, X2 is the quantity of good 2 that is bought. The price of good 1 is $10 and the price for good 2 is $2. If the consumer's income is $100 what will the consumer's optimal utility level be? b. Using Lagrange multilplier method. optimise the utility function x0.25 y0.25 subject to the budget constraint 24=x/10+y