e utility function for this economy is u(x,y) = xy. What is the optimal basket (x,y) for this econo %3D produce? 5 (10, 380) D (50, 100) O (100, 200)
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- Rick always likes to consume a cup of tea with a serving of noodles at any given time of the day. He earns a monthly allowance of 150. A cup of tea cost him Rs5 and serving of noodles cost Rs 10. Given this what will be Rick’s optimal consumption bundle?Consider 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?How does a consumer’s optimal choice of goods change if all prices and the consumer’s income double? (Hint: focus on the budget constraint. You don’t have to, but you can use an example to support your answer).5. Output is produced according to a production process given by: Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then what is the cost-minimizing combination of K and L capable of producing 32 units of output?
- 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/FA consumer prefers to consume 1 unit of x with each unit of y. if the price of x is $12 and the price of y is $4 , and he has income of $120, what is the optimal pair (x*,y*) to consume? a. (12,12) b. (20,20) c. (22,22) d. (40,40)Henry's utility function is u(x,y)=max{x+3y,3x+y}. (a) Suppose Henry's current consumption bundle is (2,1.5), what is his current utility level? If he consumes the bundle (1.5,2), will his utility change from the current utility level?
- Elsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = BW where B is the amount of bananas she consumes and W the amount of water. Her production function for bananas is B = 6LB where LB is the amount of labour time she devotes to bananas. Her production function for water is W = 2LW where LW is the amount of labour time she devotes to water. If the total time she has available is 10, what should she do to maximize her utility?what is the derivative of the utility function UU = log (100-2PPii) + log(PPjj+PPdd) with respect to PPjj. Budget constaint XXii = 100 - 2PPiiSylvia’s utility function over waffle fries, F, and frozen yogurt, Y is given by U = 2 ∗ F ∗ Y. Her marginal utility from waffle fries is MUF = 2Y, and her marginal utility from frozen yogurt is MUY= 2F. A pack of frozen waffle fries sells for $4. The price of a cup of frozen yogurt is $6. Sylvia has a budget of $120 to allocate to these items each month. a) For Sylvia’s utility functions above, draw a set of indifference curves showing utility levels U = 20, U = 30, and U = 40 b) What is the equation for Sylvia’s budget line? Draw it (with frozen yogurt –Y– on the vertical axis), and label the slope and intercepts. c) What is Sylvia’s marginal rate of substitution? d) If Sylvia maximizes her utility, how much of each food should she consume? Solve for her optimal bundle. Show how to determine this bundle on a diagram using indifference curves and a budget line. e) Briefly explain if each of the four conditions of the utility-maximizing behavior is satisfied with the bundle you…
- Consider an economy with one consumption good, 100 identical consumers and 100identical firms. Each consumer is endowed with one unit of time and one unit ofcapital. The agent can spend time either working or enjoying leisure. A represen-tative consumerís utility function is u (x; l) = ln x + 2 ln l, where x is consumptionof goods and l is leisure. Each firm hires consumers to work and rents capital fromconsumers to produce goods: y = f (K; L) = K^1/2L^1/2, where L is the amount oflabor hired and K is the amount of capital rented. Both consumers and firms takegoods price p, wage rate w and rental rate r as given. Normalize p = 1. 1. Set up a representative consumerís utility-maximization problem.Derive the Marshallian demands for consumption and leisure as functions ofwage w and rental rate r 2. Set up a representative firm's profit-maximization problem. Writedown the first-order conditions regarding the choices of K and L 3. Set up all the market-clearing conditions. 4. Use the…A consumer utility function is U = 1 log x1 + log x2. His budget constraint is given by 2x1 + 4x2 = 36. Find out how many units of x1 and x2 should the consumer buy in order to maximize his utility.Jane has utility function u(x,y)=x4y5. The price of x is px, the price of y is py, and Jane’s income is W. What is the expression of her consumption of y as a function of prices and income (her optimal consumption is determined by the tangency rule)? Qy(px,py,W)= 9W/5py. Qy(px,py,W)= 5W/9py. Qy(px,py,W)= 4W/3py. Qy(px,py,W)= 5W/4py. Qy(px,py,W)= 4W/5py.
