Suppose that consumer has the following utility function: U(X,Y)= X1/2y1/4. Suppose also that Px 2,Py-3 and 1-144. What would be the optimal consumption of X and Y at the equilibrium, espectively? 36, 24 12,40 24, 32 48, 16
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- suppose that the utility function of a consumer is given by TU(x,y)=3x2 y and the price of x and y are $1 and $2 per unit, respectively. if the income of the consumer is $600 and if he spends all of his income on the consumption of commodities of x and y, find the optimum amount of x and y that the consumer will consume at equilibrium and find MRTSx,y.A consumer prefers to consume two commodities in fixed proportions. Specifically, she prefers to consume 1 unit of x2 and 4 units of x1 at the same time. Represent her utility function and find the most preferred and affordable consumption bundle for prices p1 and p2Suppose that an agent has utility function u(x,y)=x+2y. What information is necessary to calculate the agent’s optimal consumption of x? price of y only price of x only income only price of x, price of y, and income price of x and y only
- Suppose that consumer I has the utility function u(x,y) = x + 2y and consumer II has the utility function u(x,y) = min{x, 2y}. Consumer I initially has 12 units of y and zero units of x, while consumer II has 12 units of x and zero units of y. It is correct to state that, in competitive equilibrium, the agents' consumption basket will be:What condition should be met in order for the consumer to maximize satisfaction in the consumption of good X and good Y? Provide the calculation that satisfies the equilibrium condition.The preferences of a typical Californian can be represented by the following utility function: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) Here, x1 and x2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p1 and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x1 ≤ 50). Call this restriction a rationing constraint. (a) If α=0.25, m=100,and p1 =p2 =1, find the optimal consumption bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does x1∗ = 50)? (b) Suppose that α = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing constraint on electricity consumption binding? (c) Now, assume that there is no rationing constraint. Assume m = 100 and p1 = p2 = 1, but α remains as a generic parameter. Solve for the optimal quantity…
- For the utility function U = Qx0.15Qy(1-0.15) find the trade-off rate between good X and good Y at Qx= 4 and Qy=19A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 15 and the marginal utility of Y is 8. The unit price of X is $3 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should Multiple Choice a. decrease consumption of product X and increase consumption of product Y. b. increase consumption of product X and increase consumption of product Y. c. decrease consumption of product Y and increase consumption of product X. d. stick with the current consumption mix because it yields maximum utility.A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 10 and the marginal utility of Y is 8. The unit price of X is $5 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should
- 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.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?..Q)Suppose we have two goods, x1 and x2, with price p1 and p2, respectively. Consider the budget constraint x1p1+x2p2≤m. If both p1 and m double (i.e. p’1=2p1 and m’=2m), the area of the feasible consumption set: a) doubles B)stays the same D) quadruples C)none of the above E) falls by half
