Quasimodo has the utility function U (x, m) = 200x – 5 + m, where x is his consumption of earplugs and m is money left over to spend on other stuff. If he has $10,000 to spend on earplugs and other stuff and if the price of earplugs rises from $50 to $70, then his net consumer's surplus falls by 600. increases by 400. falls by 2800.
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- 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 programSuppose 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 onlyA 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 a consumer has a budget of $200 to spend on two goods, X and Y, whose prices are $20 and $10, respectively. If the consumer is observed to buy 5 units of X and 10 units of Y, where the respective Marginal Utilities of X and Y are, 50 and 40 utils, is the consumer in equilibrium? Explain why or why not. If the consumer is not in equilibrium under conditions in d), suggest another combination that would possibly achieve equilibrium. Explain your answer.A consumer is in equilibrium and is spending income in such a way that the marginal utility of product X is 40 units and that of Y is 32 units. If the unit price of X is $5, then the price of Y must be:
- Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.A 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.Victor is the manager of a local bank branch in College Station where he consumes bundles of two commodities x and y. Prices in College Station are px=1 and py=5. He is offered a transfer to Dallas where prices are px=2 and py=8; Victor’s utility function is U(x,y)=xy and his income in College Station is $5000. (Victor’s utility maximization is always characterized by the tangency rule). Will Victor be able to afford what he was buying in College Station if he is offered a salary in Dallas that guarantees his welfare is the same with the transfer? A. Yes B. No
- 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…James works for a delivery company in College Station where he consumes bundles of two commodities x and y. Prices in College Station are px=1 and py=5. He is offered a transfer to Dallas where prices are px=2 and py=5; James is guaranteed a salary in Dallas with which he would be able to buy exactly what he buys in College Station. James’s utility function is U(x,y)=x1/3y2/3 and his income in College Station is $2500. What happens to James’ utility if he accepts the transfer (James’ utility maximization is always characterized by the tangency rule)?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.