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find optimal bundle from diagram
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- (a) A consumer has utility u(x,y,z) = ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz=1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? (HINT: MUx = 1/x, MUy= 2/y, MUz = 3/z and remeber the "equivalent bang for the buck" condition). (b) Forget about (a). Suppose you have t= 29 hours in total to spend on 3 projects X,Y and Z to make some money. If you spend x hours on project X, you make 2 sqrt(x) dollars; If you spend y hours on project Y, you make 3 sqrt(y) dollars; If you spend z hours on project Z, you make 4sqrt(z) dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x? on y? on z?a halving price of the prices of good A and Good B have the same effects on the budget line as doubling income. is this true or false and how woukld it look like using ana equation of a budget lineIntialy mr. John is at equilibrium such that the last dollar spent on each of several products gives hi identical marginal utility i.e MUorange/porange=MUApple/pApple=...=MUn/pn where Mu orange =aditional utility derived from consuming one more unit of Apple ,pApple=price of a unit of Apple etc Q.how will Mr.Jhon react if the price of orange and other goods remain constant?and how can the equilibrium be restored?
- Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.An increase in the price of Wood will shift thesupply of furniture to the left or inwards.Select one:Oa. FalseO b. True
- Maya divides her income between coffee andcroissanls (both of which arc normal goods). An earlyfrost in Brazil causes a large increase in the price ofcoffee in the U nitcd Stites.a. Show the eflcct ol the frost on Maya's budgetconstraint.b. Shm" the effect ol the frost on Maya's optinu,loonsumption bwl<ile assunling that the substitutioneflcct outweiglls the income effect for croiss:mls.c. Show the eflcct of the frost on Maya's optimalconsumption bw,dle assuming that the incomeeffect outweighs the substitution effect forcroissantsAnn can finish a project either this week or next week. The delayed rewardsare 10 in either case. (The project can be done only once or not at all).Next week is busy and the cost of finishing the project are lower thisweek. Theimmediate costs are 4 this week and 6 next week.Ann has a quasi-hyperbolic utility withδ= 1 andβ <1. Imagine that Anndoes not finish the project this week. Then she should finish it next week (A) ifβ >0.6; (B) ifβ >0.4; (C) only ifβ= 1; (D) for anyβ.11. Suppose thatβ= 0.5 and Ann correctly anticipates her choice next week. Thenshe should finish the project (A) this week; (B) next week; (C) never; (D) not enough information. Suppose thatβ= 0.5, and Ann can commit to finish the project next week (e.g.by imposing a heavy cost on herself if the project is not finished nextweek).Then she will (A) do the project this week;(B) commit to do it next week and finish it then;(C) do it next week without commitment;(D) commit and then not finish it.Ann can finish a project either this week or next week. The delayed rewardsare 10 in either case. (The project can be done only once or not at all).Next week is busy and the cost of finishing the project are lower thisweek. Theimmediate costs are 4 this week and 6 next week.Ann has a quasi-hyperbolic utility withδ= 1 andβ <1. Imagine that Anndoes not finish the project this week. Then she should finish it next week (A) ifβ >0.6; (B) ifβ >0.4; (C) only ifβ= 1; (D) for anyβ.11. Suppose thatβ= 0.5 and Ann correctly anticipates her choice next week. Thenshe should finish the project (A) this week; (B) next week; (C) never; (D) not enough information. Suppose thatβ= 0.5, and Ann can commit to finish the project next week (e.g.by imposing a heavy cost on herself if the project is not finished nextweek).Then she will (A) do the project this week;(B) commit to do it next week and finish it then;(C) do it next week without commitment;(D) commit and then not finish it. Can you…
- Each day Paul, who is in third grade, eats lunch at school. He likes only Twinkies (t) and soda (s), andthese provide him a utility ofutility = U (t s) =square root (ts).a. If Twinkies cost $0.10 each and soda costs $0.25 per cup, how should Paul spend the $1 hismother gives him in order to maximize his utility?b. If the school tries to discourage Twinkie consumption by raising the price to $0.40, by howmuch will Paul’s mother have to increase his lunch allowance to provide him with the same levelof utility he received in part (a)?After Marc consumed his second cup of coffee, which gave his 15 units of satisfaction, his total utility is 40. From this we can deduce that Marc’s marginal utility is a) zero b) positibe c) negative d) increasingI like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?
