Consider an exchange economy with two consumers, Jack and Blue, who trade only two goods: Cookies and Hats. Quantities of Cookies are measured vertically, and quantities of Hats are measured horizontally. Jacks origin should be placed at the bottom left. Hats Cookies IC IC₂ Blues с
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- 5 Three Goods Consider a pure exchange economy with three goods: x1, x2 and x3. Consumer A’s utility function is U A = min {x1, x2}. He starts with one unit of x1 and none of the other goods. Consumer B’s utility function is U B = min {x2, x3}. He starts with one unit of x2 and none of the other goods. Consumer C’s utility function is U C = min {x1, x3}. He starts with one unit of x3 and none of the other goods. Find the general equilibrium prices and allocationBased on the diagram below, a. What is Bart's income? b. What is the price of Good B at point K? c. What is the price of Good B at point L? d. When in equilibrium point K, how much will she spend on Good B? e. When in equilibrium point L, how much will she spent on Good B?Q. 4 Two consumers, A and B, live in a pure exchange economy with two good, x and y. Consumer A is endowed with 0 unit of x, 14 units of y; Consumer B is endowed with 4 unit of x, 6 units of y. They both have the utility function U=x1/4y3/4. What will be consumer A’s consumption of good X?
- Carol needs to decide how to spend her wealth on sh and chicken.For Carol, 1 lb of sh is equivalent to 2 lb of chicken. Her preferences2Intermediate Microeconomics NYUAD, Spring 2023can be represented by the utility functionu(x; y) = 2x + ywhere x is the quantity of sh (in lbs) and y is the quantity of chicken(in lbs). The consumption set is R2+.(a) Draw two typical indi erence curves for Carol, one correspondingto a utility level of u1 and one corresponding to a utility level u2,where 0 < u1 < u2. Make sure you label the slope of the indif-ference curves and the intercepts with the horizontal and verticalaxes.(b) Suppose the price of sh is $1:5 per lb and and the price of chickenis $1 per lb. Carol has $20 to spend on sh and chicken.(i) Draw Carol's budget set, labeling the slope and the interceptpoints clearly.(ii) How much sh and chicken will Carol choose to purchase?If an economy can produce various combinationsof food and shelter along a productionpossibilities curve (PPC), then if we increase theproduction of shelter along the PPC, which ofthe following is true?a. We also increase the production of food.b. We must decrease the production of food.This forgone food production representsthe opportunity cost of the increase inshelter.c. We cannot change the production of food.d. The concept of opportunity cost does notapply along PPC.Anne likes to have bagels and orange juice for breakfast. A consumption bundle consists of a quan- tity of bagels, x (number of bagels), and a quantity of orange juice, y (liters of orange juice). For all of the following questions you can assume that the consumption set is R2 . This means that bagels and orange juice can be consumed in any non-negative quantity. Anne has a wealth of $10 to spend. At supermarket-ABC the price of bagels is pX = 2$/bagel and the price of orange juice is pY = 4$/liter. At supermarket-XYZ the price of bagels is qX = 4$/bagel and the price of orange juice is qY = 2$/liter. Supermarket-ABC is on the East Side; supermarket-XYZ is on the West Side; Anne lives in the mid- dle. Suppose that Anne can travel for free to either one of the two supermarkets, but she can only go to one of them to do her shopping. Anne knows what the prices of bagels and orange juice are at both supermarkets before she decides where to shop. This means that the budget set is now…
- Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Herpreferences over these lollies are Cobb-Douglas, and can be presented by the utility functionu(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frogcosts 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectlydivisible goods.(a) Find Ginny’s optimal bundle.(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the timeshe is there, she is left only with 75 Knuts. What is her optimal bundle now?(c) Now, consider the general case, where Ginny’s income is m, the price of Every FlavourBeans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat ChocolateFrogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .(d) Find the good on which Ginny will always spend more than half of her income.(e) Find the own-price, cross-price, and income elasticities of good 2…Ginny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Herpreferences over these lollies are Cobb-Douglas, and can be presented by the utility functionu(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frogcosts 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectlydivisible goods.(a) Find Ginny’s optimal bundle.(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the timeshe is there, she is left only with 75 Knuts. What is her optimal bundle now?(c) Now, consider the general case, where Ginny’s income is m, the price of Every FlavourBeans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat ChocolateFrogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .(d) Find the good on which Ginny will always spend more than half of her income.(e) Find the own-price, cross-price, and income elasticities of good 2.Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 Tux 8 14 18 20 20 Tuy 6 10 13 15 16 Mux Muy Mux/px Muy/py A) Calculate the MUx and MUy and fill the table in the 4th and 5th rows. B) If the two products (X&Y) are free goods how many of X and Y should the cons consumer take to maximize utility? C) What is the maximum utility of X and Y if they are free?.
- Draw Marie’s budget constraint with pies on thehorizontal axis and magazines on the vertical axis. Whatis the slope of the budget constraint?Suppose Tom and Jerry can buy/ sell apples at price Pa and bananas at price Pb. Both are price-takers. Given these prices, they seek to maximize utility by choosing how many apples and bananas to buy/sell. Tom's utility Ut (At,Bt)= log At + logBt s.t. Pa(At) + Pb (Bt) = 12 Pa + 6 Pb Jerry utility Uj (Aj,Bj)= log Aj + logBj s.t. Pa(Aj) + Pb (Bj) = 9 Pa + 15 Pb How many apples and bananas should Tom and Jerry consume? Answer in terms of Pa and PbAssume that, a consumer has $1200 to spend on two goods, X and Y. If the price of a pair of good X is $20 per unit and the price of good Y is $15 each, which of the following combinations that the consumer can purchase from good X and Good Y?