Alia only likes tacos, which she buys from two local restaurants - Alberto's and Roberto's - so let's define good x=Alberto's tacos and good y=Roberto's tacos. U(x,y) = 2x +3y a) Find and write down formally Alia's demand functions x (p,Py,1) and y (pz. Py, I), including for the threshold case. Can you find a compact way of expressing her indirect utility function? Holding I=$24, Py=$4: b) draw the price consumption curve for x; c) draw the demand curve for x
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- Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers (C). Her market research has found that consumer demand for this product can beexpressed as a function of the price of the charger itself (PC), the price of phones (PF), andthe consmer’s income (I). Consumer demand can be described by the function C(PC, PF, I) =(i−10PC)/ (PF) Suppose her chargers come in all different capacities to meet any quantity demanded, so youdon’t need to worry about restricting C to whole numbers for this problem. (a) Does this product satisfy the law of demand?Explain.Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers (C). Her market research has found that consumer demand for this product can beexpressed as a function of the price of the charger itself (PC), the price of phones (PF), andthe consmer’s income (I). Consumer demand can be described by the function C(PC, PF, I) =(i−10PC)/ (PF) Suppose her chargers come in all different capacities to meet any quantity demanded, so youdon’t need to worry about restricting C to whole numbers for this problem. (a) Does this product satisfy the law of demand?Explain. (b) Calculate consumers’ income elasticity as a function of the parameters. (c) Anaya is targeting a market whose income is expected to double over the next five years.Explain whether she should expect the demand for chargers to increase or decrease, andby how much, using the language of normal, inferior, luxury, and necessity goods. (d) Calculate the cross-price elasticity ofCwith respect toPF. (e)…Kari and Hector both are interested in buying pizza slices for lunch. Kari's inverse demand for pizza slices is given by P = 250 – ()Q, where Pis the price of a pizza slice (in cents) and Q is the number of slices. Hector's inverse demand is given by P = 150 -)0. Suppose that Kari and Hector are the only two consumers in the market for pizza slices. Assuming that both Kari and Hector are consuming some pizza each, which of the following functions describes the relevant portion of the market demand curve? Choose one: O A. Q = 0 – (4 + 10)P - 400 В. Р%3D 400 + ( 4+10 C. P = – 400Q (4+10) O D. Q %3D 2,500 — (4 + 10)Р O O
- Guerdon always puts half a sliced banana, q, , on his bowl of cereal, q, The two 14 goods are perfect complements. What is his utility function? Derive his demand curve for bananas graphically and mathematically. 12- 10- e, Guerdon's utility function (as a function of q, and q2) is 6- VA U= min/2q1.92} 4- O B. U=q, +92- 2- 0+ OC. U=29, + q92- 10 12 14 16 18 20 6 22 Bananas O D. U=0.5q1 + q2- OE. U=q, xq2- 5.00- 4.50- Guerdon's demand function for bananas (as a function of the price of bananas, P1. the price of a bowl of cereal, p2, and income, Y) is 4,00- 3.50- 91 = (p1 + 2p2) (Properly format your expression using the tools in the E 3.00 palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ character.) 2.50- * 2.00- P. 1.50- 1.00- 0.50- 0.00+ 10 12 14 Bananas tv 80 DI DD F1 F3 F4 F5 F6 F7 F8 F10 @ %23 $ & 1 3 4 7 Q W E Y U S F H. J く C V M option command command optic ーの * CO Cereal (bowls) p. S per banana B * * N AHiro, Francesca, and Luis are the only three buyers of gold in a small mining town. Their inverse demand functions for gold are as follows: Hiro: p = 20 - Qu Francesca: p = 10- Luis: p= 5-0 QQF. and Q are the quantities (in ounces) demanded by Hiro, Francesca, and Luis, respectively. L 9th attempt Because Hiro, Francesca, and Luis always go shopping for gold together, the seller must sell at the same price all of them. Suppose the seller is selling 13.00 ounces of gold. Then the marginal revenue equals $13.5 Give your answer to two decimals.Show that the two utility functions given below generate identical demand functions for goods X and Y UCXY) log(X)+log(Y C) UCxY) (XY05 The demand function for good X and the demand function for good Y for both utility functions equal O A. X= and Y Pv Px О В. Х- and Y 2Pv Ос. X Y= 21 PXPY O D. Х- and Y 2P. 2Py ОЕ. X= Y= РХPY
- a. Determine the demand functions of x and y in the case of a Cobb-Douglas type utility function, in the following cases: α=0.40;β=0.60 Graph the demand functions of the two goods (price as a function of quantity) assuming the individual's income is $500 - Determine what is the quantity demanded of x and y, if the price of good x is USD 1, the price of good y is USD 4, and income is USD 500 - Now, explain what happens to the quantity demanded if the prices of the goods are doubles holding income constant.10:55 Sun 8 Aug 30% Screenshot_20210808-073803_Office.jpg a) Choose X, and X, to max the utility fxn, UX,X)=chX;+(l-a)hX, st: M = P, X, + P¿X ; a) Consider a price decrease for good 1 from P toP" . Write down the Demand functions for good 1 when prices are P, and when prices drop from R toP" b) Obtain the SE and IE associated with the price change21:45 Sat 7 Aug 26% O Screenshot_20210807-213016_Office.jpg 21:30 a) Choose X, and X, to max the utility fxn, U(X,X) =ahX;+(l-a)\n X, st: M = P, X 1 + P,X , a) Consider a price decrease for good 1 from P, toP . Write down the Demand functions for good 1 when prices are P, and when prices drop from PtoP b) What is the compensating income, M° associated with the price change? C) Obtain the SE and IE associated with the price change II
- 14.3 (0) Quasimodo consumes earplugs and other things. His utility function for earplugs x and money to spend on other goods y is given by u(x, y) = 100x 2:² 2 +y. (a) What kind of utility function does Quasimodo have? (b) What is his inverse demand curve for earplugs?. (c) If the price of earplugs is $50, how many earplugs will he consume? (d) If the price of earplugs is $80, how many earplugs will he consume? (e) Suppose that Quasimodo has $4,000 in total to spend a month. What is his total utility for earplugs and money to spend on other things if the price of earplugs is $50?Suppose that Paolo and Sharon are the only consumers of ice cream cones in a particular market. The following table shows their monthly demand schedules: Price Paolo’s Quantity Demanded Sharon’s Quantity Demanded (Dollars per cone) (Cones) (Cones) 1 8 16 2 5 12 3 3 8 4 1 6 5 0 4 On the following graph, plot Paolo’s demand for ice cream cones using the green points (triangle symbol). Next, plot Sharon’s demand for ice cream cones using the purple points (diamond symbol). Finally, plot the market demand for ice cream cones using the blue points (circle symbol). Note: Line segments will automatically connect the points. Remember to plot from left to right.Assume that the Demand elasticity of a good is -1 and the Supply elasticity is +2. Assume also that (i) that the price of a complement decreases and therefore Demand shifts out by +2% and (ii) because one of the inputs in production declined in price, the Supply shifts by +2%. In partial equilibrium, the % change in the equilibrium price is -2% -1% 0% 1% 2%