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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- David's utility function for good X and Y is given by U (X,Y) =X2y3. Where px,py and I are the price of good X, price of good Y and consumer income respectively. E). Suppose david faces a new utility such as U(X, Y)=25x0.2 Y0.75 for consuming commodity X and Y, redo question b and c. Derive the demand function for good X and Y What combination of X and Y maximizes the consumer at I=100,px=4,and py=5 F). Suppose david faces another new utility function such as U (X, Y) =15xy2 for consuming commodity X and Y,redo question b and c Derive the demand function for good X and Y What combination of X and Y maximizes the consumer at I=100,px=4,and py=5Nathan and Joe are shopping for video games. The demand function of George for Track and field games is Q = 40 - 4P, and Georgia’s demand function is Q = 36 - 3P. What will their combined demand be if the price is $2? $10? If we add George and Georgia’s demand functions, we get: At $2 a game, both George and Georgia’s will have positive demand for field games, and so we can use the combined equation to getAt $10 a game, however, George’s demand function gives negative demand, which we know means he just has 0 demand for field games. In this case, we ignore George's function, and just use Georgia’s to figure out their combined demand, since using the combined function would give the wrong answer.Kerem perceives canned tuna (Y) as an inferior good and fresh tuna (X) as anormal good. If his income increases by 100%, and his income elasticity of both types of tuna is 1. Show the effect of this increase in income on the change in his optimal choice of canned and fresh tuna, highlighting his income-consumption curve.Clearly label your graph. Reflect the proportional changes in your graph.
- ABC Co, a store that sells various types of sports clothing and other sports items, is planning to introduce a new design of Arizona Diamondbacks’ baseball caps. A consultant has estimated the demand curve to be Q = 2,000 - 100P where Q is cap sales and P is price. How many caps could ABC sell at $6 each? How much would the price have to be to sell 1,800 caps? Suppose ABC were to use the caps as a promotion. How many caps could ABC give away free? At what price would no caps be sold? Calculate the point price elasticity of demand at a price of $6.N=2 video broadcasting websites, You and Twi, must decide the number of minutes of ads to be displayed for every video that the user elects to watch. Let tY be the number of ad-minutes per video set by You, and tT the number of ad-minutes per video set by Twi. Streaming one video costs You cY=0.02, while it costs Twi cT=0.03. There are 100 million potential users, and each watches videos according to the following demand curves: qY((tY,tT) =10-2tY+tT=10-2tT+tY a- What is the cross-price elasticity between You and Twi? b- Suppose, for now, that You and Twi enter an (illegal) agreement by which they set tY=tT=t Derive the total number of users in the market as a function of t. Derive the profits for each website as a function of t. c- Now let the two platforms compete by each setting their number of ad-minutes: i. What is the best reply of You? What is the best reply of Twi? ii. Find the Nash Equilibrium of the game. iii. How many total users choose You and how many total users choose…Be fast Suppose there are three (3) consumers in a market for bottles of perfume; Mutumbu, Jasanu and Julius The individual demand for perfumes for each of these consumers is given as 10 bottles for Mutumbu, 15 bottles for Jasanu and 25 bottles for Julius at $60 per bottle for perfume. Thus, the market demand for perfumes if the market price is $60 is: (a)40 bottles (b)60 bottles (c)80 bottles (d) None of the above
- Suppose there are two agents Ahmet and Berk in an economy, and both consume two goods X and Y. Also assume that price of X is 2 YTL and Y is the numeraire good, thus price of Y is 1 YTL. Ahmet and Berk has the following utility functions:UAhmet (XA,YA)= 5ln(XA)+ln(YA)UBerk (XB,YB)= XB0,5 YB0,5a. Now assume that both X and Y are private goods. Write down the optimality condition for both agents. Then, write down the optimal level of X as a function of Y for both agents.b. Now assume that X is a public good, but Y is a private good. Write down the optimality condition for good X. Then, write down the optimal level of X as a function of Y for both agents.c. Now compare the consumption levels for X in parts a and b.What is the demand for goods L and Y given the utility function U(L,Y) = L+2Y where the price of L is $1 dollar per unit and the price of y is $Z per unit.Suppose you are the managing director of a firm that produces two goods: A and B. The priceelasticity of demand for good A is 0.75 and for good B it is 2.5. The firm is experiencing seriouscash flow problems and you have to increase total revenue as soon as possible. If you were ina position to set the price for these two goods, what would be your pricing strategy for eachproduct?
- Now suppose that the good is an inferior good. Would the demand schedule still be valid for an inferior goodDavid perceives canned tuna (Y) as an inferior good and fresh tuna (X) as a normal good. If his income increases by 100%, and his income elasticity of both types of tuna is 1. Show the effect of this increase in income on the change in his optimal choice of canned and fresh tuna, highlighting his income-consumption curve. Clearly label your graph. Reflect the proportional changes in your graph.What is the form of the inverse demand function for good 1 in the caseof perfect complements?