The consumer's utility function is the following: U=x1x2 The consumer's optimal values of x and x2 are the given by the following: x= 1 I I 2 2P 2P 1 2 The compensated demand equations for x, is the following: x = I 1 1/2 lc 2 1 Assume the prices are the following: P =35, P=23, and I=1709. The price of x, changes to P₁₁ =18. What is the income effect? 1
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- 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 IISuppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the quantity of pizza demanded, P is the price of a pizza, and Pb is the price of a burrito. What is the slope of this demand function, and what information does the slope provide?..
- If Philip's utility function is U=4 (41) 05+42. 0.5 what are his demand functions for the two goods? Let the price of q, be p,, let the price of q, be p2, and let income be Y. Philip's demand for q, as a function of p, and p, is 91 and his demand for good q, is (Properly format your expressions using the tools in the palette. Hover over tools to see keyboard shortcuts. Eg, a subscript oa. 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.Suppose we have a market with 200 individuals with preferences over two goods, x and y. 1. Consider that all 200 individuals have the utility function U = x²/3y¹/3 and that each individual has the same income and is subject to the same prices. Calculate the market demand for x as a function of income and prices. 2. Find the own price elasticity of demand for good x. Is the elasticity constant or is it changing at different values of P? 3. Suppose now that we know m = 135, P = 3, 4. What is the market demand for x? This should be a number. and Py 4. Consider now that 100 individuals (type A) have the utility function U = x²/³y¹/³ and the other 100 (type B) have the utility function U = x¹/3y2/3. Each individual still has the same 'y income and is subject to the same prices. Calculate the market demand for x as a function of income and prices. 5. Suppose now that we know m = 250, P = 5, and Py 3. What is the market demand for x? This should be a number. = =
- 19:32 Fri 6 Aug 91% Screenshot_20210806-193021_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) Write down the demand functions for goods 1 and 2 b) 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 c) What is the compensating income, M associated with the price change? Obtain the SE and IE associated with the price change 24Suppose the demand curves for goods A, B, and C have the following functional forms, where Q denotes quantity demanded, P denotes price, and M denotes income: QA = 120 - 3.5PA - 6PB + 14M QB = 100 - 2PB + 3PC + 1.1M Qc = 1500 -0.5Pc - 300M. Based on these demand curves, which of the following goods are known to be normal goods? A, B and C B A and B only C AIf you have demand function ²= 20-2P₁ + 3 P₂ +4P3 + 2/ when P₁: price & good (1), and P2 and be the price of other goods and Y incom A- Find reduce form when P₁₂ = 1 and 1²3 = 3 Y = 100 B- Find The slope demand function
- A consumer’s preferences over two goods x and y are given bythe utility function U(x, y) = xαyβ with α, β > 0. The prices of the goods are px = 2 and py = 4.The consumer has an income of I > 0.(a) For what values of α and β are these utility functions strictly monotone?(b) For what values of α and β will the consumer demand (i.e., Walrasian demand) be more x than y?(c) For what values of α and β are these goods gross substitutes? For what values of α and β are these goods gross complements? Provide a justification for your answer.The demand function for a particular good is x = a + bp. What are the associated direct and indirect utility functions?Consider two consumers, A and B, who consume two goods, x and y. Assume that the utility function for A is U₁ = A₁ and the utility function for B is UB = XBYB. Consumer A is endowed with 10 units of x an 10 units of y. Consumer B is endowed with 10 units of x and 40 units of y. Assume the price of y is set to $1. What is the expression for Consumer A's demand for x? XA 10p, +10 Pr 10p, +40 Pr 10pz +10 4pz 10p, +40 4pz