3. Construct compensated demand functions for q and q2 for the utility function U = 2q,92 +91. Compute the own price elasticity&1, the cross price elasticity &12, and income elasticity &.
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- 9. Verify the Slutsky equation in terms of elasticities (equation ??) for the quasilinear utility function.Consider the following utility functions: U(X.) X2+2r For the above utility function, derive the demand functions for X and Y as funetions of prices and a-) income. Explain whether these goods are nomal goods Explain whether two goods are complements or substitutes Sppose now that Price of good Y isS48 and income equals 1440, Using three distinct values of price of X (P 6.P -12.P-24) draw Price consumption curve and then using Price Consumption curve draw the b-) demand curve for X. Suppose Price of good Y is $48 and price of X is equal to 6. Using three distinet income values ( I 1440,7 = 2880.1 = 4320). draw Income Consumption curve and then using Income Consumption curve draw the Engel curve for good X. d-) Consider initially that Income (I) $1440, Pr 6 and Py 48. What is the initial optimal consumption levels of X and Y? Suppose that P, rises from S6 to $12. Find the substitution effect, income effect and total effect on good X. Explain the steps carefully and support your result…What is the cross-price elasticity of turkey for these preferences? ax* Cross-price elasticity of turkey : Ex.P, =) ) aPy 2.51 X* 2.5Px+Py P, = $0.50,I = 36, P, = $0.60
- Assume a piece of jewelry, and 3 consecutive drops in its price, from ??1 to ??2, from ??2 to ??3 and from ??3 to ??4. Alia’s preferences are such that her demand is relatively elastic between ??1 and ??2, relatively inelastic between ??2 and ??3, and that she perceives that piece of jewelry as a Giffen good between prices ??3 and ??4. How would her priceconsumption curve look like in an indifference curves framework with well-behaved preferences? Clearly label your graph.If the utility function for a consumer is defined by U=6X^0.6Y^0.7 . Given that the consumer's income is 300 currency units and unit price of goods X and Y are 12 and 15 currency units respectively, calculate the equilibrium quantity of both goods. Compute the price elasticity of demand for both goods and interpret your results. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of both goodsAssume a piece of jewelry and 2 consecutive drops in its price. Also consider Alia’s demand to be relative elastic in the price range from ?1 to ?2, and that she perceives jewelry as a Giffen good in the price range from ?2 to ?3. Draw her price-consumption curve with well-behaved preferences. Clearly label your graph.
- Q.No.2 Given Q, = 50 – 5P, – 15P, – 50P, – 0.199Y, whereas P1, P2, P3 are prices and y is consumer income at a specific time. Pı=50, P2=70 P3= 60 and Y= 15000 (a)Use price and income elasticity's determine the relationship between good's? (b) Determine the effect on Q1 of a 10 percent price increase for each of the other goods individually. (c Comprebensively comments on vour resultsSuppose we observe that an individual's demand for good 1 is: 1/(2p,+p2) (where I- income). From this we can conclude that: Goods 1 and 2 are perfect complements O The price of good 1 is higher than the price of good 2 Two answers are correct O Goods 1 and 2 are perfect substitutes Three answers are correct No answer is correct Goods 1 and 2 are normal goods O These goods may be perfect substitutes or perfect complements, it depends upon the utility functionyour answer. 2. The utility function of a consumer over two goods x and y is given by u(x,y) = 20 ln x + 2y The price of y is 1. Let p denote the price of x. The consumer has an income of M> 10. The consumer's price elasticity of demand for x has a lower absolute value compared to the income elasticity of demand for y. Is this true or false? Explain by calculating both elasticities.
- a) A consumer has a utility function given by U = x025 y0.75 He has an income of £100, the price of good x is £5 and the price of good y is £10. How much of the 2 goods x and y does the consumer buy? Take a picture of your workings and upload with your answer, or type out your workings. b) For the utility function above, what is the cross-price elasticity of demand for good x with respect to the price of good y? Take a picture of your workings and upload with your answer, or type out your workings. c) For the utility function above, what is the elasticity of demand of good x with respect to its own price? Take a picture of your workings and upload with your answer, or type out your workings.Draw the following scenario: Assume a piece of jewelry and 2 consecutive drops in its price. Also consider Alia’s demand to be relative elastic in the price range from ? 1to ? 2, and that she perceives jewelry as a Giffen good in the price range from ? 2to ? 4. Draw her price-consumption curve with well-behaved preferences. Clearly label your graph. The graph may be something like this:If the demand function face by the consumer for good X is given by X=15+MP-120 Where X = Quantity demanded, M = income and P = Price of product X. Assume his original income is Kshs. 3200 per month and price of good X has increased from Kshs. 10 per unit to Kshs. 20 per unit. Calculate the magnitude of total effect (TE), substitution effect (SE) and income effect (IE) resulting from this change in price.