2. Consider a consumer with utility function u(x1, 22. 23) for three goods, where the cross- price elasticities are null. Show that the ratio of substitution effects 23 is equal to 513
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- 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 goodsIf 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.You are given the following utility function (and there is obviously an income constraint). Derive the Marshallian demand function (half the points) and identify the income elasticity of both goods (half the points). u=x1x2
- 1/2 1/2 2. Cynthia has preferences represented by the utility function u(x) = x¹/² + x¹/² (a) Calculate Cynthia's marginal rate of substitution. (b) Calculate Cynthia's Marshallian Demand functions x(p, 1) and x(p,1). (c) Does Cynthia consider either of these goods to be Inferior Goods? (d) Show that Cynthia's demands generate an indirect utility function V(p,1)=√√IP₁P2 (e) Solve for Cynthia's expenditure function.Suppose the weighted marginal utility for two goods x and y at a position of consumer equilibrium 70. If the price of good x is r10 and the relevant marginal utility for y is 140 what is the price of good y and the relevant marginal utility for xyour 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.
- Jerry spends his entire budget on bread and gasoline. His preferences are complete, transitive, monotonic, and convex. For Jerry, bread is an inferior good that follows the law of demand. Moreover, his cross-price elasticity of demand for gasoline with respect to the price of bread is negative. Suppose the price of bread increases, all else constant. a. Create a chart to show the total, income, and substitution effects on bread and gasoline of the increase in the price of bread. b. Use budget lines and indifference curves to graphically illustrate the three effects. Be sure to label each effect on your graph (or through the chart from part a) and plot bread on the x-axis and gasoline on the y-axisConsider 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…1/2 Consider a consumer with the utility function u(x, y) = 2x¹2 + y, an income of I = Rs 100, and price of good y is Rs 1. A) Find the demand functions for goods x and y. B) If, ceteris paribus, price of good x decreases from Rs 4 to Rs 3, what is the compensating variation? 1.
- Consider the utility function: U(x,y)= -4(3x-12)² - (2y-10)² Determine the marginal utility for the two commoditiesConstant Elasticity of Substitution utility function U(x. y) = (x^a*y^ (1-a))^b + y. I am looking for a this form of CES utility function to derive demand functions. (Note = > a is alfa, b is lambda).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.
