1. Consider a consumer with the utility function u(x, y) = 2x¹/2 + y, an income of I = Rs100, 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?
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- Suppose a consumer utility function is given by U(X,Y)=XY+8X the price of good X and Y are 2 birr and 6 birr respectively the consumer has total income of 160 birr to be spent on two goods A) find the utility maximizing quantities of good X and Y B) find MRXSY at equilibriumFor normal goodsA) the substitution effect of a price decrease will decrease the quantity of the good demanded while theincome effect of a price decrease will increase the quantity of the good demanded.B) the substitution and income effects of a price decrease will both increase the quantity of the gooddemanded.C) the substitution and income effects of a price decrease will both decrease the quantity of the gooddemanded.D) the substitution effect of a price decrease will increase the quantity of the good demanded while theincome effect of a price decrease will decrease the quantity of the good demanded.1 Jane consumes two goods, shoes, s, and housing, h. Her income is M and the prices 57/317/3 of s and h are Ps and Ph, respectively. Jane's utility function is Us Find the following: a Marshallian demand functions b. Derive the price elasticity for housing. What is the cross price elasticity for housing? Derive the expenditure-income elasticity for housing (that is, the % change in expenditure on h when there is a 1% change in income)? What about the Cobb-Douglas demand functions explains these elasticities. C. Derive the indirect utility function and expenditure function d. Using Shephard's Lemma, derive the Hicksian demand functions e. Perform a Slutsky decomposition for housing (that is, what is the total effect on quantity demanded when there is a change in price and also what is the income and substitution effect). Now assume income is $1,500, the price of shoes is $8 and the price of housing is $125. f. What is the quantity demanded of housing? Now assume the government…
- When Sam has an income of 1.000 , he consumes 30 units of good A and 50 units of good B After Sam's income increases to $1,500 , he consumers 60 units of good A and 40 units of good B. Which of the following statements is correct ? a- Good A is a normal good and good B is an inferior good b- Both goods A and B are inferior goods c- Good A is an inferior good, and good B is a normal good d- Both goods A and B are normal goodsThe utility function of a consumer is given as follows. U(x, y) = x²y³, MU, = 2xy3 and MU, = 3x?y?. a. Derive the demand functions for good x and good y. b. Draw a demand curve. Draw an Engel curve. Is good x a normal good? С.2. A consumer's demand for the single good x is given by x(p, y) = y/p, where p is the good's price, and y is the consumer's income. Let income be $7. Find the compensating variation for an increase in the price of this good from $1 to $4.
- Mariah consumes music downloads (M) and concert tickets (C). Her utility function is giveh by U = 0.5M? + 2C². a. Using calculus, what is the marginal utility of music downloads? b. Using calculus, what is the marginal utility of concert tickets? Write the equation for the MRSMC (i.e., the MRS of C for M; M is increasing, C is С. decreasing). d. Would the bundles of (M = 4 and C = 1) and (M = 2 and C = 2) be on the same %3D %3D %3D %3D indifference curve? How would you know? e. Calculate the MRSMC when M = 4 and C =1 and when M = 2 and C = 2. Explain why the %3D %3D values of MRSMC differ across these two bundles. f. Based on your answers above, are Mariah's indifference curves convex? Explain using the values calculated. er thisJerry 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-axisA consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $2
- Anatoly's marginal utility for DVDS (D) is MU X and his marginal utility for Xbox games (X) is MUx D. Anatoly's income is $120, the price of a DVD is $20.00, and the price of an Xbox game is $10.00. How many DVDS and Xbox games does Anatoly consume to maximize his satisfaction? Anatoly consumesDVDs andXbox games. (Enter your responses using integers.)Explain why it is that as the consumer purchases more of a good, her marginal utility falls while her total utility rises.A consumer has a utility function given by U = x0.25 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?
