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For the utility function, U = 2x1/2 + y
What are the income and substitution effect of price changes in Px and Py respectively?
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- Consider a consumer with preferences over two goods, x and y. Preferences are given by U(x,y) = xy. Suppose the consumer’s income is $72 and the price of good y is $1. Suppose the price of good x is initially $4 and subsequently rises to $9. Find the numerical values of the income and substitution effects on the consumption of good xSuppose 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 equilibriumJoan has the following utility function: u(x, y) = 5x + 3y. Consider that income is I = $8, and prices are given as pa = $4, p = $2. (e) Assume the price of y increases to 4. Find the total, income and substitution effects for x. Consider this price change a "large" price change.
- The income effect of an increase in the price of a normal good that a consumer buys on a regular basis will be ___________ and the substitution effect will be _________.a) positive; negativeb) negative; negativec) negative; positived) positive; positivee) One cannot tell.Sally consumes two goods, X and Y. Her utility function is given by the expression U = 2XY3. The current market price for X is $20, while the market price for Y is $10. Sally's current income is $500. a. Write the equation for Sally's budget constraint. What is the slope of her budget line? b. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint.Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30
- Philip's utility function is U(q1,q2)=4q10.26+q2. Part 2 Calculate the substitution, income, and total effects for a change in the price of q1 on the demand forq1. The substitution effect for a change in p1 is ε*= .... the income effect is θξ=... and the total effect is ε=... (Round your responses to 2 decimal places and include a minus sign as necessary.)Consider the following utility function и(х, у) %3 3х + 4y a. Is the utility function homothetic? Explain. b. Under what condition will the consumer purchase good x alone?Assume the price of good A goes up and the consumer decreases purchases of good A and decreases purchases of all other goods. How might you explain this lack of substitution into other goods? The indifference curve for good A and other goods must be linear The income effect is greater than the substitution effect Good A is a luxury item Good A is inferior
- Compute marginal utilities and marginal rate of substitution for each of the utility functions given below. a) U(X,Y)= 1- e-ax -e-by b) U(X,Y)= XY + 3X + 5Y c) U(X,Y)= (0.3Xm +0.78m)/1 X1-a y1-b d) U(X,Y)= + 1-a 1-bUtility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…Lynn has a Cobb-Douglas utility function U(x1, x2) =XaYb What share of her budget does she spend on x1 (recorded music tracks) and x2 (live music) in terms of her income m = $30, prices of the two goods, p1 = $0.5 and p2= $1?
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