3. If U(z, y) = 1yl/2 and the budget is M pir1 +P2T2: a. What is Walrasian Demand? What does it represent? b. What hat is the Indirect Utility Function? What does it represent? c. Using Part B as a starting point, use Roy's Identity to recover Walrasian Demand.
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- Suppose U = 2X + Y, I = 20, Px = 2, and Py = 2. (a) Find Marshallian demand for X and Y . (b) What is Marshallian demand for X and Y if the price of X increases to 5? How much of the change in demand for X is the income effect and how much is the substitution effect? (c) How much is compensating variation for the price change described in part (b)? (d) How much is equivalent variation for the price change described in part (b)? ( Please solve all the subparts ASAP I will give you thumbs up . )Lan's utility function is U = xa y1-a where x denotes her consumption of good X, y denotes her consumption of good Y and a = 0.8. The price of good X is Px = 7, the price of good Y is Py = 14 and Lan's income is M = 338. If each price increases by 2 dollars, how much money must Lan be given to compensate her for the price increase?If BC2 is the relevant budget constraint, then which bundle (combination of X and Y goods) will maximize this consumer's untility? A. A. B. B. C. C. D. D. E. E. F. F. G. G. H. H. I. I. J. J.
- The utility function is max(2x,y). If the price of x is 1, the price of y is p, and his income is m, how much y does he demand? Please show your workI need answers of C,F 1. Think about a utility function U(x,y) =xy, the budget constraint is px*x +py*y= m. a. Please derive the Marshallian demand functions. b. Please derive the indirect utility function. c. Please derive the expenditure function. If originally m = 8, px=1, py=4. d. Now px has increased to 2. f. Based on (c), after the price change, how much should be compensated to maintain his original utility level?I need help with this homeowrk question i am unsure if i have it correct. Suppose a consumer’s utility function is given by U(X,Y) = X^1/2*Y^1/2. Also, the consumer has $36 to spend, and the price of good X is P(x) = $4. Let good Y be a “composite” good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X.if P(x) increases to 9 and the new bundle of the customers demands are 2 units of x and 18 units of y, how much additional money would the consumer need in order to have the same utility level after the price change as before the price change? (Note: this amount of additional money is called the Compensating Variation.) and of the total change in the quantity demanded of good X, how much is due to the substitution effect and how much is due to the income effect? (Note: since there is an increase in the price of good X, these values will be…
- Khan lives in a world with two consumption goods x and y. Her utility function is U (x, y) = √x² + y². a. If px = $3,py = $4, and her income, I, is equal to $50, what will be the quantities of x and y that Maya should buy to maximize her utility? Make sure that you write out the Lagrangian and the first-order conditions. (Hint: It may be easier to maximize U² than U). Have you found a true maximum? Explain your answer.Mike has two identical brothers. Each of them have the same utility function below. If Mike and his brothers are the only people in the market, what is the aggregate demand at each price of X below? (Each of their income is $100 and the price of Y is always $1). U (x,y) = x^2/5 Y^3/5 Price of X=$8 Price of X=$4 Price of X=$2 Price of X=$1A consumer has the following indirect utility function:U∗(Px, Py, M) = M2/2PxPy1. What is the consumers Marshallian demand for good x?2. What is the expenditure function?3. What is the Hicksian demand for good x?
- Q6. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. Suppose as Case 1, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e. (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space. d. Now suppose Case 2, where assuming if income increases to $120, holding all else the same, do the same analysis (parts a-c) and contrast your answers to Case 1. For part c, you should draw old (Case 1) and new (Case 2) budget lines/point of optimality.At the utility max point the rate at which a consumer is willing to trade C0 for C1 is equal to 1 plus the interest rate (MRS = 1+r). Suppose U(C0,C1)=lnC0+lnC1, MRS=1+r, and C1=(1+r)C0. If the consumer has income of $100 and saves $60 at 10%, what are C0 and C1? options: $50, $60 $40, $66 $50, $52.50 $40, $60Suppose the MU of good X is 20 its price is K4 and the MU of good Y is 50 its priceis K5. The individual to whom this information applies is spending K20 on eachgood. Is he or she maximising satisfaction? Why or why not?