The following is an example of a "net seller" of good 1, when the price vector is (2,1): a. The consumer is endowed with bundle (3,6) and the Marshallian demands are (2,9). O b. The consumer is endowed with bundle (3,6) and the Marshallian demands are (4,4). c. The consumer is endowed with bundle (3,6) and the Marshallian demands are (2,7). O d. The consumer is endowed with bundle (3,6) and the Marshallian demands are (2,8 ).
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- a)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese meals and use the utility maximization conditions to find the demand for Vietnamese food of the typical consumer (keep in mind that since utility is quasi-linear, you can find demand without information about the consumer’s weekly budget). b) Sum across consumers to find the weekly market demand for Vietnamese meals in NYC.Economics A consumer’s demands x, y for two different goods are chosen to maximize the utility function U (x,y) = √x + √y (x ≥ 0, y ≥ 0) subject to the budget constraint px+qy = m (where p,q,m > 0).(a) Find the utility-maximizing demands for both goods, as well as the Lagrange multiplier λ, all as functions of the three variables (p,q,m). Simplify all expressions as much as possible.(b) Find the maximized utility U*(p, q, m). Simplify the expression as much as possible(c) Show that (dU/dm)* is the Lagrangian multiplier λ.Consider a consumer who has utility function U(x,y)= x + 2y, where x is the amount of good 1, and y is the amount of good 2, and income of 90. Suppose the price of good 1 is 5 dollars per unit, and the price of good 2 is 15 dollars per unit. What is the consumer's quantity demanded of each good? I.e. which consumption bundle (x,y) that the consumer can afford maximizes their utility? O(4.5,3) O (20,6) (18,0) O (0,6)
- 1. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good. 2. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y2 , derive the Hicksian demand function for good Y.3. Suppose that initially PX = 2, PY = 8, I = 96 and the Marshallian demand function for good Y is given by Y∗ = (0.5I/ PY)+(0.5PX/PY)− 0.5. Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (XA,YA) = X0.25Y0.75, UB (XB,YB) = X0.75Y 0.25Show that pareto-improvement is possible if,…Moe's income is $320 per week and he spends it on two goods, X and Y. Good X costs $8 and good Y costs $4 per unit. His utility function is U = 4.5XY. (a) Calculate Moe's utility-maximizing purchases of X and Y. (b) Calculate Moe's constrained utility- maximum if his income decreases by $2.00? (c) If the price of Y doubles, with no change in the price of X, by how much would his income have to increase to enable him to maintain his initial level of utility (as in part (a) above)?The inverse demand function of a group of consumers for a given type of widgets is given by the following expression: π=−10q+2000 $ ( I ) where q is the demand and π is the unit price for this product. A. Determine the maximum consumption of these consumers. B. Determine the price that no consumer is prepared to pay for this product. C. Determine the maximum net consumers’ surplus. Explain why the consumers will not be able to realize this surplus. D. For a price π of 1000 $/unit, calculate the consumption, the consumers’ gross surplus, the revenue collected by the producers, and the consumers’ net surplus. E. If the price π increases by 20% (The new price π=1200), calculate the change in consumption and the change in the revenue collected by the producers. F. What is the price elasticity of demand for this product and this group of consumers when the price π is 1000 $/unit. G. Derive an expression for the gross consumers’ surplus. H. The supply function for the widget…
- Sanghoon has a utility function over audiobooks, A, and movie downloads, M, given by Linh has a utility function given by 0 U= √AM. U=AM. Explain why Sanghoon and Linh have the same ordering over any two bundles and therefore have the same ordinal preferences. Sanghoon and Linh have the same ordering over any two bundles and therefore have the same ordinal preferences because A. Sanghoon's utility function is the inverse of Linh's utility function. B. Sanghoon's utility function is a monotonic transformation of Linh's utility function. C. Sanghoon's utility function is a function of the same goods as Linh's utility function. D. Sanghoon's utility function generates the same cardinal values as Linh's utility function.Warren has $144 to spend on hamburgers (h) and gelato (g). His utility function is u(h,g)=2√hg+10. Hamburgers cost pH= $4 and gelato costs pG= $4. (i) Find Warren's optimal bundle. (ii) Now suppose the government imposes a $5 unit tax on hamburgers, which raises the price to $9.What is Warren's optimal bundle now? (iii) Finally, suppose that the government gives Warrena lump-sum subsidy of $72 while still imposing the tax. What is Warren's optimal bundle inthis case? (iv) Suppose that the government had simply imposed the tax (without a subsidy).Use the answers from(i) –(iii) to find the substitution and income effects from the increase in the price of hamburger.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.
- If Philip's utility function is U=4 (41) 05+42. 0.5 what are his demand functions for the two goods? Let the price of q, be p,, let the price of q, be p2, and let income be Y. Philip's demand for q, as a function of p, and p, is 91 and his demand for good q, is (Properly format your expressions using the tools in the palette. Hover over tools to see keyboard shortcuts. Eg, a subscript oAssume Jim consumes two goods: X and Y. He has a utility function of U=X²Y on bundles of (X, Y). The price for good X is twice the price of good Y. If Jim bought a combination of the two goods, and in doing so achieves a utility of 1000, how much of good X did Jim buy? a) 25 b) 5 c) 10 d) 2014.3 (0) Quasimodo consumes earplugs and other things. His utility function for earplugs x and money to spend on other goods y is given by u(x, y) = 100x 2:² 2 +y. (a) What kind of utility function does Quasimodo have? (b) What is his inverse demand curve for earplugs?. (c) If the price of earplugs is $50, how many earplugs will he consume? (d) If the price of earplugs is $80, how many earplugs will he consume? (e) Suppose that Quasimodo has $4,000 in total to spend a month. What is his total utility for earplugs and money to spend on other things if the price of earplugs is $50?