You are provided of the following demand function: Qxd 10,000 - %3D 4PX + 5PY + 2M + Al where PX is the price of X, PY is the price of good Y, M is income, and Al is the amount of advertising on X. Suppose the present price of good X is $50, PY = $100, M = $25,000, and Al = 1,000 units. What is the quantity demanded of good X? *
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- Let the consumer have the utility function a. Show that the utility maximizing demands are and b. Letting p1 = p2 = 1, use the inverse elasticity rule to show that the optimal tax rates are related by c. Setting w = 100, r1 = 0:75, and r2 = 0:5, find the tax rates required to achieve revenue of R = 0:5 and R = 10. d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.Considering, QDx = - 4Px -0.02R + 2Pz, and assuming that the individual's income (R) is equal to $600, and the price of the good z (Pz) equals $10, if the individual's income (R) reduce to $300, will the individual's demand for good x increase or decrease? CALCULATE and GRAPHICALLY ILLUSTRATE the behavior of demand for good x. Then inform what kind of property this is.Assume that product X is quantified in the following manner:QDX= -2PX + 0,5PY - 0,2PZ + 1,2I. In which:QDX is a quality of product XPX is the price of product XPY is the price of product YPZ is the price of product ZI is the entry of the center of the userMake an argument to determine whether the demand curve for product X will change and how it will change for each of the following cases:i. Consumer income increasesii. The price of product X decreasesiii. The price of product Y increasesiv. The price of product Z decreases
- Spreadsheet exercises. Suppose that the market for video games is competitive with demand function Qd = 130 − 4p + 2Y + 3pm − 2pc, where Qd is the quantity demanded, p is the market price, Y is the monthly budget that anaverage consumer has available for entertainment, pm is the average price of a movie, and pc is the price of a controller that is required to play these games. 1. Given that Y = $100, pm = $30, and pc = $30, use Excel to calculate quantity demanded for p = $10 to p = $80 in $5 increments. Use Excel’s charting tool to draw the demand curve. 2. Now, Y increases to $120. Recalculate the demand schedule in part 1. Use Excel’s charting tool to draw the new demand curve in the same diagram. 3. Let Y = $100 and pc = $30 again, but let pm increase to $40. Recalculate the demand schedule in part 1. Use Excel’s charting tool to draw the graph of the new demandcurve. 4. Let Y = $100, pm = $30, and pc increase to $40. Recalculate the demand schedule in part 1 and use Excel to draw…Suppose a consumer’s preferences over two goods x_1 and x_2 are given by u = Square root (X_1,X_2). Her income is M and the two goods cost p1 and p2 per unit respectively. a) Derive her utility at the optimal consumption point as a function of prices and income. b) Now suppose the government imposes a proportional tax t on the value of the good x_1 (such as VAT). If the consumer approaches the government for income compensation to remain as well off as before the tax (i.e. compensating variation in income), how much money would she ask for? c) If instead, the government decides to maintain consumer’s utility level not through lump-sum transfer but by introducing a proportional subsidy S on the price of good 2, then what should be the size of the subsidy? d) Based on your answer in part c) discuss how much would it cost for the government to introduce both a tax and a subsidy at the same time? Can you think of any situation when this policy would make sense?Consider a person who consumes water and bread, deriving utility by xy if x is the amount of water consumed and y is the amount of bread consumed. Suppose this person's income is Rs. 10, the unit price of bread is Rs. 3 and the unit price of water facing this person is Re. 1. The price of water incorporates a per unit subsidy of Re. 1, i.e., for every unit of water consumed by this person, she pays Re. 1 to the water supplier and the government pays Re. 1 to the water supplier. Suppose this person's demand is (x0, y0). ,If the government provides this person a lump-sum income subsidy that exactly offsets her utility loss on account of removal of the water subsidy, then the required lump-sum subsidy is
- Q1: The demand for good X is given by Qx d = 6,000 − 1/2 Px − Py + 9 Pz + 1/10 M. Research shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while the average income of individuals consuming this product is M = $80,000. a. How many units of good X will be purchased when Px = $5,230? The calculation should be handwrittenAn individual utility function is given by U(x,y) = x·y. Let I = $800, px = $20 and py = $40. Suppose that a tax t of $10 per unit is imposed on good x. Assume that the full burden of this excise tax is borne by this consumer, i.e. the new price this individual faces for good x is p’x = px + t = $20+ $10 = $30. Compute this persons utility level with this excise tax. It is equal to?The Federal election is just around the corner. The competition between the two candidates, Sam and Jenny , is fierce. As a consumer (and Australian voter), you only care about public transportation and child care. Let public transportation be good X and child care be good Y . Each trip in the public transportation costs $10 and each day of child care service costs $100. Your after-tax income is $500 per week. Assume that you always consume a positive amount of both X and Y (also known as interior bundles). Your utility function is given by: U(x, y) = αxβ + 2y + 1 Write down the MRS in terms of α, β, x, and y Draw two indifference curves. Do the indifference curves have the same slope along any vertical line (when x is held constant)? Illustrate and explain. Is it possible to establish whether Y is a normal or inferior good? Explain. Based on your answer in part (c), is the price elasticity of Hicksian demand for Y greater, smaller, or equal to that of Marshallian demand?…
- Assume the demand function for good X can be written as: QX = 30 - 3PX + 2PY + 0.2I Where PX is the price of good X PY is the price of good Y I is the consumer income. a) Based on the demand curve above, is X a normal or inferior good? b) Based on the demand curve above, what is the relationship between good X and good Y? c) What is the equation of the demand curve if consumer incomes are $40,000 (use $40, income in thousands) and the price of good Y is $35?Let the following demand and supply equations be respectively:D = 5p ́ ́-4p ́ + 11S = 6p ́ ́-2p ́ + 5p-4Find p (t) with the hypothesis that the market is in equilibrium with the conditionsinitials p (0) = 4 and p ́ (0) = 7A4Gary's demand function for good X is xG = 0.5 M/p where p is the price of the good and M denotes Gary's income. What is the slope of the Gary's compensated demand curve, assuming p= 7 and M = 209 dollars