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- Dan's utility function is U(x,y) =9.5 x2.4y4.9. Dan's income is 129.1 dollars, the price of good X is 4.8 and the price of good Y is 6.3, What is the slope of Dan's income expansion path, dy/dx, on a graph where good X appears on the horizontal axis and good Y appears on the vertical axis. Remember not to enter ratios below, such as 3/4, 2/9 etc. Instead enter the number in decimal form.Suppose a consumer with a utility function U(x,y) =x 0.5 y 0.5 and an income of $500.00. Considering that X and Y products are sold by the kilo and that their prices are 25.00 and 50.00 respectively, calculate: a) Maximizing amounts of x and y for the consumer b) Graphically sketch the consumer balance c) Discuss the following statement: "if the consumer's income increases by 20%, the consumer will also consume 20% more of each of the products"Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is U (A, O) = AO³ MUA = 0³ MUO 3A0² . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. = When you set up the optimal decision rule for your consumer problem, which of the following statements best describes how much you will buy of apples and oranges at your consumer equilibrium? For each peck of apples, you will buy 1/3 pounds of oranges. For each peck of apples, you will buy 1 pounds of oranges. O For each peck of apples, you will buy 3 pounds of oranges. O For each peck of apples, you will buy 6 pounds of oranges.
- Suppose that there are two goods, gl and g2, that Jane consumes. Demand functions for these two goods are given as follows: gl * = gl(pg1), pg2 ,Inc) g2 * = g2(pg1), pg2 ,Inc) where pg1, pg2 ,Inc refer prices of the goods and income, respectively. Explain and demonstrate (on the graph) the substitution and income effect for both an increase and decrease in price good g1. Use the notations given in the question.Economics Consider a household whose preferences are described by the utility function U(X1, X2) = X1X2 where X1 and X2 are household’s consumption of goods 1 and 2 respectively. Consider that household’s budget constraint is: P1X1 +P2X2 =I. (a) Derive the household’s demand functions for goods X1 and X2. (b) Derive the household’s compensated demand function for goods 1 and 2, i.e., obtain functions of the form Xi = fi (P1, P2, U) , I = 1, 2 where U is the household’s level of utility. (c) Assume that in the initial situation the commodity prices, P1 and P2, and the household income level, I, are given by P1 = $1, P2 = $1 and I = $2. Sketch the compensated and uncompensated demand curves for good 2 with P1 held constant at the initial level. In the compensated case, U is held constant at the initial level while in the uncompensated case, I is held constant. (d) By how much must I be increased if P2 increases to $2 (P1 remains at $1) and our household is to maintain its…1
- Q3: Are the following utility functions quasi-linear, quasi-concave, quasi-convex, homogenous of degree 0, homogenous of degree 1? Show your working: 1) U(x,y) = min(x,y) 2) U(x,y) = (x" + yajaVictor is the manager of a local bank branch in College Station where he consumes bundles of two commodities x and y. Prices in College Station are px=1 and py=5. He is offered a transfer to Dallas where prices are px=2 and py=8; Victor’s utility function is U(x,y)=xy and his income in College Station is $5000. (Victor’s utility maximization is always characterized by the tangency rule). Will Victor be able to afford what he was buying in College Station if he is offered a salary in Dallas that guarantees his welfare is the same with the transfer? A. Yes B. NoProblem 3 (10 points; 5 points for each part): Richard has a total utility function of: TU = 10q₁q₁²+24q2q2² +9192, where q₁ and q2 are goods. Richard is currently consuming at q₁ = 4 and q₂ = 6, which is also his utility maximizing consumption level. (Richard's optimal point is an interior solution). (a) How much additional utility would Richard receive if he were to increase his consumption of q2 from 6 to 7? (5 points). (b) How much q2 is Richard willing to pay (in terms of q2) in order to consume the 5th unit of q₁? (5 points).
- ECON302 TPS2: Demand Suppose that Graham enjoys painting green people. He has very particular preferences and must have exactly 3 gallons of yellow paint for each 2 gallons of blue paint. Let Y be the number of gallons of yellow paint and B be the number of gallons of blue paint. Also, let PÅ be the price of blue paint. Suppose Graham has $20 to spend on paint. Also, the price of yellow paint is Py = $1 per gallon. a) Graph Graham's price consumption curve for the prices PB = $1, and PB = 2, PB = $4. Please put the number of gallons of B on the vertical axis and the number of gallons of Y on the horizontal axis. Be sure to label your graph carefully and accurately.Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…Kerem perceives canned tuna (Y) as an inferior good and fresh tuna (X) as anormal good. If his income increases by 100%, and his income elasticity of both types of tuna is 1. Show the effect of this increase in income on the change in his optimal choice of canned and fresh tuna, highlighting his income-consumption curve.Clearly label your graph. Reflect the proportional changes in your graph.