a) Choose X, and X, to max the utility fxn, '(X,X,)=chX;+Q-g}hX; st: M - R X, + P,X; a) Write down the demand functions for goods 1 and 2 b) Consider a price decrease for good 1 from R toP" . Write down the demand functions for good 1 when prices are P, and when prices drop from R toP" c) What is the compensating income, Mª associated with the price change? Obtain the SE and IE associated with the price change
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- David's utility function for good X and Y is given by U (X,Y) =X2y3. Where px,py and I are the price of good X, price of good Y and consumer income respectively. E). Suppose david faces a new utility such as U(X, Y)=25x0.2 Y0.75 for consuming commodity X and Y, redo question b and c. Derive the demand function for good X and Y What combination of X and Y maximizes the consumer at I=100,px=4,and py=5 F). Suppose david faces another new utility function such as U (X, Y) =15xy2 for consuming commodity X and Y,redo question b and c Derive the demand function for good X and Y What combination of X and Y maximizes the consumer at I=100,px=4,and py=5If the demand function face by the consumer for good X is given by X=15+MP-120 Where X = Quantity demanded, M = income and P = Price of product X. Assume his original income is Kshs. 3200 per month and price of good X has increased from Kshs. 10 per unit to Kshs. 20 per unit. Calculate the magnitude of total effect (TE), substitution effect (SE) and income effect (IE) resulting from this change in price.The Utility Function is U(q1, q2) = q11/6 . q21/3 a.) Solve for the amount of good #1 the individual would demand if good #1 and good #2 both have a price of $1 (p1= p2 =1) and the individual has an income of $9 ( Y = 9). b.) If the individual's income increased by 1%, what would be the resulting percentage change in their quantity demanded of good #1?
- The demand for good X is given by Qd = 6,000 – 1/2 Px – Py + 9Pz + 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 = $70,000. A. Indicate whether goods Y and Z are substitutes or complements for good X. B. Is X an inferior or a normal good? C. How many units of goods X will be purchased when Px = $5,230? D. Determine the demand function and the inverse demand function for good X. Graph the demand curve for good X.Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = lnx + 2lny (MUx = 1/x, MUy = 2/y). a. Derive his demand functions for x and y. Are they homogeneous in income and prices? b. Assuming I = $60 and px = $1, graph his demand curve for y. c. Repeat part (b) for the case in which px = $2.1.(a) Derive own-price elasticity of demand (eii), income elasticity of demand (hi) and cross-price elasticity of demand (eij) for the Cobb-Douglas Utility Function. (b) With respect to Cobb Douglas preferences, what happens to the demand for each of two products (x and y) when the price of product y increases, as a result of: (i) the substitution effect; (ii) the income effect; and, (iii) the overall price effect?
- If the utility function for a consumer is defined by U=6X^3/5Y^2/5 Given that the consumer's income is 300 currency units and unit price of goods X and Y are 12 and 15 currency units respectively, calculate the equilibrium quantity of both goods. Compute the price elasticity of demand for both goods and interpret your results. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of both goodsGiven a demand function of Qd = 20 – 4P + 0.7Y, what is the YED for a product at a point where Price is $1, Quantity is 9 billion bushel and Income is $50? Based upon this calculation for YED, the product would be considered a normal good. A. True B. FalseKaren has perfect complement preferences over toothbrushes B and toothpaste P, with the associated utility function U(B,P) = min (3B, 2P). Suppose the price of a toothbrush is $6, the price of toothpaste is $4 a tube, and she has $72 to buy her entire year's supply of toothbrushes and toothpaste. How many toothbrushes and tubes of toothpaste will she buy?
- Suppose a consumer’s utility from consuming the two goods x and y is given by: U(x,y)= x + (y1-1/a))/(1-(1/a)) Determine the uncompensated and compensated own- and cross-price elasticities.Suppose a consumer’s utility from consuming the two goods x and y is given by: PHOTO a) Determine the uncompensated own- and cross-price elasticities. b) Determine the compensated own- and cross-price elasticities.Chiara has the utility function U(x1,x2) = x1(x2+5). The price of x1 is 5$ and the price of x2 is 2$. Income is 25$. A)How much of each good does Chiara demand? (without lagrangian) B)If Chiara’s income doubles, but prices remain unchanged, will Chiara’s demand double? C)How does ordinary demand change when income doubles (50$) and the price of x2 also double?