Ben gets utility from apples and bananas and his preferences can be represented by the utility function U(A,B)=4A+B. If the price of apples is 3 times the price of bananas, what is Ben's ordinary demand function for apples, A*(p A, P B, I)? OA (P A, PB, 1)=0 A*(p A, P B, 1)=1/P A OA (P A, PB, 1)=21p A OA (P A, PB, 1)=1/(3p A) O A*(p A, P B, 1)=1/(4p A
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- Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $1,000 and can buy apples at $10 per pound and kumquats at $10 per poun utility function is U(a, k) = 4a + 3k. What is his marginal utility for apples and his marginal utility for kumquats? Andy's marginal utility for apples (MUa) is MU, = and his marginal utility for kumquats (MU,) is MU, = (Enter your responses as whole numbers.) What bundle of apples and kumquats should he purchase to maximize his utility? Andy should consume apples and kumquats. (Enter your responses as whole numbers.) React tv MacBook Air 80 DI DD F1 F2 F3 F5 F6 F7 F8 F9 F10 E11 @ #3 $ % へ & 1 2 7 8. 9 Q W E Y { A F J L Z C V く M ption command command option .. .. V エ ト3) Oğuz has the utility function U(x1,X2) = x:*x2². (X: nuts, X2: berries). %3D a) If Oğuz has 25 units of nuts and 17 units of berries, the price of nuts is 2 and the price of berries is 1 liras, what would be the optimal consumption of Oğuz? b) Assume the prices change, so that nuts cost 1 and berries cost 3 liras. What is the new demand? In this change, What is the pure substitution effect? What is the income effect? c) In the change calculated in part (b), what is the pure substitution effect? d) In the change calculated in part (b), what is the income effect? In the change calculated in part (b), what is the endowment effect?You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.
- Karen 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?Harry consumes 2 goods, X and Y and he spends N$60 per month. The price of good X is N$4 and the price of good Y is N$10. Harry's utility function is U(X, Y) = XY. (i) What is Harry's marginal rate of substitution? (5) (ii) What is the expression for Harry's budget constraint? (3) (iii) What is the slope of Harry's budget constraint? (2) (iv)Find the values of good X and Y maximizes Harry's utility. Show all your work. (6) (v) Illustrate Harry's utility maximizing combination on a clearly labelled graph. (4) (vi) Suppose the price of good X increased to N$6. Illustrate Harry's income and substitution effects on a well labelled graph. Show your work. (10) (vii) Suppose Genie is consuming two goods, coffee and beer. She spends all her income on a combination of coffee and beer where MUcoffee/Peoffee is 5 and MUbeer/Pbeer is 3. Explain why this combination is not maximizing her satisfaction. What should she do to maximize her utility? (5)Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $1,000 and can buy apples at $10 per pound and kumquats at $10 per pounc utility function is U(a, k) = 4a + 3k. What is his marginal utility for apples and his marginal utility for kumquats? Andy's marginal utility for apples (MU) is MU, = and his marginal utility for kumquats (MU) is MU, = (Enter your responses as whole numbers.) What bundle of apples and kumquats should he purchase to maximize his utility? Andy should consume apples and kumquats. (Enter your responses as whole numbers.) React tv MacBook Air 80 DI DD F1 F2 F3 F5 F6 F7 F8 F9 F10 @ #3 $ % & 1 2 4 7 8. 9 Q W E Y { A S F G H. J C V M ption command command option .. .. V B
- If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.A consumer with I dollars budget has the utility u(x,y) = x(y+1) over amounts of cake (x) and ice cream (y) she consumes. The prices are px , py respectively. (a) Derive her demand for cake (x), as a function of prices px , py and her budget I. (b) Looking at the demand function in (a), is cake a normal good or an inferior good? Are cake and ice cream complements or substitutes? (c) Calculate the (i) (own) price, (ii) income, (iii) cross- price elasticity of demand for cake at the point where I = 80, px =10, py = 20.1 Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza (Z). The price of each pizza is 16. dollars and the price of each burger is 8 dollars. Alice's utility is given by: u(B, Z) = B'/2 +4Z!/2 + 47!/2 a) Find Alice's budget constraint. Set up the Lagrangian and find her optimal consumption. What is her new consumption if the price of burgers becomes 16 dollars?
- Ambrose's utility function is = 4x1/2, + x2. If the price of nuts (good 1) is $1, the price of berries (good 2) is $9, and his income is $369, how many units of berries will Ambrose choose? a) 5 b) 8 c) 10 d) 4 e) 325Sally the Sleek's preferences can be described by the utility function U(x, y) = x*y/1000. Prices are Px = 4 and py = 3; she has an income of $80 to spend. (a) If Sally initially consumed 5 units of x and 20 units of y, how much additional utility does she get from spending one small fraction of a dollar more on good x? How much additional utility does she get from spending one (small fraction of a) dollar more on good y? (b) By how much would her utility change if she stayed on the same budget and consumed 4 (small fractions of a) dollars worth more of x? Judging from this, can the allocation of x = 5 and y = 20 be optimal? (c) How much should Sally consume of x and y in order to maximize utility, given her income?1/2 1/2 2. Cynthia has preferences represented by the utility function u(x) = x¹/² + x¹/² (a) Calculate Cynthia's marginal rate of substitution. (b) Calculate Cynthia's Marshallian Demand functions x(p, 1) and x(p,1). (c) Does Cynthia consider either of these goods to be Inferior Goods? (d) Show that Cynthia's demands generate an indirect utility function V(p,1)=√√IP₁P2 (e) Solve for Cynthia's expenditure function.
