Question 2. Bank Run. Consider the Diamond-Dybvig model we discussed in class. Suppose marginal utility of consuming c is given by c-². Gross interest rate is R = 1.5. Time preference is ẞ = 0.9. Probability of becoming first type is λ = 0.2. a) What is the efficient consumption level of type 1 (c)) and type 2 ( c). You need to solve for optimality condition and resource constraint. Answer must be numeric. b) Explain why 1 < c^, and c½ < R is better than c₁ = 1 and C2 = R. c) Now consider the contract we discussed in class that the bank offers. Suppose r₁ = 1. Explain why there wouldn't be a bank run in this situation. Why this is not a desirable contract?
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- f) i) Find the degree of homogeneity of the following functions and comment on their returns to scale i. Q = K² + 5KL – 4L² ii. Q = 13KSL ii. A consumer has the following utility function a. U = Ax“yf Find the MU, and MU, iii. Given the following consumption function C = 70 + 0.85Y Find the corresponding savings function and marginal propensity to saveAnswer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSEQuestion No 03. Sales are the function of advertising in The Dawn and Diva Magazine (X, Y). S=XY? If the price of advertising in The Dawn and Diva Magazine is Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing the sales of Dawn and Diva Magazine find out the best combination of advertisement in newspapers and magazines by using Lagrangian multiplier.
- 1. Someone is willing to maximize his/her utility. Assume he/she knows his/her u(x,y) =x^0,5y^0,5 (Cobb-Douglas) (a) Find his/her optimal consumption given the income = 20, Px=2, Py=4! (b) Depict his/her optimal consumption graph! 2. Suppose that x and y (from your answer in number 1) are now perfect complement with u(x,y) = min(x,y). (a) Find his/her optimal consumption (given the same income and prices)! (b) Depict his/her optimal consumption graph!Someone is willing to maximize his/her utility. Assume he/she knows his/her u(x,y) = x^0,5y^0,5 (Cobb-Douglas) (a) Find his/her optimal consumption given the income = 20, Px=2, Py=4! (b) Depict his/her optimal consumption graph!c) If the value of timber is the following increasing function of time: V = 2t Expressed in units of Rs. 1000. Assuming a discount rate of r and also assuming zero upkeep cost during the period of timber growth, what is the optimal time to cut the timber for sale? Calculate optimal time for r = 5% Question 03. a) Maximize the utility function U = X0Y025 subject to budget constraint 680 = 8X + 5Y Also show that above utility function is homogenous and homothetic. 5P+ P? and b) Find the demand function Q =f (P) if elasticity of demand is - Q = 500 when P = 10 c) Write down the first order and second order conditions for maximum and function y = f(x1, X2, X3,.......... Xn). minimum of a
- Sales are the function of advertising in The Dawn and Diva Magazine (X, Y). S = XY2 If the price of advertising in The Dawn and Diva Magazine is Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing the sales of Dawn and Diva Magazine find out the best combination of advertisement in newspapers and magazines by using Lagrangian multiplier.Sarah is considering two investment proposals. Proposal A is to purchase a new computer. Proposal B is to purchase a new printer. She will not buy the printer unless she buys the computer. The relationship between Proposals A and B is best described by which of the following? a. B and A are mutually exclusive b. B is contingent on A c. A is contingent on B d. Not enough information is given to determine a relationshipFor example, the economy of a country can be explained by several models as follows: Consumer: The consumer derives his satisfaction from his current consumption, future consumption and his free time (u(C,C',l,l'). He maximizes his utility by: C+wl+11+rC'+w'1+rl'=wh+π-T+w'h+'-T'1+r It is assumed that consumer preferences meet the general conditions that are often used (more is better, preference for diversity, all goods are normal, substitution effect is more dominant). Firm: In the first period, the firm has K capital and employs N workers to produce Y output: Y outputs: Y=zF(K,N) The profit in the first period is =Y-wN-I Where I is the company's investment. Investments increase the capital stock for the second period: K'=1-dK+I In the second period the firm will produce output of Y': Y'=z'F(K',N') Then the profits obtained in the second period are: '=Y'-w'N' Firms choose the demand for labor (N, N') and the demand for investment I to maximize their value: V=π+π'1-r…
- QUESTION 1 x0.80Qy(1-0.80); and the budget 153 = 11Qx + 12Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.9. as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1). Qx For the utility function U = Please enter your responseActivity 2 a Suppose the utility function for Guyo is given by U= f(X, X,) = X,.25 X,0.-75, Given that the price of commodity X, is Kshs. 10 per unit and that of community X, is Kshs. 15 per unit. Using Lagrangian multiplier technique determine units of the two commodities Guyo will buy given an income of Kshs. 40,000 in order to maximize his utility. b. Suppose the utility function for Faith is given by U = f(Y, X) = Y3 X2l3. Given that the price of commodity Y is Kshs. 3 per unit and that of community X is Kshs. 5 per unit. Using Lagrangian multiplier technique determine units of the two commodities Faith will buy given an income of Kşhs. 9,000 in order to maximize her utility. University of Nairobí iso 9001:2015 160 Certified http://www.uonbi.ac.keTransfer and revenue effect:The consumer gets positive benefits from consuming bread (B) and cake (K). Consumer utility is as follows: U(B,K) = 20·B2·K The price of bread is 200 ISK. but the price of a cake is 400 ISK. Consumer consumption is set restrictions as his income is ISK 20,000. Put cakes on x-axis and bread on pictures y-axis. a) Show the equation for the locating ratio of bread for one cake. Draw the equivalence curve on a graph and interpret what the equation position ratio says at each point in the equivalence process. b) Find the most efficient consumption combination and draw on the picture. c) The state decides to tax bread so its price rises to 400. Who is the most cost-effective consumption mix based on changing prices? Change change consumption patterns in the separate effects of displacement and income effects. Show the most efficient the consumption composition in the picture and differentiate the changed consumption due to price changes intransfer and income…