consumption

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Q7: An individual lives for only two periods and has preferences given by the follow- ing intertemporal utility function: U = lng + aln(1-h₁) + B[lno₂+ a ln(1 — h₂)] (1) where, c₁, c₂ denotes consumption in period 1 and period 2 respectively h₁, h₂ denote the labour supply in period 1 and 2 respectively. Therefore 1-h is the amount of leisure time in period 1. The term 3 is the discount factor. The problem of the individual at period 1 is to choose consumption in both periods and labour supply in both periods subject to the following budget constraints: +8= why and 0₂= w₂h₂ + (1+r)s where s denote the saving, w denotes the wates and r denotes the real interest rate. (a) Provide an economic interpretation of the two budget constraints written above. (b) Combine the two budget constraints written above and prove the economic interpretation of of life time budget constraint. (c) Set the Lagrangean function and find the first order conditions with respect to C₁ C₂, hi and h₂. (d) Find the…

Find the derivative of the function. y = In(6x) Find the derivative of the function. y= In(3x² - x)+6x 1 dp Find - if p = In(q² + +9). dq dp dq = Find the derivative of the function. y = In(x8) li Find y'. y' = Find the derivative of the function. f(x) = In(8x+9) y = 2x - In(8x)

Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u(x, L) = xL, where a represents consumption of the good and L represents leisure. Suppose that this worker can choose any L € [0, 1], and receives income w(1 – L); w represents the wage rate. Let p denote the price of the consumption good. In addition to her wage income, the worker also has a fixed income of y ≥ 0. (a) Write down the utility maximization problem for this consumer. Solution: The problem is max x L s.t. px ≤w(1 L) + y. x>0, LE [0,1] The budget constraint may also be written with equality since preferences are monotone. (b) Find the Marshallian demands for the consumption good and leisure. Solution: Using FOCs will find the maximum since preferences are Cobb-Douglas (and therefore convex). Dividing the FOCs L= Xp and x = Xw gives wL = px. Substituting into the budget constraint and checking the restriction L = [0, 1], we get and x(p, w, y) L(p, w, y) = = = 1 w+y…

21. Let U=x 2 +y 2 is the utility function of a worker who has 10 hours that to be allocatedbetween labour supply (L) and leisure (x). Let y is a consumption good whose price is 1.Wage rate (w) is Rs 1 and non-wage income is 20. Find out L.a) 10 b) 0 c) 5 d) 8 e) none 22. On the basis of the above question, hen w=0 and non-wage income is 40, find out L.a) 10 b) 0 c) 5 d) 8 e) none

Table 1 shows the financial position of Bank Uno once $3381.00 has been deposited. Assume that the required reserve ratio is 9.00%, that banks do not keep excess reserves, and that all the money loaned out from Bank Uno is deposited into Bank Duo (whose loans go to other banks not shown here). Once the lending and depositing process is complete, what will the accounts look like in Tables 2 and 3? Specify all answers to two decimal places. Table 1. Bank Uno's Initial T-Account Assets Liabilities Reserves: $3381.00 Deposits: $3381.00 Table 2. Bank Uno's T-Account After Loans Assets Liabilities Reserves: ? Deposits: ? Loans: ?   Table 3. Bank Duo's T-Account After Deposits and Loans Assets Liabilities Reserves: ? Deposits: ? Loans: ?   What are Bank Uno's deposits in Table 2? $   What are Bank Uno's reserves in Table 2? $   What are Bank Duo's loans in Table 3? $   What are Bank Uno's loans in Table 2? $

Kevin has a wage income of $10,000 in the present and $15,000 in the future.  His utility is given as U = min (4cp, 5cf), where cp denotes consumption today and cf consumption in the future.  The relevant interest rate is 10%. ​ a. If the interest rate were to increase to 15 percent,would Kevin be better off or worse off?  Explain. b.​ Find two measures to indicate how much better off or worse off Kevin is as a result of the increase in interest rates.  Explain.

A convenience store manager earns a base salary plus a small bonus of $60 for each of ten different possible monthly milestones he meets. If the manager meets a milestone, the full bonus is paid. However, if the manager falls even one penny short, none of that bonus is paid. Suppose each of the ten milestones requires 40 hours of effort to meet, and that the manager has 160 hours of effort to allocate to work each month. In order to maximize the total monthly bonus, the manager should allocate hours toward meeting each of    milestones and hours toward meeting each of the remaining    sales milestones.

Consider a representative consumer with preferences over consumption e and leisure I given by u(e,l) = 1/4 * ln(c) + 3/4 * ln(l) Assume that the price of consumption is normalized to p = 1 and the consumer has h = 24 hours of total time available to divide between work and leisure. The consumer's wage per hour of work is w = 24 The consumer also receives dividend (profit) income of pi = 39 and pays lump-sum taxes of T = 7 (a) Write out the consumer's budget equation, and draw a graph of the budget constraint. (b) Solve for the optimal decisions e and 1. How many hours per day is the consumer working? (c) Suppose the consumer's wage decreases to w = 16 Solve for the new optimal choices of c and I". Relative to the solution in part (b), do consumption, leisure, and hours worked increase, decrease, or stay the same? Give an intuitive explanation for why these changes occur. (d) When the wage changes in part e, determine whether the consumer experiences an income effect, a substitution…