An individual has preferences over contingent consumption in two states of nature {a, b}, given by u (x(a), x(b)) = logx(a) +2logx(b), and current income m = sured in units of consumption. The prices of contingent contracts for deliveries of a unit of consumption in the two states of nature are (p(a), p(b)) = (1,4). Find the optimal consumption plan (x*(a), x*(b)) of this individual and answer: compute the value of the consumption plan in state a, i.e., p(a)x* (a). 6, mea-

An individual has preferences over contingent consumption in two states of nature {a, b}, given by u (x(a), x(b)) = logx(a) +2logx(b), and current income m = sured in units of consumption. The prices of contingent contracts for deliveries of a unit of consumption in the two states of nature are (p(a), p(b)) = (1,4). Find the optimal consumption plan (x(a), x(b)) of this individual and answer: compute the value of the consumption plan in state a, i.e., p(a)x* (a). 6, mea-

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q1) Sales are a function of advertising in newspapers and magazines (X, Y). S = XY2 The price of advertising in newspapers and magazines is Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing sales, find out the best combination of advertisements in newspapers and magazines by using the Lagrangian multiplier. (Hint: Make equation of the budget line with the help of the above information).
ASAP Suppose the consumer has the utility function U(C,l)=0.5 √C+√ l and has h = 24 hours available, some of which are used as leisure (l) and some supplied to the labor market (NS). Hours of work are paid at the real wage w. The profit income is π = 15. The consumer pays no tax. Writedown the budget constraint and the maximization prob- lem (a Lagrangian) and find the first order conditions for the consumer. Find an expression for the quantity of labor supplied
how to construct the change prices(p1 * w1 + p * w).
Penelope utility function is U (a, b) = a+ 10b−b2, where a is the amount of applesconsumed and b is the amount of bananas consumed. He has $100 income. Theprice of apple is $0.5 per lb. Price of banana’s though increases with its purchase.Specifically, buying, b pounds of bananas will cost Pedro b2.a. What is Penelopes optimal consumption?b. Now, he suddenly acquires an extra $100 income. How this will changehis allocation?
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For the utility function U=Qx0.370,(1-0.37) and the budget 194 140x+6Qy find the CHANGE in optimal consumption of X if income increases by a factor of 1.4. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14=1.1).
1. An individual derives utility from the consumption of a basket of goods, c and leisure time, given by U(c, l) =cºl(1-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L + l = 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given. (a) Solve for the optimal labor supply.
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A consum sumer of two goods has indirect utility v(p, w) = √w -1/2 P₁ + P₂ (a) Find the indirect money-metric utility e(p, v(p, w)). (b) Calculate the compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5). can you explain the notation please break it down each part of it, please teach How do you know where to place the values? The indirect money-metric utility e(p, v(p, w)) can be calculated as follows: e(p, v(p, w)) = v(p, w) - ((p1* w1) + (p2 * w2)) plugging in the values from the problem, we get: e(p, v(p, w)) = (sqrt(w))/p1^-0.5+p2^-0.5- ((44) + (9 * 5)) e(p, v(p, w)) = 2 - 41 CV = 2 e(p, v(p, w)) = -39 The compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5) can be calculated as follows: CV = e(p', w')- e(p, w) plugging in the values from the problem, we get: CV-39 (-41) This means that the consu would be willing to pay up to $2 in order to maintain their original level of utility.
Assume a consumer has current-period income y = 200, future-period income y′ = 150, current and future taxes t = 40 and t′ = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume according to the following utility function: U (c, c′ ) = ln(c) + ln(c′ ). Show mathematically the lifetime budget constraint for this consumer. Find the optimal consumption in the current and future periods and optimal saving. Suppose that instead of r = 0.05 the interest rate is r = 0.1. Repeat parts (a) and (b). Does the substitution effect or the income effect dominate?
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Q2: Let a consumer’s daily hours of work is denoted by H, and hours of leisure by L. Consumer has no other source of income except wages for hours worked. She consumes what she earns each day. Her utility function is U(C, N) = ln(C) + 3 ln(N) Where C stands for the dollar amount of her consumption. Now answer following questions (a) Suppose the wage rate is 50Rs. per hour. Write down the consumer’s utility function and budget constraint with C and H as the choice variables. (b) How many hours will she choose to work, and what will be the resulting utility?