1. Suppose that the representative consumer has a utility function defined over consumption over two dates of the form $ U(c_1, c_2) = c_1^{\frac{1}{2}} c_2^{\frac{1}{2}} $. The general form of the slope of the indifference curve for the representative consumer is $ -c_2/c_1 $. Moreover, remember that $ c_1 = y_1 - s $ and $ c_2 = y_2 + s(1 + r) $.a. Assume that the representative consumer has an endowment of consumption goods in the two periods of $ y_1 = 20 $ and $ y_2 = 10 $. Assuming an interest rate $ r = 1 $, compute the equilibrium allocation and the implied savings.b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that $ y_2 = 0 $. What happens to the savings $ s $ in the first period?c. In the previous part, the interest rate remained at 1. Now, consider the savings function, that is, the relationship between the real rate of interest and the amount saved. The equilibrium interest rate is then determined as a market price in the Saving-Investment diagram.Given the typical shape of the investment curve, what would happen in response to the rate of interest in response to an attack of pessimism? Would the change in price (the interest rate) amplify or reduce the magnitude of the shock to the quantity of savings? Explain with the help of a graph.

Utility function : U = c10.5 c20.5 In period 1 - Budget Constraint : c1 + S = y1 In period 2 -…

1. Suppose that the representative consumer has a utility function defined over 11 consumption over two dates of the form U(C₁, C₂) = C₁zc₂2. The general form of the slope of the indifference curve for the representative consumer is - C₂/C₁. Moreover, remember that c₁ = Y₁ - S and C₂ = y₂ + s(1 + r). Assume that the representative consumer has an endowment of consumption goods in the two periods of y₁ = 20 and y₂ = 10. Assuming an interest rate r = 1, compute the equilibrium allocation and the implied savings. b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that y₂ = 0. What happens to the savings s in

1. Suppose that the representative consumer has a utility function defined over 11 consumption over two dates of the form U(C₁, C₂) = C₁zc₂2. The general form of the slope of the indifference curve for the representative consumer is - C₂/C₁. Moreover, remember that c₁ = Y₁ - S and C₂ = y₂ + s(1 + r). Assume that the representative consumer has an endowment of consumption goods in the two periods of y₁ = 20 and y₂ = 10. Assuming an interest rate r = 1, compute the equilibrium allocation and the implied savings. b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that y₂ = 0. What happens to the savings s in

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Given the following utility functions for Consumer A and Consumer B and their budget contraints: UA = X0.5Y0.5 UB = X0.2Y0.8 I= Px (X) + Py(Y) and given that: Px = 3, Py= 6 and I = 100 Fill in the blanks in the following table (round to two decimal places): Part 1: Part 2: Part 3: Part 4: For Consumer A, what is the optimal choice of X? Number For Consumer A, what is the optimal choice of Y? Number For Consumer B, what is the optimal choice of X? Number For Consumer B, what is the optimal choice of Y? Number
2. Suppose Jill derives utility from not only consuming goods, but also from enjoying leisure time. Let her utility function be defined as follows: U=C.25.R.75 where C is a consumption good that can be bought at a price of $1 and R is hours of leisure (relaxation) consumed per day. There are 24 hours in a day and leisure is defined as time spent not working. Jill has a job that pays $w per hour, a trust fund that pays her $M per day, and she can work any number of hours per day, L, she desires. C, consumption good; R, Leisure (relaxation); L, labor M, non-wage income; w, wage rate. a. Derive her labor supply function? b. Assume M = $100, at what wage is her quantity supplied of hours = 0?
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i. Write down the Lagrangian form and solve the utility maximization problem. ii. Assume that the income increases from 100 to $101. What is the increase in the optimal value of u(x,y)?
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Solve it correctly please. I will rate accordingly.
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Please use Kuhn Tucker 5. A consumer's utility function is: u(x) = x1+ /®2 (c) Verify the properties of the indirect utility function. (d) Calculate the expenditure function and verify its properties.
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