Q2. Consider a consumer with the following Marshallian demand: 21 -and y = I X = Px +2p, Px +2p, Does this demand satisfy implications of the classical consumer model?
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- In a two-period model, suppose that a consumer's utility function is: U(C₁, C₂) = log(c₁) + log(c₂) where C₁, C₂ are the consumption of a good (orange) in the two periods. Let the endowment real income in the two periods be 2, 1 respectively. The real interest rate is unknown and is to be determined in the equilibrium. Assume that all consumers are identical. ** Part a Solve the demand for C₁ given any real interest rate r*. ** Part b Find the level of the real interest rate such that the market clears in Period 1.= Mary has the following utility function: u(x, y) I = 10 and the prices originally are p = 1 and py (a) What are Mary's marshallian demands? 3 ln(x) + 2y. Her income is given by = 2Derive the Slutsky equation step by step. What is the significance of this equation? What is the difference between the Hicksian and the Marshallian demand functions? Do not use chatgpt
- Economics Consider a CIA model where the utility function of consumers is: U = log (c.) a. Find the first-order conditions and envelope conditions for a representative household with preferences given by this form of u(c). b. Find k and c in the steady state.Consider a 2-good economy with a rational consumer who has weakly monotone and weakly convex preferences. He lives for one period, has some fixed income M, and doesn't have any initial endowment of goods. Which of the following is true? a. The Hicksian and the Marshallian demand curves have the same slope if the income effect is zero. b. The Hicksian demand curve for good 1 is always steeper than the Marshallian demand curve for good 1. c. The Hicksian demand curve for good 1 is always steeper than the Marshallian demand curve for good 1 only if good 1 is an inferior good. d. None of the above.Recall that a consumer with utility has Marshallian demand u(x₁, x2) = min{x1,2x2} x(p, w) = W 2w 2p1 + P2' 2p1 + P2 (a) Find the indirect money-metric utility function for reference prices p. (b) Calculate the equivalent variation associated with a change in prices from (4, 1) to (2, 1) when the consumer has wealth 10. (c) For the same change, without calculating the compensating variation, explain whether it is larger than, smaller than, or the same as the equivalent variation.
- skip if you already did this or else downvoteQuestion 3: Consider the two-period model. The consumer has an asset, which is worth A in the current period. The current and future incomes are y and y'. There are no taxes. The maximum amount that the consumer can borrow in the current period is A. The market interest rate is r and the consumer's asset will be worth (1 + r) A in the future period. The consumer's indifference curves are linear with slope steeper than 1+r. 1. Illustrate the consumer's budget constraint and equilibrium in a graph with current consumption (c) on x axis and future consumption (c') on y axis. Clearly mark the consumer's endowment point (y, y'). 2 2. Suppose the current-period value of the consumer's asset doubles to 2A. Illustrate the consumer's new budget constraint and equilibrium in the same graph. Explain your answer.At least during 2020 international travel and vacationing was very re- stricted. National travel was also restricted as was things that one usually does on a vaction, e.g. going to a restaurant. Let's assume that a typical consumer has the following utility function over going on a vacation trip (v) and other consumption goods (0): U(v, 0) = v0.10,0.90 Assume that the relative price of a vacation trip in terms of other goods was equal to one (p = = 1) and the yearly disposable income of the average consumer was I= 300, 000kr. (a) Solve the consumer's utility maximization problem. How much would she had spent on vacationing and other goods if there had been no pandemic? What would her utility have been? (b) The restrictions to travel during the pandemic could be expressed in the way that the average consumer could not (was not allowed) to spend more than 5000kr (or equivalently consume more than 5000 units of v). If we assume that both income and the relative price of vacationing was…
- Consider a government that raises money in a two-good economy by taxing good 1 at a rate of t per unit. The government is considering replacing these taxes with a lump-sum tax to the consumer that raises the same revenue. Thus, if the consumer consumes x units of good 1 before the change in taxes, she must pay the government a lump sum of tx after the change. Suppose, moreover, that prices change only by the amount of the tax; i.e., if prices are (p₁+t, p2) before the change, then they become (P₁, P2) after. Let x = (x1, x₂) be the consumer's demand before the change, and x' (x1,x2) the consumer's demand after. Suppose that x = x'. = (a) Is one of x or x' revealed preferred to the other (and if so, which)? (b) Assuming that the consumer's demand satisfies the Weak Axiom of Revealed Preference, does the change in taxes lead to an increase or decrease in consumption of Good 1, or is it impossible to determine? What about Good 2?TRUE or FALSE. If the statement is correct, write TRUE on your answer sheet. If the statement is incorrect, write FALSE. Explain why you answered TRUE or FALSE. The substitution effect is always negative since you need to reduce the consumption of lanzones in order to increase the consumption of rambutan to attain a higher indifference curve.1. Use the method of Lagrange multipliers with inequality first-order conditions to determine if corner solutions arise with the following utility functions. If not, explain why not. If so, outline the condition under which a corner solution arises and find the Marshallian demands in these cases. (a) U(1, y) = (x+1)y (b) U(x, y) = Vr+ V %3D 2. Find the Marshallian demands for r and y for the utility function in part (a) of the previous question when an interior solution exists. Use your solution to confirm the condition that you found previously for a corner solution to arise.