Please help with #9 a and b. For question 2 i found that p2 = $0.9417 in the market clearing equation, forquestion 7, the equilibrium interest rate was 11.98% and for question 8, there was no equilibrium interestrate. Thank you!!9. Begin from the baseline preferences and endowments.A. A third person named Zena joins our economy. Zena is very impatient with utility function0.80 In (C₁) +0.20 In (C₂).However, Zena has no endowment and hence no wealth.Incorporate Zena into the market clearing equation and determine the equilibrium interestrate.[=J%B. Explain the relationship between the interest rate in this case and what you calculated fromquestions 2,7, and 8. Write at least five sentences.

The objective of the question is to determine the impact of a new entrant, Zena, on the equilibrium…

Answered: Please help with #9 a and b. For…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Angelina lives on an island where she produces two goods, apples (x) and bananas (V), according to the production possibility frontier 200 = x² +y², and she consumes all the %3D goods herself. Her utility function is U (x, y) = xy³. Find her utility maximizing x and y as well as the value of 2 (Lagrange multiplier).
1. Suppose that the representative consumer has a utility function defined over consumption over two dates of the form U(C₁, C₂) = c₁²c₂². 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). a. 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 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…
1. Consider the utility function given by u (x1, x2) = x1x3, and budget constraint given by P1x1 + P2x2 = w. (a) Solve the EMP to find the Hicksian demand function, h (p, u). (b) Find the expenditure function e (p, u). (c) Recover h (p, u) from e (p, u). (d) Noting that the indirect utility function corresponding to the UMP for this form is 4w3 v (P1, P2, w): 27p1p3' demonstrate that v (.) and e (.) are inverses of each other. (e) Using only the indirect utility function above, recover the optimal consumption bundle of the UMP (i.e., Walrasian demand function). (f) Using your answer to (e), identify the substitution effect on the quantity demanded of good 1 of a change in the price of good 1. 1; and consider the Hicksian demand curve for good 1 corresponding to , and Walrasian demand curve for good 1 corresponding to w = 1. At what price and quantity for good 1 do they intersect? Which is steeper at this point of intersection? (g) Assume P2 What does that signify? (h) Using your…
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3. Consider the following utility function, a (1.2) = min , br), 00 (a) in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? Derive the Marshadian demand functions. (Explain your derivation
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The utility maximization problem is given by 0-1 Ө-1\0-1 max uf = Cit,C2t,St 0 + a, (c2t) subject to Cit + St = Wt + e C2t = (1+ rt+1)s, By solving the maximization problem, characterize the saving function depending on the value of 0, i.e., there are three cases.
A consumer can consume two goods, A and B, and has the utility function U-15A1/281/2, The consumer's budget is $900, the price of good A is $15 per unit and the price of good B is $45 per unit. (Assume A is the horizontal axis good and B is the vertical axis good. Both goods are infinitely divisible, but round numerical answers to 2 decimal places as necessary) What is the consumer's marginal rate of substitution? What is the consumer's marginal rate of transformation? What is the formula for the consumer's budget constraint? What is the consumer's utility-maximizing bundle given the utility function and budget constraint? A B H
Khan lives in a world with two consumption goods x and y. Her utility function is U (x, y) = √x² + y². a. If px = $3,py = $4, and her income, I, is equal to $50, what will be the quantities of x and y that Maya should buy to maximize her utility? Make sure that you write out the Lagrangian and the first-order conditions. (Hint: It may be easier to maximize U² than U). Have you found a true maximum? Explain your answer.
2. Mr. A has the following utility function and budget constraints: Max 0.1Ln(C1) + 0.7Ln(C2) Subject to S1 + C1 = 100 C2 + S2 = (1 + r)S1 where C1 and C2 are consumption level at young and that at old respectively. Likewise, S1 and S2 are saving at young and saving at old respectively. a) Find out Mr. A’s optimal consumption levels (i.e. C1*, C2*) and optimal savings (i.e. S1*, S2*) in terms of interest rate r. b) Show clearly the results in part a) in a suitable diagram (with C1 as x-axis and C2 as y-axis). c) Is Mr. A a saver ? or a borrower ? d) If r is equal to 0 (i.e. saving gives no returns), will Mr. A still choose to save when he is young (i.e. is S1 still bigger than 0) ? Why ? e) Suppose that Mr. A is not allowed to save (i.e. S1 = 0). What are his optimal consumption levels ? Show his optimal consumption levels in the same diagram you prepare for part a) (with a suitable indifference curve). f) If r increases,…
2. Consider a small island economy where the government is contemplating imposing a tax on bananas to raise revenue for public projects. The islanders' utility from consuming bananas (B) and coconuts (C) is given by the Cobb-Douglas utility function: U(B, C)=B°C1-a where a = 0.3. (a) Write down the consumer's optimization problem and derive the demand functions for bananas and coconuts. (b) Suppose the initial prices are PB $2 and Pc = = $4, and the consumer's income is I = $100. Calculate the initial quantities of bananas and coconuts consumed. (c) Calculate the compensating variation (CV) and equivalent variation (EV) for a tax rate of t = $0.50. Interpret your results in terms of the impact on consumer welfare. (d) Determine the tax revenue per consumer after the tax is imposed, assuming supply is perfectly elastic so the tax falls entirely on consumers. (e) Compare the impacts on consumer welfare between a flat tax equal to the revenue found in part (d) and the per-unit tax.
The expression, M = PXX+ PYY is called a budget constraint where M = amount of money available for expenditure; PX= price of commodity X; PY= price of commodity Y; PXX= expenditure on commodity X; PYY= expenditure on commodity Y. Use M = PXX+PYY to express Y as a function of X and note that the graph of this function is called a budget line. Algebraically derive: (1) the y-intercept; (2) the x-intercept. State what determines the slope of the budget line. Graph the function for M = 120; PX= 3; PY= 5 andshow what happens to the original budget line if M decreases by 25% with PX, PY constant.

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