Illustrate general equilibrium and the Laffer curve in the context of a repre- sentative consumer with a utility function: U(C,1) = In(C) + In(1) that he or she maximises subject to a constraint: C = w(1 - t)(h – 1) +* where w,h,l,C, t and a are wages, hours of time available, leisure, gonsumption, tax rate, and dividend income. The production function for this economy is given by Y = C+G = A(h – 1)/2
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- Part 1: Illustrate general equilibrium and the Laffer curve in the context of a repre- sentative consumer with a utility function: U(C.I) = In(C) + In() that he or she maximises subject to a constraint: C= w(1 – t)(h – 1) + * where w, h,1, C,t and a are wages, hours of time available, leisure, consumption, tax rate, and dividend income. The production function for this economy is given by Y = C+G = A(h - 1)/2 Assume that h = 1, A =1 and that the government has a balanced budget. (a) Find the equilibrium by matching the Marginal Rate of Substitution to the Marginal Rate of Transformation and then substitute into the constraint. Also take into account that profits are non-zero for this setup. (b) Plot the government tax revenue for 0For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +Xb1.3. Consider the following utility function for a consumer who consumes two goods, x1 and X2, and answer the questions below: u(x1, x2) = In(x1)+ x2 (a) Calculate the marginal rate of substitution (MRS) for this utility function. (b) Does u(x) exhibit strictly monotonic preferences? Explain. (c) Is u(x) a homothetic function or not? Explain. (d) Is u(x) quasi-concave/quasi-convex/neither where x1 0? Provide support for your an- swer.Illustrate general equilibrium and the Laffer curve in the context of a repre- sentative consumer with a utility function: U(C,1) = In(C) + In(1) that he or she maximises subject to a constraint: C = w(1 – t)(h – 1) + T where w, h, l, C, t and 7 are wages, hours of time available, leisure, consumption, tax rate, and dividend income. The production function for this economy is given by Y = C+G = A(h – 1)'/2 Assume that h = 1, A = 1 and that the government has a balanced budget. (a) Find the equilibrium by matching the Marginal Rate of Substitution to the Marginal Rate of Transformation and then substitute into the constraint. Also take into account that profits are non-zero for this setup.Illustrate general equilibrium and the Laffer curve in the context of a repre- sentative consumer with a utility function: U(C,1) = In(C) + In(1) that he or she maximises subject to a constraint: C = w(1 – t)(h – 1) + T where w, h, l, C,t and T are wages, hours of time available, leisure, consumption, tax rate, and dividend income. The production function for this economy is given by Y = C + G = A(h – 1)'/2 %3D Assume that h = 1, A = 1 and that the government has a balanced budget. (b) Plot the government tax revenue for 0What condition should be met in order for the consumer to maximize satisfaction in the consumption of good X and good Y? Provide the calculation that satisfies the equilibrium condition.Consider a consumer who consumes pizzas and soft drinks. The utility function is given by U(p, s) = pa 8B, where p represents the quantity of pizzas consumed and S represents the quantity of soft drinks consumed, and a and Bare positive constants representing the consumer's preferences for each good. Assume a = 2 and ẞ = 1. If the prices of pizzas and soft drinks are $10 and $2 respectively, and the consumer has $50 to spend, which of the following statements is wrong? The slope of the budget constraint indicates that for every extra soda drink the consumer buys, they must give up 5 pizzas. The slope of the budget constraint indicates that for every extra pizza that the consumer buys, they must give up 5 soda drinks. If this consumer buys O soda drinks, their total utility will be 0. If this consumer buys 1 pizza, their consumption of soda drinks will be 20.Please can i get help with the illustrating the graphs? An individual has a utility function, U(x, y) = x ∙ y, with a budget constraint, 120 = 2x + y.(a) Derive the individual’s optimal consumption for x and y, as well as the utility level associated with them. Graph the utility function and budget line. Indicate the point corresponding to your answer.(b) Evaluate the price effect when the budget constraint changes to 120 = 4x + y, specifying the income and substitution effect. Illustrate these on the graph indicating the points corresponding to your answer.(c) Based on (b), what type of goods are x and y?Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively, then: a) What is the value of MRS at the optimal point and what does this value mean? b) What is the optimal consumption bundle i.e (F*,C*)? c) Also plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space Case # 2 assuming if income increases to $120, holding all else the same, do the same analysis (parts a-c) and contrast your answers to Case 1. For part c, you should draw old (Case 1) and new (Case 2) budget lines/point of optimality.Please answer and explain case 2 and compare their budget lines/point of optimality.Recommended textbooks for youEconomics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage LearningExploring EconomicsEconomicsISBN:9781544336329Author:Robert L. SextonPublisher:SAGE Publications, IncEconomics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage LearningExploring EconomicsEconomicsISBN:9781544336329Author:Robert L. SextonPublisher:SAGE Publications, Inc