The representative firm has technology described by a linear production function Y = 190N. Compared to the previous question, labor productivity decreased. The representative household has preferences over consumption and leisure represented by the following utility function u(c, l)=√c+18√√. At the equilibrium, how much output is produced?
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- A worker receives a wage rate w and has L hours of leisure every day (the total endowment of hours is 24 hours per day). The government gives a subsidy of rate s of her income (i.e. her income is (1+s) times what it would be without the subsidy). The worker cannot save, and initially faces no tax. She consumes a single consumption good, c. 1. Write a budget constraint for this individual and plot it. 2. Suppose that the worker has well-behaved preferences, i.e. she likes more consumption and leisure rather than less, she dislikes working, and she has decreasing marginal utility in consumption and leisure. a. Display graphically what the optimal consumption-leisure choice for this worker (no need for exact numbers as we don’t know the utility function; give intuition) 3. Imagine that instead of a subsidy rate, s, the government imposes income tax at rate t. What is the new budget constraint? Display on the same picture. In the new optimum, is the consumption higher? Explain the answer…Consider an economy with two goods, consumption c and leisure l, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to l = 24 – h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and It hours of work can be represented by the utility function U(c, h) = c- (a) What is this consumer's budget constraint? (b) Solve for the consumer's utility maximizing hours of work h*(w, 1 - T, Y) and con- sumption c*(w, 1 - T, Y). (c) Repeat part (b) for a consumer with the utility function U(c, h) = alog(c) - Blog(h).George enjoys bananas and leisure. He sleeps 8 hours per day. Of the remaining 16 hours, for each hour he works he is paid 2 bananas. He also receives 6 bananas in dividends but has to pay 6 bananas in taxes. Draw George’s budget constraint (put consumption on the vertical axis and leisure on the horizontal). Make sure to show the vertical and horizontal intercepts as well as the slope. Now suppose that George chooses to work 6 hours per day. Find how many hours o f leisure and how many bananas he will consume, and show his optimal choice on the budget line using an indifference curve. Suppose that the government uses some of the taxes to give back to George income assistance of 4 bananas. Show the impact of the measure on George’s budget constraint Use an indifference curve to show George’s new optimal allocation and explain what will happen to his consumption of bananas and leisure if both are normal goods. The graphs below shows the behaviour of consumption of durables and…
- 1.1 Derive the marginal utility of good X (MUx) and marginal utility of good Y (MUy) from the utility function: U = f(x; y) = x²y³ - 10x using partial differential calculus. 1.2 Derive the MPL and MPK equations, if TP = f (L; K) = 10L² +20L²K² +3K² using partial differential calculus.The representative consumer has the following utility function: U(c, I) = In c + In I where c is the consumption good, and I is the leisure hours. She has h hours of time available which she can allocate between work and leisure. For each hour of work, she earns w units of consumption good. She also earns t as dividend (profit) income which is measured in consumption goods. The government collects revenues using a consumption tax; in particular, the representative consumer pays t units of goods to the government for each unit of consumption good she buys. Note that there is no lump-sum tax. (a) Determine the consumer's budget constraint. (b) Solve for the c and I that maximize the utility of the consumer. (c) Suppose that the tax ratet increases. What is the impact of this increase in the tax rate, t, on the consumer's choice for c and l? What is the impact of this on the labour hours of the consumer?Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24 - h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function: h'+p U(C,h) = c-B- 1+ p where ß> 0 and p > 0 are parameters. TENTO COITS ar answer aneren ananm pally. p (j) Suppose instead that the consumer's utility function was U(c, h) = min(c, -h). Would the EB from a unit excise tax be larger or smaller compared with the original utility function. Explain your answer in 4 sentences.
- Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function: h²+p U(c,h) = c-B- where ß> 0 and p > 0 are parameters. 1+ P a) What is this consumer's budget constraint? (e) Suppose now that the income tax liability is increased to T = 0.3. Calculate the consumer's utility at their new utility maximizing consumption and labour supply bundle after the tax change. (h) Using the excess burden formula, calculate…Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24 - h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function: U(C,h) = c-B- where ß> 0 and p > 0 are parameters. ‚h¹- P 1+ p a) What is this consumer's budget constraint? b) Solve for the consumer's utility maximizing hours of work h*(w, 1-T) and consumption c* (w, 1 - T, Y). c) What is the compensated own-price elasticity for the supply of hours of work? For parts (d) - (h), assume the following: w = $50,…Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24 - h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function: h¹+p U(C,h) = c-B- where ß> 0 and p > 0 are parameters. 1+ p (d) Suppose the income tax rate is initially zero (i.e. T = 0). Calculate the consumer's utility at their utility maximizing consumption and labour supply bundle. (f) Calculate the change in the consumer's surplus (i.e. utility) following the tax change. i) Now suppose that p = 1…
- Consider an individual who receives utility from consumption, c, and leisure, l. The individual has L time to allocate to work, n, and leisure. The individual’s consumption is a function of how much he works. In particular, c = root n. The individual’s maximization problem is max U =ln(c)+θl subject to c = √n n+l=L where θ > 0. Solve the maximization problem. Hint: Substitute both constraints into the objective function.Consider an economy with two goods, consumption c and leisure I, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24 h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function: h¹. P U(C,h) = c-B- where ß> 0 and p > 0 are parameters. 1+ p a) What is this consumer's budget constraint? b) Solve for the consumer's utility maximizing hours of work h*(w, 1-T) and consumption c* (w, 1-T, Y). c) What is the compensated own-price elasticity for the supply of hours of work?What are the determinants for an individual demand? Receive with the help of indifference curves and the budget outline the optimal consumption plan. How do you transfer the optimal consumption plan into an individual demand function?