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- Ivan faces a labor supply decision. His well-behaved preferences over the two goods "hours of leisure' L and 'consumption' c can be represented by u= 4(L)1/2 +c. He has no non-labor income and can choose how many hours to work at the wage rate u per hour. The price per unit of consumption is p, and his available free time is T hours Use the tangency method to find Ivan's demand functions for leisure and consumption (as functions of u, p. and T)2. Assume the technology is described by y =(x,x2)i and that prices of inputs are wi w: respectively. (a) Find the conditional factor demands for inputs x, and x2.Question You are the manager of a firm and you are required to optimize the Cobb Douglas function given the following parameters. The maximum amount of money available is$1600 where the price of K = 12 and the price of L=6. That is PK=12 and PL=6. The function is given as q=K0.4+L0.6. What is the constraint equation? a. none of the above b. 12K - 6L = 1600 c. 12K/6L = 1600 d. 12K+6L=1600
- An individual’s utility function is given by where is the amount of leisure measured in hours per week and is income earned measured in cedis per week. Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?Suppose that a salesperson earns a basic monthly salary of $800 plus a commission rate is 15% and the possible bonuses are lump-sum amount of $1000 if her monthly sales exceed $10,000 and a further lump-sum of $2,500 if her monthly sales exceed $15,000. Find the function that relates sales to earnings for this salesperson and graph it. At which points is the function discontinuous? Interpret the incentives created by this pay scheme?This question will analyze the impact on a person's labour supply from a shock to their partner's job. Assume leisure is a normal good. Let's assume Vanessa has a wage rate of $20 per hour. Recently her partner, Bill, had to take a wage cut at work, with his wage falling from $45 per hour to $30 per hour, but allowed them to continue working 40 hours per week. Analyze the decision of the household over choice consumption and Vanessa's leisure, taking Bill's hours as given (constant).
- Emma is employed at a contract where he can vary his labour supply between 0 and 40 hours per week. She derives utility from consumption, c, and leisure, L. Her preferences are represented by the following utility function: U(c,L) = min(c, L). The unit price of consumption is p, and the hourly wage rate is w. (a) Derive an expression for Emma's labour supply. (b) The government contemplates introducing a consumption boosting policy including a monthly transfer of money for which Emma is eligible. At what size of the transfer will Emma decide to not work? Assume that the unit price of consumption is 30 and the hourly wage rate is 50Ivan faces a labor supply decision. His well-behaved preferences over the two goods "hours of leisure' L and 'consumption' c can be represented by u= 4(L)1/2 +c. He has no non-labor income and can choose how many hours to work at the wage rate u per hour. The price per unit of consumption is p, and his available free time is T hours .a) Sketch Ivan's budget set, with axes, intercepts, and slope labeled (these will depend on the parameters w, p, and T) .b) Use the tangency method to find Ivan's demand functions for leisure and consumption (as functions of u, p. and T) .c) Let's think about Ivan's "time expansion path" (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T). Sketch it and explain why it has this shape. with reference to Ivan's demand functions.d) In terms of parameters from the model, what is the most that Ivan would be willing to pay to have an extra hour of free time (that is, to increase T by 1)? Why?Ivan faces a labor supply decision. His well-behaved preferences over the two goods "hours of leisure' L and 'consumption' c can be represented by u= 4(L)1/2 +c. He has no non-labor income and can choose how many hours to work at the wage rate u per hour. The price per unit of consumption is p, and his available free time is T hours .a)Sketch Ivan's budget set, with axes, intercepts, and slope labeled (these will depend on the parameters w, p, and T) .b)Use the tangency method to find Ivan's demand functions for leisure and consumption (as functions of u, p. and T) .c) Let's think about Ivan's "time expansion path" (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T). Sketch it and explain why it has this shape. with reference to Ivan's demand functions.d) (3 points) In terms of parameters from the model, what is the most that Ivan would be willing to pay to have an extra hour of free time (that is, to increase T by 1)? Why?
- What is task definition (as a situational variable)?Give an example of how it can influence theconsumption process.Consider a consumer who could earn $400 per week and has 50 weeks available each year to allocate between work (H) and nonmarket time (L). They have no non-labour income. Their utility function is U = C2L , where C is the value of consumption goods. What is their optimal choice for the number of weeks in nonmarket time and consumption? Show this in a diagram. Suppose the government introduces a policy that (i) offers no benefits to people who do not work, (ii) offers a wage subsidy on earnings at a rate of 25%, with a maximum benefit of $5000, and (iii) the benefit is subject to reduction at a rate of 25% for every dollar earned above $20,000 in the year. Show the person’s new budget constraint in a new diagram, and discuss how the person’s optimal choice might change (you do not have to calculate this, but point to where it is likely on the new budget constraint). Discuss how income and substitution effects play a role.(a) Dividing MUX and MUY by their respective prices compute the weighted marginal utility or marginal utility of money expenditure and draw up Table 2 showing diminishing returns for the consumption of the 6 units? (b) Briefly state what you can infer on this equation; MUX/PX = MUY/PY as far as equi marginal principle and managerial economics is concerned? C)Given that MUX/PX and MUY/PY are equal to 6 when 5 units of X and 3 units of Y are purchased. By purchasing these combinations of X and Y, calculate the amount the consumer will spend and derive the maximum satisfaction from combination of these units. (d) Applying the above principle illustrate in terms of a figure, and draw marginal utility curves for goods X and Y. You need to use marginal utility and price i.e. Marginal utility per Kwacha spent on good X = MUX/PX, and that of Y = MUY/PY. The MUX/PX curve should be shown in figure (a) while the MUY/PY curve should be shown in Fig (b). Please do not draw negative…