Please pair the formulas and concepts listed below! Q/L U=ax+by, ahol a,b>0 ε = (AQ/AP)/(Q/P) Px*X+Py*Y<=l Choos Choose... utility function for perfect complements Budget Set price elasticity marginal product of labour income elastisity average product of labour Budget Line utility function for perfect substitutes utility function for convex preferences
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- According to the income effect, if an employee receives higher wages, ceteris paribus, it leads to fewer hours worked. True O False Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.Consider a representative agent with the utility function U = ln(Ct)+ Nt The budget constraint is Ct = wtNt +Dt where wt is the wage and Dt is non-wage income (i.e. a dividend from ownership in the firm). The agent lives for only one period (period t), and hence its problem is static. (a) Derive an optimality condition characterizing optimal household behav- ior. (b) Solve for the optimal quantities of consumption and labor. Plz do fast asap, urgent.Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure. U(c,l) = lnC + 4lnl Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?
- It is easy to conclude that when hiring workers in the short run whose marginalproductivity rises, the average product of labor will rise as well. However, if workersproductivity declines, average product of labor may still be rising. Explain why this mayhappen.Demonstrate using clearly labeled diagrams that the labor supply for leisure being normal (SE>IE) ismost inelastic, for leisure being inferior is most elastic and for neither case is somewhere in the middle.Strong income effect weakening and eventually eliminating the substitution effect explains why an individuals labor supply cure bends backward at high wage levels. True or galse
- Consider the representative consumer who decides consumption and leisure. Theenvironment is the same as in Lecture 5. Keep the same notation. The preference is givenby U (C,L) = αln C + (1 −α) ln L. Assume h = 1, i.e., the time endowment is one day.(a) Write down the utility maximization problem.(b) Derive the demand for consumption and the supply for labour.(c) Suppose the non-wage income π −T increases while the wage rate w falls at the sametime. The size of the changes can be different. Determine the effects on consumptiondemand and labour supply (i.e., leisure demand). Use the indifference map to explainyour results in terms of income and substitution effects for the following cases:(i) The increase in π −T exactly cancels out the drop in w, i.e., |∆ (π −T)|= |∆w|.(ii) The increase in π −T is greater than the drop in w, i.e., |∆ (π −T)|> |∆w|.(iii) The increase in π −T is smaller than the drop in w, i.e., |∆ (π −T)|< |∆w|.(d) Suppose the utility function is Cobb-Douglas: U…Please answer according to the picture: What are the parameters of the problem? Find the conditional factor demand functions. Label them l*(w, r, y) and k*(w, r, y). Find the cost function: c(w, r, y). What is its interpretation?Please Answer according to the picture. What are the parameters of the problem? Find the conditional factor demand functions. Label them l(w,r,y) and k(w,r,y).Find the cost function: c(w,r,y). What is its interpretation?
- How is cross elasticity and income elasticity relevant to Indigo’s managerialdecision making?Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure. U(c,l) = lnC + 4lnl a) Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker? b) Provide the functional form of the income effect from a marginal decrease in income. c) Provide the functional form of the substitution and total income effects of a marginal increase in wage.Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure U(c,l) = lnC + 4lnl 1) Provide the functional form of the income effect from a marginal decrease in income. 2) Provide the functional form of the substitution and total income effects of a marginal increase in wage. 3) Show that the Slutsky equation holds for this worker.