Please explain to me what every different variable means in this question 1) In period t, a parental household (indexed by i) equipped with human capital hearns a labour income of whi, where w > 0 represents a constant wage rate. Thishousehold derives utility out of own consumption , the number of children nand their level of human capital h+1 Education is provided by teachers who areequipped with the economy's average level of human capital hf. Human capital perchild evolves from one period to another according toh₁+1 = (e+ē)" (hi)*(h?) ¹—7,0 0 is a constant parameter and e represents the level of education perchild.The households' utility function is specified asU₂ = In(c) + [In(ni) + 3 ln(hi+1)]with 7,3 > 0.Raising one child to adulthood requires a share of 0 << 1 units of time. Moreover,education is subsidised at a rate 0 ≤ se < 1, such that education costs per childamount to whe(1 - se).a. Solve household i's optimisation problem and explain the economic rationale ofyour results.b. Let's define a variable a capturing the households' relative human capital en-dowment with respect to the economy's average, such thathiShow that relative human capital of household i, evolves according toĐỀ+= = 8)² )" . (²) ²zat (1-se)ē)2- - (1 - se)ē(3)(4)c. Suppose the +1-locus (4) intercepts from above at z = 1 with the 45-degreeline. What does this information imply for the evolution of inequality? Explainthe impact of the education subsidy on the +1-locus with an appropriatediagram.Remark: No derivations are required here. Just provide a decent rationaleand do as asked!

Utility FunctionBudget ConstraintHousehold Income - Cost of educating children =

In period t, a parental household (indexed by 2) equipped with human capi earns a labour income of whi, where w > 0 represents a constant wage rate_ household derives utility out of own consumption , the number of childr and their level of human capital h+1 Education is provided by teachers w equipped with the economy's average level of human capital h. Human capit child evolves from one period to another according to ht+1=(e+e)" (hi)* (h²)¹, 0 <1,7 <1 where e > 0 is a constant parameter and e represents the level of educatio

In period t, a parental household (indexed by 2) equipped with human capi earns a labour income of whi, where w > 0 represents a constant wage rate_ household derives utility out of own consumption , the number of childr and their level of human capital h+1 Education is provided by teachers w equipped with the economy's average level of human capital h. Human capit child evolves from one period to another according to ht+1=(e+e)" (hi)* (h²)¹, 0 <1,7 <1 where e > 0 is a constant parameter and e represents the level of educatio

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter3: Scarcity, Trade-offs, And Production Possibilities

Section: Chapter Questions

Problem 3P

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Cowles Foundationfor Research in Economicsat Yale UniversityCowles Foundation Discussion Paper No. 2021ARE WE APPROACHING AN ECONOMIC SINGULARITY?INFORMATION TECHNOLOGY AND THE FUTUREOF ECONOMIC GROWTHWilliam D. NordhausSeptember 2015An author index to the working papers in theCowles Foundation Discussion Paper Series is located at:http://cowles.yale.edu/This paper can be downloaded without charge from theSocial Science Research Network Electronic Paper Collection:http://ssrn.com/abstract=2658259Electronic copy available at: http://ssrn.com/abstract=2658259Are We Approaching an Economic Singularity?Information Technology and the Future of Economic GrowthWilliam D. Nordhaus1September 1, 2015AbstractWhat are the prospects for long-run economic growth? The presentstudy looks at a recently launched hypothesis, which I label Singularity.The idea here is that rapid growth in computation and artificialintelligence will cross some boundary or Singularity after whicheconomic growth will…
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…
In period t, a parental household (indexed by i) equipped with human capital hit earns a labour income of wh^i_t, where w > 0 represents a constant wage rate. This household derives utility out of own consumption c^i_t, the number of children nit and their level of human capital h^i_(t+1). Education is provided by teachers who are equipped with the economy’s average level of human capital h^T_t . Human capital per child evolves from one period to another according to h^i_(t+1) =(e^i_t +e ̄)^η(h^i_t)^τ(h^T_t )^(1−τ), 0 < η, τ < 1 (1) where e ̄ > 0 is a constant parameter and e^i_t represents the level of education per child.The households’ utility function is specified as U_t^i = ln(c^i_t) + γ[ln(n^i_t) + βln(h^i_(t+1))] (2) with γ,β > 0.Raising one child to adulthood requires a share of 0 < z < 1 units of time. Moreover, education is subsidised at a rate 0 ≤ s_e < 1, such that education costs per child amount to wh^T_t e^i_t(1 − s_e). Solve household i’s…
In period t, a parental household (indexed by i) equipped with human capital hit earns a labour income of wh^i_t, where w > 0 represents a constant wage rate. This household derives utility out of own consumption c^i_t, the number of children nit and their level of human capital h^i_(t+1). Education is provided by teachers who are equipped with the economy’s average level of human capital h^T_t . Human capital per child evolves from one period to another according to h^i_(t+1) =(e^i_t +e ̄)^η(h^i_t)^τ(h^T_t )^(1−τ), 0 < η, τ < 1 (1) where e ̄ > 0 is a constant parameter and e^i_t represents the level of education per child.The households’ utility function is specified as U_t^i = ln(c^i_t) + γ[ln(n^i_t) + βln(h^i_(t+1))] (2) with γ,β > 0.Raising one child to adulthood requires a share of 0 < z < 1 units of time. Moreover, education is subsidised at a rate 0 ≤ s_e < 1, such that education costs per child amount to wh^T_t e^i_t(1 − s_e). Let’s define a…
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a) Present the Lagrangian (constrained maximisation) problem for the household under this modified specification and derive the first order conditions in this case. Hint: the household chooses c1, c2, ℓ1 and ℓ2. b) Use the first order conditions for ℓ1 and ℓ2 to derive an expression for the relative amount of leisure time chosen by the household over the two periods, i.e. derive an expression for (1–ℓ1)/(1–ℓ2). Explain how an increase in the relative wage (w2/w1) affects the household’s decision about how much leisure to enjoy in each period. c) Calculate the intertemporal elasticity of substitution between period 1 and period 2 leisure time in this case. Explain how the magnitude of this elasticity influences the household’s decision-making in the model. d) Use the first order conditions for c1 and c2 to derive an expression for the relative amount of consumption chosen by the household over the two time periods, i.e. derive an expression for c2/c1. Provide an economic interpretation…
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.
Tatum is a mother of Anny (1 year old). Tatum derives utility from income Y (i.e. a disposable income that she can spend on consumption goods other than childcare) and leisure L according to the utility function U(Y,L)=Y*L . She has non-labour income of $300 per day. Her time endowment is 16 hours per day that can be spent either on Leisure (which mostly consists of caring for Anny) or labour market work. If Tatum works she has to leave Anny in the child care. Tatum’s wage is $30 per hour, while the childcare cost $5 per hour. Tatum only uses childcare when she works. Compute how many hours Tatum will work under these circumstances. Round your answer to the second decimal point.
Imagine that the wage-schooling locus is given by w(s)=s^(1/3). What will be the optimal level of education for an individual to take if next period’s earnings in any given time are worth 95% of current earnings for that individual? Answer is s=20/57 I need step by step calculations
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.Provide the functional form of the income effect from a marginal decrease in income and provide the functional form of the substitution and total income effects of a marginal increase in wage.
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.