John's technology for producing apple pie (a) is represented by a = vĪ +2 where Lis labor. His utility function from his consumption of apple pies (a) and his labor (L) is given by u (a, L) = 2a – 4L². Assume John is the only consumer and producer of apple pies in his household and suppose the price of apple pies is set at $1. The market equilibrium wage rate for John's labor supply is a) $1 b) $2
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- Elsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = BW where B is the amount of bananas she consumes and W the amount of water. Her production function for bananas is B = 6LB where LB is the amount of labour time she devotes to bananas. Her production function for water is W = 2LW where LW is the amount of labour time she devotes to water. If the total time she has available is 10, what should she do to maximize her utility?Ana decides every day how many hours to work and how much beef to consume. She spends all income earned from work each day on consumption of beef. Her utility function for free time (t, 24 hours minus hours worked) and consumption (y) is: U(t,y)=2t^1/2 + y The price per unit of beef consumed is 4 and her hourly wage is 1. Using a diagram and appropriate algebra, explain what Ana’s optimal number of hours work and units of beef consumed are each day. Ana reads a book about the impact of beef consumption on climate change and realises that there is a cost to society of her beef consumption. She takes account of this impact on society in her own decisions, incorporating a disutility of -0.03y per unit of beef consumed. She still only consumes beef and spends all income earned each day on this consumption. Explain, using a diagram and appropriate algebra, how recognition of the impact of her consumption choice on climate change impacts on Ana’s daily free time and beef…Trey works as a waiter for Puff & Stuff catering for a wage of w 11. In addition to his %3D labor income from waiting, Trey makes supplemental income with his household production time by streaming video games on Twitch. He doesn't have any unearned income (V=0). Trey's preferences over consumption and household production are given by the utility function below: u (H, C) = 2\H + VC Assume Trey has 16 hours each day to split between household production and consumption, if he spends 10% of his time at home streaming and earns an hourly rate of P = 7, what will be his optimal allocation of household production? (hint: assume that Trey's utility-max condition remains unchanged and his supplemental income will only impact his budget constraint)
- Elsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = 4BW where B is the amount of bananas she consumes and Wthe amount of water. Her production function for bananas is B=Lg where Lg is the amount of labour time she devotes to bananas. Her production function for water is W = Lwwhere Lwis the amount of labour time she devotes to water. If the total time she has available is 70, what should she do to maximize her utility? (Enter your answers in whole numbers.) LB= Lw=[A) Ana decides every day how many hours to work and how much beef to consume. She spends all income earned from work each day on consumption of beef. Her utility function for free time (t, 24 hours minus hours worked) and consumption (y) is: U(t, y) = 2t + y The price per unit of beef consumed is 4 and her hourly wage is 1. • Using a diagram and appropriate algebra, explain what Ana's optimal number of hours work and units of beef consumed are each day. Ana reads a book about the impact of beef consumption on climate change and realises that there is a cost to society of her beef consumption. She takes account of this impact on society in her own decisions, incorporating a disutility of -0.03y per unit of beef consumed. She still only consumes beef and spends all income earned each day on this consumption. • Explain, using a diagram and appropriate algebra, how recognition of the impact of her consumption choice on climate change impacts on Ana's daily free time and beef consumption…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)
- In a standard consumer optimization problem in microeconomics, a consumer purchases any pair of goods untilU1U2=p1p2(?), at an interior solution, where Ux is the marginal utility of good x for the consumer and px is the price of good x, where x={1,2}. What is the corresponding optimality condition for a worker-consumer in his labour-leisure optimization problem and why is it just a variation on the standard optimality condition (?)?Susan obtains utility by consuming carrots C and enjoying leisure L. Suppose that she has a daily non-wage income Y of £100 and is paid a fixed hourly wage rate of £10 for every hour she works in a local coffee shop. Assume that Susan is a utility maximiser and is free to choose x hours of work per day where 0 ≤ x ≤ 10. Assume also that the unit price of C is £1. a) Suppose that L is measured on the horizontal axis and C on the vertical axis. Use these axes to draw the set of all C and L combinations that Susan can choose from. Write down Susan’s budget equation. b) Suppose that Susan’s preferences over carrots and leisure are expressed by the following utility function: U(C,L) = min{C, 10L}. Calculate Susan’s optimal consumption bundle, both algebraically and graphically. Calculate the value of MRS at the optimal choice. c) Suppose instead that Susan’s preferences are such that indifference curves in the L-C space are strictly convex to the origin, and that she chooses to work 5…Construction workers in the town of Cortland, NY have Cobb-Douglas utility for labor and consumption, UL=(20-L)C, MRS=C20-L where L is the number of hours of labor supplied in a day and C is the dollar amount of consumption goods purchased with wage income (pc=$1 ). R=20-L is the number of hours of leisure that the worker has during the day. Derive the labor supply function for workers in Cortland. Draw the labor supply curve on a graph with L on the horizontal axis and w on the vertical axis.
- Suppose the utility function of a person consuming two commodities X and Y with income Birr 600 is given by U =2xy. If the per unit price of X is Birr 20 and per unit price of Y is Birr 40. a) Calculate the utility maximizing level of consumption of X1 and X2. b) Find the MRSX, Y at the optimum.If the production function of a firm is given by Q=,and the input prices are r = Birr 8 per unit and w = Birr 2 per unit,A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete? The production function for puffed rice is given by q , where q is the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. Calculate the q = 1,000 isoquant for this production function and show it on a graph. If K = 10, how many workers are required to produce q = 1,000? What is the average productivity of puffed-rice workers? Suppose technical progress shifts the production function to , answer parts a and b for this new situation.Pat is a representative consumer in the neighbourhood market for Jr Chickens. Their utility function for JCs and all other goods is given by: U(JC,Y) = 10JC – (JC^2)/2 + Y MUc = 10- JC MUy= 1 Every McDonald's franchise has the following production function for Jr Chickens: JC = 4K^(1/2) + 2L^(1/2) MPx = 2/K^(1/2) MPL= 1/L^(1/2) a. Derive Pat's Marshallian demand for Jr. Chickens. You can assume Pat has a trust fund and can always afford it. b. There are five other people in the neighbourhood who like Jr Chickens. What is the neighbourhood's market demand for JCs? c. What is the price elasticity of demand when P= 1, 5 and 9? Note: dQ/dP = -5. d. Derive the conditional factor demands for K and L for a McDonald's franchise.