3. Suppose that the production function of an economy is given by Y = √N. The (representative) firm hires workers (N) at a wage rate w. Assume that the firm maximizes profits by choosing how much to produce and how many workers (hours) to hire. (Remember that the profit function is Y - WN.) The representative consumer has preferences given by the utility function U(-) = log (c) + log (1), with a marginal rate of substitution given by c/l, where c is consumption and / is the leisure time. The endowment of time of an individual is 24, which has to be allocated between labor and leisure. (Recall that N + 1 = 24.) a. Derive an expression for the labor demand function.
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- The utility function of Master Enterprise is U (T, M) = T'/4 M³/4 Where T and M are the two goods that the Enterprise sells. The owner of the Enterprise is interested in finding out the demand function of its product. Help him: • Find the demand function for Good T and Good M. • Use an Income of $8000 and the Price of Good I as $5.00 while the price of Good M as $12 to find the optimum bundles of Good T and M.A firm has a productivity equation Q = L K² where L is labour and K is capital. The unit cost (cost for each unit of production) is c = 2. The price in the market for the good is 15. The wage for each hour is w=10. Also, there is a fix cost equal to K Furthermore, there is a worker with utility equation U = C² R where C is the consumption and the price of consumption good is P 1. The maximum working hours (T) per week are 100. So, T = L + R where R is the leisure time. с = Calculate the optimum decision for working hours, leisure time and consumption by the consumer. Then calculate the capital investment by the firm for the maximisation of the profits. (Hind: This is the only worker for the firm and he will decide for the working hours, so the firm will decide for the capital. Assume that L = Q)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.
- 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.Consider an economy with a single consumer whose preferences are given by U = log(x) - , where x is consumption and labor supply. Assume that the consumption good is produced using labor alone with a constant-returns-to-scale technology. Units of measurement are chosen so that the producer prices of both the consumption good and the wage rate are equal to 1. a. Let the consumer’s budget constraint be qx = , where the consumer price is q = 1 + t, and t is the commodity tax. By maximizing utility, find the demand function and the labor supply function. b. Assume the revenue requirement of the government is 1 10 of a unit of labor. Draw the production possibilities for the economy and the consumer’s offer curve. c. By using the offer curve and the production possibilities, show that the optimal allocation with commodity taxation has x = 9/10 and = 1. d. Calculate the optimal commodity tax. e. By deriving the first-best allocation, show that the commodity…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?
- (Short Answers) 1. Jie works in a university. He can work as many hours as he wishes at a wage rate of w. Let C be the number of dollars he has to spend on consumption and let R be the number of hours of leisure that he chooses. Assume that Jie has the utility function U(C, R) = In(C) + In (R). He carms $4 per hour and has 80 hours per week to devote to labor or leisure, and has no income from sources other than labor. a) How many consumptions does he choose? How many hours of leisure does he choose? b) Suppose that Jie's wage rate will rise to $6 per hour from next year. How many hours of leisure per week will he choose next year? You are required to decompose his change in demand into the substitution effect, ordinary income effect and endowment income effect. c) Suppose that Jie will get $4 per hour for the first 35 hours that he works and $6 per hour for every hour beyond 35 hours a week from next year. How many hours of leisure per week will he choose next year?The utility function of Master Enterprise is U (T, M) = T/4 M³/4 Where T and M are the two goods that the Enterprise sells. The owner of the Enterprise is interested in finding out the demand function of its product. Help him: Find the demand function for Good T and Good M.Consider an individual whose utility function is U(C, R) = 2C - (4 - R) 2 where R is the amount of leisure the consumer experiences per day. Suppose that the individual normally sleeps T hours a day, and they can spend the remaining hours between work and leisure. The individual receives an hourly wage of w > 0 and has also an income of Y > 0 a day from non - labour sources. The price of consumption goods is p per unit.
- 1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y)=LY+2L a. b. C. Calculate the demand function for L and show it on a graph (L vs W). Calculate the labor supply (H) and show it on a graph (H vs W). What will happen to L, Y and H if the wage per hour (W) will decrease? =Use the following general linear supply function to answer the next question: Qs = 60 + 8P - 4P + 20F, where Qs is the quantity supplied of the good, Pis the price of the good, P is the price of an input, and Fis the number of firms producing the good. When P = $20 and F= 60, the INVERSE supply function is Multiple Choice P= 132,5 + 0.125Qs. P= -147,5 + 0.125Qs. P= 260 + 8Qs P= 147.5 + 8Qs.Consider an economy with 2 consumption goods and N consumers, all with the same utility function: 1-a u(x1, x2) = xĩxa, where and E (0, 1) . The goods prices are pi income y1 and the rest have income y2. 2 and p2. Among the consumers, half of them each have (a) Each firm has the cost function c(q) = Bq². Solve for the equilibrium price P2. ' There are n firms operating in the competitive market for good 2.