Labor Market and Real Output: In the labor market, there is one representative worker and a representative firm. Worker supply hours of working (NS), and firm demand hours of work in order to produce output (Y). The production function that capture firm's production process is Y = f(N) = z√KN, where in the short run z=2 and K=100. Worker has a natural log utility function U(c, l) = In(c) + In(l). h=10, T T = 10. Please draw labor supply and labor demand in a graph and determine the equilibrium w*, N*, and Y*. If you cannot solve w*, N*, and Y*, you can just show where they are in the graph. (Note: MRS,c=and MPN: 2√N = Now, TFP (z) increases. What happen to the equilbirium outcomes (w*, N*, and Y*)? Please show it in an another graph. Are the changes the same as the example that we discussed in the class?
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- Given the production function per hour Q(x, y) = 2x² - 4y² + 40x + 40y, where x is a worker receiving $1 per hour and y is a worker receiving $2 per hour. The budget constraint is $410. What is the value of ? (given that your bordered hessian (or variable vector) is in the order of X, x and y, respectively)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 (?)?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.
- A worker has 110 hours available in a week that can be used for leisure (L) or work (h). The utility function is U = (1 - α)ln(C) + α ln(L), where C is consumption. a) The price per unit of consumption is 1, the hourly wage is w, and the worker has a non-labor income of V. Show that the labor supply is: h* = (110(1-a)- (av)/w). Also, find the demand for consumption and leisure. b) What is the effect on labor supply of i) an increase in the hourly wage and ii) an increase in non-labor income? c) Set α = ½. What are C, L, and h when w = 200 and V = 10000? What is the reservation wage? d) What is the effect on labor supply of i) a 30% income tax and ii) a 10% wealth tax (on V)? e) What is the labor supply if V increases to 11600? f) An increase in V to 11600 gives the worker the same utility as w = 250 and V = 10000 (you do not need to show it). What are the income, substitution, and total effects on labor supply of an increase in wage from 200 to 250 while V remains at 10000?…If a firm's production function is Leontief and the wage rate goes up, the: Multiple Choice firm must use more capital in order to minimize the cost of producing a given level of output. firm must use more labor in order to minimize the cost of producing a given level of output. firm must use less labor in order to minimize the cost of producing a given level of output. cost minimizing combination of capital and labor does not change.A student has a part-time job in a restaurant. For this she is paid $8 per hour. Her utility function for earning $I and spending S hours studying is U(I,S) = I^1/4 S^3/4 (The utility function is a measure of the `usefulness' or `worth' to the student of a certain combination of money and study time). The total amount of time she spends each week working in the restaurant and studying is 100 hours. How should she divide up her time in order to maximise her utility?
- For the Cobb-Douglas production function P and isocost line (budget constraint, in dollars), find the amounts of labor L and capital K that maximize production, and also find the maximum production. Then evaluate and give an interpretation for |å| and use it to answer the question. (a) Maximize P = 2000L3/5K2/5 with budget constraint 15L + 32OK = 8000. L = K = P = (b) Evaluate and give an interpretation for |21. Each additional dollar of budget increases production by this amount. (c) Approximate the increase in production if the budget is increased by $80. unitsSuppose the two factors are perfect complements and the production function is given by y=min { 13x1,2x2} Where x1=300, X2=50 What will be level of production and draw corresponding iso quant?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.
- A firm has two variable factors and a productionfunction f(x1, x2) = 6x1/21X21/3. The price of its output is 3, the price of factor 1 is 3, and the priceof factor 2 is 2.– What is the optimal production output level?– What is the maximum profit-level?Consider a consumer with the following utility function for consumption and leisure: U(R,C) = 160 In N +Y where N is the hours of leisure ("recreation") consumed per day (24 maximum) and Y is dollars spent on consumption (p = 1). The consumer has an hourly wage w. (a) Assume the consumer derives all income from work at a wage rate w. Derive the labor supply function, LS (w). (b) For what values of w does the consumer work zero hours? (Hint: does a corner solution arise?) (c) Suppose that w = 10. How many hours does this consumer work? If the wage rate increases to w' = 16, how many hours do they work? What is the total effect on the supply of labor?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)