Consider the following production function: Q (K.L)= 5K2/3Į 1/3 What is the value of its elasticity of factor substitution (0): 2/3 1/3 – 1 3 O b.0 = -1 Oc.o= 2K213-111/3 3 O d.0 = 1
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- 1a) Consider the production function Q = 0 + 6L + 5L2 - .2L3. The range of labor covering Stage II of production is ____ to ____. You can use Excel spreadsheet or otherwise to answer this question. b) A firm’s production function is Q = 600*L -1.0*L2. The firm is currently employing 83 units of labor. What is the elasticity of production? You can use a excel spreadsheet or otherwise to answer this question c) A firm’s LRTC = 600Q - .5Q2 + .001Q3. At what level of output does the firm experience minimum efficient scale? Use either Excel Spreadsheet, Excel Solver or OtherwiseAmy is a graduate student living in Dallas who works as a caddy to supplement their normal income. At an hourly wage rate of $15, they are willing to caddy 5 hours per week. Upping the wage to $25 per hour, they are willing to caddy 14 hours per week. Using the midpoint method, the elasticity of Amy’s labor supply between the wages of $15 and $25 per hour is approximately (0.06, 0.53, 1.89, 10.56) , which means that Amy’s supply of labor over this wage range is (elastic/inelastic) .Let 10p + x = 100 be the demand equation, where p is the price per item when x items are demanded. (a) Find the total revenue when the level of production is: (i) 40; (ii) 41; (b) Find the exact revenue derived from the 41st item. (c) Find the approximate revenue derived from the 41st item. (d) What is the error if the derivative is used to approximate the marginal revenue?
- What is the cheapest way of producing 850 units of output if a firm operates with theproduction function 0.5 0.5 Q = 30K L and can buy input K at 75 $ per unit and L at 40 $per unit?Consider the cost minimization problemMin C(x1, x2) = w1x1 + w2x2S.t x1ρ + x2ρ = yρDerive the conditional factor demand functions?What effect would each of the following factors have on elasticity of demand for resource A, which is used to produce product Z? Due to technological change, much less of resource A is used relative to resources B and C in the production process.
- Calculating the price elasticity of supply Van is a stay-at-home parent who lives in Chicago and provides math tutoring for extra cash. At a wage of $30 per hour, he is willing to tutor 6 hours per week. At $50 per hour, he is willing to tutor 16 hours per week. Using the midpoint method, the elasticity of Van’s labor supply between the wages of $30 and $50 per hour is approximately (0.05 / 0.55 / 1.82 / 22), which means that Van’s supply of labor over this wage range is ( elastic / inelastic).Given the following cost function, determine the underlying production function. 1 2C(m, w, y) = 10mwy, where y is the output and m and w, are the prices of two inputs x1 and x2 respectively.A company has 350 employees who work 120 hours a month each. Each worker earns $21 per hour. There is a profitable project the company would like to start, but it would require an additional 21,000 working hours within three months to be completed, and all the employees are fully loaded with other projects. The company does not want to hire new staff; they would like the project to be completed by the current workforce instead.Given that the wage elasticity of labor supply is 0.8, calculate the hourly wage the company should offer its employees to encourage them to work on the new project. Use the midpoint method and round to two decimal places throughout your calculations.
- A firm uses a production function of the form Y=z*K^0.33*Nd^0.67 and chooses labor input Nd to maximize profits taking the wage rate w that it pays per unit of labor as given. First, write down the profit function of the firm. Assume z=10, K=100, and wage w = $20. The government now introduces a wage subsidy to help out the firm. The wage subsidy s = $4 per unit of work. Given this subsidy solve for the new optimal output level of the firm. Y* =Take a Cobb-Douglas production function, find its Elasticities w.r.t output and Elasticity of Substitution with the help of partial derivatives.A firm faces perfectly elastic demand for its output at a price of $6 per unit of output. The firm, however, faces an upward-sloping labor supply curve of E = 20w - 120 where E is the number of workers hired each hour and w is the hourly wage rate. Thus, the firm faces an upward-sloped marginal cost of labor curve of MCE = 6 + 0.1E Each hour of labor produces five units of output. How many workers should the firm hire each hour to maximize profits? What wage will the firm pay? What are the firm’s hourly profits?