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- Consider an economy with production function given by Y = AK0:5L0:5 where A is the total factorproductivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is xed and equal to 1. Assume A=100.a. Write the rm's problem of choosing labor demand. Derive the demand for labor as a functionof the real wage.b. Assume labor supply is inelastic and xed at L= 100. Find the equilibrium values of the wageand the employment level for this economy. Display graphically the labor supply and the labordemand curves. Carefully label your graph.c. Suppose the economy faces a positive productivity shock and TFP is now A=200. Displaygraphically the new labor demand function. What are the equilibrium values of employment andthe real wage?d. Compute the total output when A=100 and when A=200. What is the output's growth rate?Compare that growth rate with the growth rate in A. How does the growth rate of output percapita compares to the growth rate in A? Explain…Suppose that a certain factory output is given by the Cobb-Douglas production function ?(?, ?) = 60?^1/3?^2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory’s output. (a) Determine whether the Cobb-Douglas production function is concave, convex, strictly concave, strictly convex or neither.please sir solve these 3 questions 33- If an increase in the price of one good leads to a fall in the quantity demanded of other than these goods are complementry good A- True B- False 34- the production function is a purely technical relationship between input and output A- True B- False 35- marginal proudact is defined as the change in TP resulting from the employment of an additional unit of a varibal factor: A- True B- False
- Why does modeling production as convex in inputs probably make sense in the real world?Answer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.Take a Cobb-Douglas production function, find its Elasticities w.r.t output and Elasticity of Substitution with the help of partial derivatives.
- Show all work and EVER STEP for solving the problem. DO NOT SKIP ANY STEPS. That is the only way I can know how you solved the problem. Directions: Given the consumption matrix C and the demand matrix d, find the production vector x that meets the consumption matrix C. Hint: Recall Leontief Input Output Models.Hi, Please help me with this Econ problem, specifically, the demand (D) line shift and responses to the two questions. Thank you!A production function has two inputs: domestic labor (Edom) and foreign labor (Efor.) The market is originally in equilibrium as shown below, and the production budget is fixed. Suppose a shock occurs that increases the marginal product of domestic labor. Assuming no changes in domestic or foreign wages, what will happen to the quantities of domestic and foreign labor employed? Initial long run equilibrium (prior to shock):
- For the production function Q = K0.6L0.8 and the budget 125 = 3K + 5L find the NEW LEVEL in the optimal employment of labor (L) after wages change by a factor of 1.4 while maintaining the same level of output. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1). I Know that the correct answer is 12.4 +/- 1 I am just unsure how to get that answer.Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r,respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of$1,500.a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in thelong run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph aspart a, graphically show the impact of the minimum wage on the optimal level of employment in thelong run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price ofcapital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts theoptimal levels of employment and capital in the long run. Clearly identify the resulting scale andsubstitution effects caused by the lower cost of capital. Could you please answer this question using the graphs please.How does any one economic variable respond to changes in another? Why would a profit-maximizing firm expand the use of each input until its marginal revenue product equals the price of the input?
