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- Question 2 Show that the Cobb – Douglas production function f(x,,x,)= Ax“x , with 0 0, x, > 0. -Sugar Enterprises manufactures high speed personal computers as its main product line. Its short run production function is given by Q = 3600K - 4.5K² where Q is the number of computers produced in a week and K pertains to the number of units of capital. c.) Compute the marginal product of the 200th unit of capital. d.) How many computers can be produced by the firm in a week if there are 200 units of capital? e.) Compute the marginal product of the 300th unit of labor. f.) How many computers can be produced by the firm in a week if there are 300 units of labor?Consider the graph below for a firm. At point T, we know that the firm K TC = Total Cost; Q=f(K, L); 100 E 70 Q, =100 TC, L 60 80 A. Is a cost minimizer but not technical efficient. B. Is a cost minimizer. O C. Is technical inefficient and a not a cost minimizer. O D. Is technical efficient but not a cost minimizer. E. None of the above.
- 3. The Chipper Cookie Company's output is given by the Cobb-Douglas Production function P = 120L0.7 K0.3, where P is the number of units produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 600 and K = 600? b. Find the marginal productivities. c. Evaluate the marginal productivities with L= 600 and K = 600. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $1200 then there is a constraint L+ K = 1200. Use Lagrange multipliers (^) to find the values of L and K that will maximize production and find the maximum production f. Find and interpret 2 for this problem. only need part e and f!Suppose that the Acme Gumball Company has a fixed proportions production function that requires it to use two gumball presses and one worker to produce 1,000 gumballs per hour. a. Explain why the cost per hour of producing 1,000 gumballs is 2v + w (where v is the hourly rent for gumball presses and w is the hourly wage). b. Assume Acme can produce any number of gumballs they want using this technology. Explain why the cost function in this case would be TC = q(2v +w), where q is output of gumballs per hour, measured in thousands of gumballs. c. What is the average and marginal cost of gumball production (again, measure output in thousands of gumballs)? (show the complete formula) Draw the graph for the average and marginal cost curves for gumballs assuming v=3, w-5 (show working) Now draw the graph for these curves for v=6, w=5.( show working) Explain why these curves have shifted.2. A competitive firm uses two variable factors to produce its output, with a production function q min{x₁, x₂}. The price of factor 1 is $8 and the price of factor 2 is $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x₁. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no butput. What is the smallest integer price that would make a firm willing to produce a positive amount? b. d. $44 $41 $29 $13 $21
- Consider the production function of the firm below. What is the total output at point C? a. 150 b. 100 c. 25 d. 75Imagine your firm has the short run production function: q = -2L4 + .5L² + 3L. What is the marginal product function? 08L³+ L 2L³ + .5L -2L³ + .5L +3 -8L³+ L +31. Suppose the total-cost function for a firm is given by C = qw 1/4 3/4 a. Use Shephard's lemma to compute the (constant output) demand functions for each input, k and 1. b. Calculate the average cost and marginal cost. c. Describe the returns to scale for the underlying production function for q.
- 1) Assume that a pIdfit maximizing fimproduces output according to the following production function: q = K0.5L0.5. Suppose price = $20, v = $8 and w= $4. Show your %3D %3D work for parts a-c and check the second order conditions for each maximization a) Suppose K=16. Find the short run total cost function (SC), the short run marginal cost function (SMC). How much is the fimgoing to produce? b) Maximize profit to get the firm's supply. Will the firm shut down? (Note: Maximize Il= pq - SC(q). c) Compute this firm's profit maximizing demand function for L. (Note: Maximize = pK0.5L0.5 – vK – wL). II=K Suppose that a firm's production function is q=5x in the short run, where there are fixed costs of $1,000, and x is the variable input whose cost is $625 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q). The total cost of producing ya level of output q is A. C(q)= 1,000. OB. OC. OD. OE C(q)= 1,000+ C(q)= 1,000+ C(q) = 1,000+ 625q² C(q)= 25 q² 25 625q² 25 0.5 q B Dollars per unit of output 2000- 1800- 1600- 1400- 1200- 1000- 800- 600 400- 200- a 12 14 10 Quantity nchack 18 (1) Incorrect1. Figure 1 shows the production function of a firm. Y В Y2 Y1 X X1 X2 a) What are the variables along (i) of the X axis? (ii) Y axis? b) Does the firm operate in the short term or long term? c) Referring to the diagram above, what is the level of input where (i) firms experiencing increased marginal output? (i) does the firm experience a declining marginal output? (i) the firm achieves maximum marginal output? (iv) the firm achieves a blank marginal output?