1. Widget factory Inc. in Wisconsin has the following production function: F(L,K) = 2L1/2 K1/2 L represent the number of labour hours. Workers at this factory are paid an hourly wage of $30 and they rent capital at $25/hour. Since this is a competitive market, the factory output the factory gets per is output is $50 per unit. Let's pretend the firm operates in the short run with capital fixed at 900, how many factory workers would Widget Factory Inc employ? What is their profit rate?
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- 1) Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q = 4K L where q is the number of reams produced, Kis the quantity of capital rented, and L is the quantity of labor hired. For this production, MP, = and MP, = The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost What ratio of capital to labor minimizes Miguel and Jake's total costs? (Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital and labor.) b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week? How much will hiring these inputs cost them?1. A shortGHH run production function of a competitive firm is given by Y=6L^(2/3)where Y represents the units of output while L is the labour required. If P = 3 and W =6. (ii). What is the firms profit at the optimal level?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)? Graph the average and marginal cost curves for gumballs assuming v=3, w-5 Now graph these curves for v=6, w=5. Explain why these curves have shifted.
- 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. The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3K1/3, where P is the number of anvils produced when L is the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. c. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. Only need paVAS e and fl7. A firm's production function takes the form: Q (L, K) = min {4L, K}, where Q represents output and L and K represent labour and capital, respectively and where w and r give the prices of labour and capital. What would be the expression for the firm's marginal costs? W 4 (b) MC = r + 4w (a) MC = r + (c) MC = (d) MC = W W+4r WK 4 + 4r W+4r +rk (e) MC = Q Q ( x + r) 4
- A firm has a fixed production cost of $4000. For the first 100 units of production, the firm has a marginal cost of $50 per unit produced. Producing more than 100 units has a marginal cost of $70 per unit produced. The firm cannot produce more than 150 units. How much does it cost to produce at q=0? at q=50? at q=100? at q=125? at q=150? Graph the firm’s marginal cost functionSuppose that in a perfectly competitive market, one individual firm uses twoinputs: Labor (L) and Capital (K) and it has the production function, y = √LK. The pricesof the inputs are WL = $1 and WK = $4. Assume that the number of firms in the industry can vary and all firms are identical. a. Show that the production technology exhibits constant returns to scale.b. Find the cost function of an individual firm, C(y).c. Derive and graph the average cost and marginal cost curve of an individualfirm.d. Derive and graph the long-run industry supply curve.e. If the market demand is given by D(p) = 10 − p. How many units of outputare traded in the long-run equilibrium?f. ) The government imposes a per-unit tax of $1. Find the tax incidence of thebuyer and the seller.Complete the following table: Assuming the price of capital (k) is $4 and the price of labor (L) is $6, and the price of commodity (Q) is $2. A) What production technique should this firm use? Technique Q K TR TC Profit(n) A. 40 9. 40 8. 6. 40 4 D 40 11 E 40 1. 9. F 40 11
- The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1Saved The following table shows the production function for a bicycle manufacturer: Number of Workers Number of Bicycles Marginal Product Marginal Revenue 1 3 2 7 3 10 $ 4 12 2 13 $ 1 a) Suppose that the weekly wage is $700. What is the marginal labor cost of the second worker per week? $ b) Suppose that the price of a bicycle is $460. What is the marginal revenue for each level of output? Instructions: Fill in the values for the marginal revenue in the table above. c) How many workers does the bicycle manufacturer employ if the price per bicycle is $460 and the weekly wage is $700? workers d) If the price per bicycle drops to $300, what happens to the number of employed workers? The number of employed workers will (Click to select) Next> 5 of 8 < Prev T e e to search ASLS f12 pause break f10 f8 f6 f7 f5 f3 f4 2 & $ 4 ## 3 8 7 5 P U Y T R E A 24. Ikea Inc., a home remodeling business. The number of square feet they can remodel in a day is described by the Cobb-Douglas production function Q= F (L,K)= 4K"L* where I. is their number of workers and K is units of capital. The wage rate is $5 a day, and a unit of capital costs $20 a day. What is their minimum cost input combination for remodeling (Q=200) 200 square feet a day? What is the total minimum cost level?