(a) The production function of Shell & John Co. is given as: Z= 4X² + 4XY + 6Y2; where, Z = output; and X & Y = inputs of production. a. Derive the MRTSXY of Shell & John Co. when X = 10 and Y = 20. (b)From part (a), is Shell & John Co. in equilibrium if both the input prices of X and Y are USD1.00 respectively? Why? (c)Based on your answer in part (b), derive the optimum values of X*, Y* and Z* if both inputs X and Y costs USD 1.00 respectively and cost constraints of USD 60.00 are assumed.
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- 4. Find the cost function and the conditional demands for inputs associated to the CES production function f(r1, #2) = A(ar{ + (1 – a)a)/e, where A, 8 > 0, 0 < a < 1, and 0#p< 1.Given the following data on input and output levels. Suppose the output price is $2 and input price is $3. Find the values of AVP and MVP when X = 2: %3D X. Y 1 10 2. 25 3 45 4 60 70 75 $30 and $50 $30 and $30 $4 and $50 $25 and $30A software firm has only two inputs to production: domestic programmers based in the firm’s U.K. office and international programmers working from home in low-cost countries.The two types of programmers are perfect substitutes but domestic programmers are more productive due to better communication in the office. The production function is:S = 2D + IWhere S is the amount of software written, D is the number of domestic programmers and I is the number of international programmers. Programmers can work part-time, so hiring 0.3 of a programmer would be possible. (c) The government is concerned about diversity and writes a law saying that at least two workers in any firm must be domestic, and that at least two workers must be international. Show the effect of this law on the firm’s isoquant, the number of each type of worker hired, and total costs.
- A software firm has only two inputs to production: domestic programmers based in the firm’s U.K. office and international programmers working from home in low-cost countries.The two types of programmers are perfect substitutes but domestic programmers are more productive due to better communication in the office. The production function is:S = 2D + IWhere S is the amount of software written, D is the number of domestic programmers and I is the number of international programmers. Programmers can work part-time, so hiring 0.3 of a programmer would be possible.(a) The firm must produce 10 pieces of software this year. Show the firm’s isoquant in a suitably labelled graph. Put “domestic programmers” on the vertical axis and “international programmers” on the horizontal axis. Label each axis from 0 to 10.Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output if it the firm decides to triple both the amount of labor and capital?b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L and K can vary with production. Compute the input demand functions as a function of Q. (4 Points) c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. At what prices of textile will the producer shut down production. (3 Points) d Now suppose Q = 10LK. The market prices of inputs are as in subpart (b) above. Compute the input demand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn. (5 Points)
- Y-2x11 y2-3X12 Q 4. ( A) Consider the following production functions: y2 are products and x is the use of input i in the production of productj. The total use of x is a function of y, and y2 given by: x1 =;+ where yi and %3D a) Find the product transformation rate. b) What will be the shape of production possibility curve? c) Are the productive competitive ORA 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?1. Let y = f(x1, x2)=x11/2+ X1X2 be a firm's production function, where x20, x220. - a. Write down the firm's production possibility set, and its input requirement set.“ b. Is this production function concave, quasi-concave? c. Is this production function homogenous, homothetic? + d. Find its returns to scale when x1=1, and x2=1.e
- A software firm has only two inputs to production: domestic programmers based in the firm's U.K. office and international programmers working from home in low-cost countries. The two types of programmers are perfect substitutes but domestic programmers are more productive due to better communication in the office. The production function is: S=2D + I Where S is the amount of software written, D is the number of domestic programmers and I is the number of international programmers. Programmers can work part-time, so hiring 0.3 of a programmer would be possible. (a) The firm must produce 10 pieces of software this year. Show the firm's isoquant in a suitably labelled graph. Put "domestic programmers" on the vertical axis and "international programmers" on the horizontal axis. Label each axis from 0 to 10. (b) A domestic programmer can be hired for £100,000 per year. An international programmer can be hired for £60,000 per year. On the same graph, show the different combinations of…A software firm has only two inputs to production: domestic programmers based in the firm’s U.K. office and international programmers working from home in low-cost countries. The two types of programmers are perfect substitutes but domestic programmers are more productive due to better communication in the office. The production function is: S = 2D + I Where S is the amount of software written, D is the number of domestic programmers and I is the number of international programmers. Programmers can work part-time, so hiring 0.3 of a programmer would be possible. (a) The firm must produce 10 pieces of software this year. Show the firm’s isoquant in a suitably labelled graph. Put “domestic programmers” on the vertical axis and “international programmers” on the horizontal axis. Label each axis from 0 to 10. (b) A domestic programmer can be hired for £100,000 per year. An international programmer can be hired for £60,000 per year. On the same graph, show the different combinations of…A software firm has only two inputs to production: domestic programmers based in the firm’s U.K. office and international programmers working from home in low-cost countries. The two types of programmers are perfect substitutes but domestic programmers are more productive due to better communication in the office. The production function is: S = 2D + I Where S is the amount of software written, D is the number of domestic programmers and I is the number of international programmers. Programmers can work part-time, so hiring 0.3 of a programmer would be possible. (a) The firm must produce 10 pieces of software this year. Show the firm’s isoquant in a suitably labelled graph. Put “domestic programmers” on the vertical axis and “international programmers” on the horizontal axis. Label each axis from 0 to 10. (b) A domestic programmer can be hired for £100,000 per year. An international programmer can be hired for £60,000 per year. On the same graph, show the different combinations of…