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- Production function of a company is given by f(x;y)= root of x + root of y where x is labor and y is capital. Cost of labor is 2 currency units, while the cost of capital is 1 currency unit. What are the minimal cost to produce 10 units of the product? What is the change in the costs, if the production volume would increase by 50 %?Consider a Leontief production function Q = Min (K/2, L/3). Price of K is 3 and price of L is 2. If the firm intends to produce 40 units, the cost minimizing K,L combination will be: a. (30,40) b. (20,30) c. (80,120) d. (120,80)E. A firm has the production function f(T1, 12) = 1750 , 50 What is the marginal rate of technical substitution (M RTS)? (a) MRTS =-1 2.5x, (b) MRTS = -x2/x1 (c) MRTS = -5x2/01 (d) MRTS =-0.5x2/21 (e) MRTS = -0.2x2/21 %3D %3D
- 1/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?b) Suppose a company has this Leontief production function Q = min(20K,50L) i) List a few combinations that will produce 500 units of outputAs a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500, the cost for one capital is $250. If the production plan is to produce 250 products, what is the firm's minimized cost? A: $7500 B: $5000 C: $12500 D: $10000
- Suppose that the cost function for a commodity is C(x) = 90 + x? dollars. (a) Find the marginal cost at x = 7 units. MC(7) = [ Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 8th unit is predicted to be $ (b) Calculate C(8) - C(7) to find the actual cost of producing 1 additional unit. $4As a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500, the cost for one capital is $250. If the firm has a budget of $7500 to produce, what is the firm's optimum output 250 200 100 150Compute the MRTS for this production function: Y (K,L) = 2K+5L
- If the production function is given by f(x1, x2) = min{x1, x2} + min{x3, x4}, what is the minimum cost of producing one unit of output?Assume that it costs a company approximately C(x) = 400,000 + 180x + 0.001x² dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.Assume that it costs a company approximately C(x) = 400,000 + 160x + 0.002x2 dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- v than the average cost from (b). This means that the average cost is ---Select--- v at a production level of 10,000 smartphones. Need Help? Watch It