wage, and rent: Find the cost minimizing amount of K for a producer to use when faced with the following production function, production goal, w= $58; r = $140 q=L3K¹;q=1200;
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- swered Costs per Unit (dollars) 1000 900 800 700 600 500 400 300 200 100 0 4 Average total cost B Marginal cost Output (units per day) Average variable cost Average fixed cost 22 24 How many units of output should be produced per day if the price of the product is $600/unit? (provide an approximate answer in whole numbers)(2 ex Production function is flu, X2)=min (x,, 2-x) Dwhat are the conditional factor demand of y = 10 OVA the firm faces w, and w₂ as input prices, what is the cost function?suppose that input prices are (w, r) >> 0, where w is the wage rate (price of a unit of labor) and r is the interest rate (price of a unit of capital). Suppose the firm must produce y > 0 units of output. (a) Formulate the firm's cost minimization problem. (b) Illustrate the solution to the cost minimization problem in an ap- propriate diagram. (c) Solve the cost minimization problem to find the firm's conditional input demand functions for labor and capital, and its cost function. (d) Assume that w = r = 4. In appropriate diagrams, illustrate the firm's (i) conditional input demand for labor, (ii) its conditional input demand for capital, (iii) its total, average and marginal costs.
- Suppose that the cost function for a commodity is C(x) = 40 + x2 dollars. (a) Find the marginal cost at x = 4 units. MC(4) = Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 5th unit is predicted to be $ (b) Calculate C(5) – C(4) to find the actual cost of producing 1 additional unit. Need Help? Read It Watch ItConsider 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)A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"
- (a) Find the marginal cost function C'(x). C'(x) Use it to estimate how fast the cost is increasing when x = 60,000. | per game system Compare this with the exact cost of producing the 60,001st game system. The cost is increasing at the rate of $ | game system is $| the estimated cost of producing the 60,001st game system found using the marginal cost function. | per game system. The exact cost of producing the 60,001st J. The actual cost of producing the 60,001st game system is --Select-- (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (Round your answer to the nearest cent.) C(x) C(60,000) - $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the unit is $760 per month, all the unit will be filled, but 1 unit will become vacant for each $20 increase in this monthly rate. If the monthly cost of maintaiing the apartment building is $12 per rented unit, what rent should be charged per month to maximize the profit? $ =Justify the statement. T/F Variable cost change with the change in the level of output in a production process.
- If you were a taxi driver, the daily revenue and cost are as the following: Revenue: $250 Variable cost (gas, your labor…): $190 Mortgage payment for car: $70 License Fee: $30 For profit maximization, will you operate your taxi business today? What is the minimum daily revenue to keep the operation in the short run? What is the minimum daily revenue to keep the operation in the long run? Please show calculation formula and/or equation.b) A firm has an average cost functionA(q) =125 +q^2 - 4 q 16where q is the firm′s output. (iv) Write an equation for the total cost function.(v) Hence calculate the level of output for which total costs are minimum.Suppose a firm uses capital K and labor L to produce output Q with the following production function: 1 Q=4KL + = 1² 3 (a) Find the marginal product of capital and the marginal product of labor. (b) Find the average production of capital and the average production of labor. (c) Does this production function have increasing, constant, or decreasing returns to scale? Explain. (d) Find the marginal rate of technical substitution (RTS). (e) Use your result in (d) to find the elasticity of substitution. (f) Find the contingent demand functions for capital and labor if w is the price of labor input and v is the price of capital input.