What is the cheapest way of producing 850 units of output if a firm operates with the production function 0.5 0.5 Q = 30K L and can buy input K at 75 $ per unit and L at 40 $ per unit?
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What is the cheapest way of producing 850 units of output if a firm operates with the
production function 0.5 0.5 Q = 30K L and can buy input K at 75 $ per unit and L at 40 $
per unit?
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- 1 A smartphone repair firm in Boston has a production function for producing phone repairs, q, defined as, — 4 -L1/2K 1/2, where L is labor measured in hours worked, and K is the number of useful tools used in the repair process. The market wage for a phone repairperson, w, is $25 per hour. The tools could be sold at a secondhand market for $4 (r). Find the (variable) cost function:. Submit your answers as a single PDF. Please try and keep solutions tidy.If the demand function for math self-help videos is given by 45 -0.4x, and the total cost function to manufacture the videos is given by 4x + 17, evaluate the marginal profit function at x = 10. Marginal Profit = This means that if production and sales increase by one unit, then total profit will O increase decrease by approximately dollars.Given the production function y 1/x05, if Price of output is P and price of input X is V and fixed cost is FC, what is the expression for marginal cost (MC) as a function of Y? O MC = Vy0.5 O MC = -2Vy-3 O MC = Vy-0.5 O MC = y/V
- Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (b) Find a function for the average cost of this company?There is a firm making custom stuffed animals. The demand function for custom stuffed animals is: P = 1000 - 20Q The cost depends on how much of each of their inputs they use. It takes 3 inputs to make a stuffed animal: cotton, oil, and chorizo. The amount required, input prices, and restrictions are below: It takes 1 pound of cotton to make a stuffed animal. Cotton costs $20 per pound. They can buy up to 23 pounds of cotton. It takes 2 barrels of oil to make a stuffed animal. Oil costs $10 per barrel. They can buy up to 44 barrels of oil. It takes 3 chorizo burritos to make a stuffed animal. Burritos cost $5 per burrito. They can buy up to 100 burritos. Set this up in Solver to help them maximize profit by choosing the best quantity of stuffed animals to produce, subject to the constraints of the maximum amount of cotton/oil/burritos they can buy. In the space below, tell the profit that the firm will earn when they maximize its profit. PLEASE SHOW EXCEL WALKTHROUGH USING SOLVER.…
- Does the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?(a) Find the conditional input demand function for inputs 1 and 2, as well as the cost function for this firm. (b) What is the firm's marginal cost when it is producing y units of output?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)
- The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 37x - 0.07x2. (a) Find the marginal cost function C'(x). C'(x) = (b) How fast is the cost going up at a production level of 100 teddy bears? When they produce 100 teddy bears, the production costs are increasing at a rate of x dollars per teddy bear In other words, the cost to produce the 101st teddy bear is approximately dollars (c) Find the average cost function C, and evaluate C(100). C(x) = C(100) = So when they produce 100 teddy bears, the average cost per teddy bear is x dollars. (d) Fill in the blanks: Since the marginal cost is less than the average cost per unit, increasing production from 100 teddy bears will cause the average cost per unit to decrease.The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula Cx) - 100 + 40x - 0.08. (a) Find the marginal cost function C(x). Cx) = 40 - 0.16x Use it to determine how fast the cost is going up (in s) at a production level of 100 teddy bears $ 24 per teddy bear Compare this with the exact cost of produong the 101" teddy bear (in ). The cost is increasing at a rate of s 24 per teddy bear. The exact cost of producing the 101" teddy bear is s Thus, there is a diference of (b) Find the average cost function C, and evaluate č100) (in s). C100) -s x per teddy bear What does the answer tell you? per teddy bear. The average cost of producing the first hundred teddy bears is s Eter an tuber1. Find the cost minimizing input demand functions (x¿(w,q)) and the cost function (c(w,q)) for the following production functions: 1/3 21382 a. f(x) = x₁