2. The output (Q) of a production process is a function of two inputs (L and K) and is given by the following relationship: Q=0.50LK -0.10L2 -0.05K² The per unit prices of inputs L and K are Rs 20 and Rs 25 respectively. The firm is interested in maximizing output subject to a cost constraint of Rs 500. Find out the optimal input mix and maximum level of output.
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- I need help pleaseDoes 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?For the manufacturing company in problem 1, let the prices of input 1 and 2 be w₁ = 10 and w₂ = 40, respectively. (A) Find the amount of each input to hire to minimize the cost of producing y = 100 units of output: min C (x1, x2) = 10x1 +40x2 subject to: 10x12x1/2 = 100
- Given the following data on input and output levels. Suppose the output price is $5 and input price is $10. Find the values of APP and MPP when X = 6: X 0 2 4 6 8 10 12 Y 0 100 250 450 600 700 750 50 and 150 6 and 200 100 and 75 75 and 100Please correct answer and don't use hand raitingb 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)
- A 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?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/VE Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy
- Green et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)What is the elasticity of substitution for the production function f(K, L) = K¹/4 [³/4? (a) o = 1 (b) o = -1 (c) o = 1 (d) σ = 3 2Let a firm's production function be f(K, L) = min{2K, L}. a) Solve for the contingent demand functions for K and L.