A firm has two variable factors and a production function f(x1, x2) = 6x1/21X21/3. The price of its output is 3, the price of factor 1 is 3, and the price of factor 2 is 2. – What is the optimal production output level? – What is the maximum profit-level?
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A firm has two variable factors and a production
function f(x1, x2) = 6x1/21X21/3. The price of its output is 3, the price of factor 1 is 3, and the price
of factor 2 is 2.
– What is the optimal production output level?
– What is the maximum profit-level?
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- X and X2 are the two factors used in production A firm's production function: fcx₁, x₂) = max {x₁, X₂} the price of X, is W₁=8, and the price of X₂ is W₂=10 The firm paproduce 100 total units of output, what is the total cost?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/VDoes the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?
- Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?2. A firm faces the production function 1 Q = f(K,L) = 80 [0, 4K-0,25 +0,4L-0,25] 0.25. It can buy the inputs K and L at prices per unit of 5 TL and 2 TL respectively. What combination of L and K should be used to maximize output if its input budget is constrained to 150 TL?4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…
- 4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…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 $10 per yarn. (5 Points)Question 2: For this problem you will analyze the elasticity of substitution and the isoquant graphs for two different production functions F₁(K, L) = 4K + 2L F₂(K, L) = K²/³ [1/3 (a) Graph the isoquant for F₁(K, L) = 4K+2L that represents an output of 8. Be sure to show your work and label the axes clearly (b) What is the marginal rate of technical substitution (MRTS) for F₁ ? (c) What is the elasticity of substitution for F₁ ? /
- Q.No.3. Consider the production function: (3) Y = 0.75X + 0.0042X2 – 0.000023X3 (a) At what level of X, the output will be maximum? (b) If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?A firm produces basketballs with two variable inputs - labour (L) and plastic (K) - and has the following production function: f (L , K) = 6L1/3K1/6 If the price of output is 4, the price of labour is $2 and the price of plastic is $3, calculate the a) profit-maximizing level of each input b) the total production and c) the profit.Given a firm which uses 2 inputs, X1 and X2; to produce a good that is described by the production function: Q = f (X1 X2) = X11/2 X21/4 The firm sells its ouput at N$80 per units. Given cost of input 1, X1; is N$4; and the cost of input 2, X2; is N$2 Solve for the profit maximizing input mix, output, and profit.