3) Suppose a production function is y = x,2 x,1, and w, is the ice of x, and w, is the price of x, and P is the price of output. 1/2 1/3 a) Find the conditional factor demands. b) Find the cost function. c) Show that dx,ldw, = dx,/dw-
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- Question A Suppose the short-run production function is q = 1L0.5. If the marginal cost of producing the 10th unit is $8, what is the wage per unit of labor? Question B A consumer has the utility function U(q1,q2) = q10.5 + q2Assume p2 = 1 and Y = 100. What is the equivalent variation of a price increase for good 1 from 1 to 4?Consider the following marginal cost function MC= 5 + 2qi. (a) Does the production process exhibits increasing returns? decreasing returns? constant returns? (b) If the price is $23. What’s the optimal production level? (c) If the price is $31. What’s the optimal production level?Exercise: A firm produces output according to the following production function: q = A K1/4 L1/4 The price of capital is labeled r and the price of labor is labeled w and there is a set-up cost labeled F. Solve the cost minimization problem and do the following: If A = 6, r = 4, w =25 and the firm wants to produce q = 36, Determine this firm’s demand for capital K*. Group of answer choices a)15 b)45 c)90 d)60
- A firm uses capital and labor to produce output according to the pproduction function q = 4pKL, for which MPL = 2pK=L and MPK = 2 L=K. a. If the wage w=$4 and the rental rate of capital r=$1,what is the least expensive way to produce 16 units of output? b. What is the minimum cost of producing 16 units? c. Show that for any level of output q, the minimum cost of producingq is $q.I am given this question: The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p = (−x/5)+200 where 0 ≤ x ≤ 1000 Suppose that the cost C, in dollars, of producing x units is C =(√x/10)+400. Assuming that all items produced are sold, find the cost C as a function of the price p. Is it safe to assume that this question has an issue since the cost C cannot be integrated into the price equation?Suppose that an economy produces 3,000 units of output, employing 60 units of inputs, and the price of the input is $30 per unit. The per-unit cost of production is A) $0.6 B) $0.30 C) $0.10 D)$ 1.00
- 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.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?Suppose that the price per unit in dollars of a cell phone production is modeled by p=$45−0.0125x, where xx is in thousands of phones produced, and the revenue represented by thousands of dollars is R=x⋅p. Find the production level that will maximize revenue. In addition to finding the production level that maximizes revenue, also find the maximum revenue. Show your steps and work
- The production function y= K0.5 L0.5 shows that the inputs are perfect substitutes. True or false.Suppose the wage rate is $10 and the rental rate on capital is $20. Consider the total cost line associated with a total cost of $200. The intercept of this line on the X-axis (capital axis) is _______ and its slope is_____. A. 20, -2 B. 10, -2 C. 10, -1/2 D. 20, -1/2 Clear my choiceExplain the producer’s equilibrium with the help of least cost factor combination, necessary and sufficient conditions. i- Maximization of output subject to cost constraint ii- Minimization of cost subject to output constraint