Consider the following production function for a firm: y=(x1-1)(x2-1), if x1≥1 and x2≥1; and y=0, if either x1<1 or x2<1: Assuming perfect competition in both inputs and output markets, find the firm’s unconditional factor demand for both x1 and x2
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- Consider the following production function for a firm: y=(x1-1)(x2-1), if x1≥1 and x2≥1; and y=0, if either x1<1 or x2<1:
- Assuming
perfect competition in both inputs and output markets, find the firm’s unconditional factordemand for both x1 and x2.
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- A competitive firm’s production function is given by y= f(x1,x2)=x1ax2b If a=b=0.5 , the price of factor 1 is 12, and the price of factor 2 is 3, find the cost minimizing input combinations and the total cost of producing 40 units of output. Redo part (1), this time by first deriving the firm’s conditional factor demand functions and the cost function.Suppose a competitive firm can sell its output for $7 per unit. The following table gives the firm’s short run production function. Labor Output 0 0 1 15 2 40 3 70 4 86 5 94 6 98 In the table below, you will determine several points on the firm’s demand curve for labor. To do this, you must determine how many workers the firm should hire for different values of the wage rate in order to maximize profit. Complete the table below: Wage Rate Per Worker Quantity Demanded of Workers $30 $50 $70 $100 Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Suppose a competitive firm can sell its output for $7 per unit. The following table gives the firm’s short run production function. Labor Output 0 0 1 15 2 40 3 70 4 86 5 94 6 98 In the table below, you will determine several points on the firm’s demand curve for labor. To do this, you must determine how many workers the firm should hire for different values of the wage rate in order to maximize profit. Complete the table below: Wage Rate Per Worker Quantity Demanded of Workers $30 $50 $70 $100 Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure. do not upload images
- Consider a production function: Q = f (L), where Q represents the output and L is thefactor of production. Let w be the per unit price of factor L and p be the per unit price ofoutput Q. Using the Envelope theorem determine the supply function and the factor demand function.Consider a firm which produces q units of output using L units of labour and whose market demand for labour is given by L* = 57- w/(14p), if w/(14p)<57 and L*=0, otherwise where p denotes the price of output and w denotes the price of labour. What is the change in the profit of the firm if the price of labour changes from w= 1 to w = 4 assuming the price of output is p=57？A competitive firm’s production function is given by y= f(x1,x2)= 4x11/2 + 10x21/2 a) The price of factor 1 is 1, the price of factor 2 is 1, and the price of output is 2. Find the profit-maximizing quantities of x1 and x2? What is the profit-maximizing quantity of output? b) Redo part (a), this time by first deriving the firm’s factor demand functions and the supply function, and then substituting the prices in these functions.
- A firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. The production function is given by: Q=60L-2L^2+180K-3K^2, where Q is total output. Determine the firm's optimal combination of capital (K) and labor (L)?Consider Delta, a price-taking single-output, single input firm with the following production function:f (z) = z4/5a) Define non decreasing returns to scale and non-increasing returns to scale in terms of the production function and give conditions under which f(z) satisfies these properties. b) Suppose that the price of the input z is ѿ =1. Set up the cost minimization problem and solve for the conditional factor demand correspondence and the cost function. c) Set up Delta's profit maximization problem using the cost function you derived in (b) above and solve for the supply correspondence and the profit function.In each of the following four cases, MRPL and MRPC refer to the marginal revenue products of labor and capital, respectively, and PL and PC refer to their prices. Indicate in each case whether the conditions are consistent with maximum profits for the firm. If not, state which resource(s) should be used in larger amounts and which resource(s) should be used in smaller amounts. a. MRPL = $8; PL = $4; MRPC = $8; PC = $4. b. MRPL = $10; PL = $12; MRPC = $14; PC = $9. c. MRPL = $6; PL = $6; MRPC = $12; PC = $12. d. MRPL = $22; PL = $26; MRPC = $16; PC = $19.
- Consider a price-taking firm whose production function is given by q = 3 (L-9)1/5 (K-5)1/9 where L and K denote respectively the amount of labour and capital the firm uses to produce q units of output. Suppose the price of labour is w = 16, the price of capital is 24 and the price of the firm's output is p=225 . Enter below the value of the firm's fixed cost.Consider a competitive firm in both input and output markets. The production function for this firm is given by q = 10 (KL)^.2. The price of K is $1 and the price of the output is $5. Derive the demand for labor when K is variable.7. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What are the demand functions for labor 1(v,w.p) and capital k(v,w,p)? [Show your work] 8. The production function for a price-taking firm is given by q = 2.5k0.4L0.4. What is the supply function q(v,w,p)? [Show your work]
