![Problem 5. This problem asks you to find the supply function of a firm that only uses one input (z) to produce one output (q). In addition, it highlights how the choices we make to represent an economic situation can influence the conclusions we arrive at. Suppose there is a firm operating in a competitive environment. The firm has a technology given by f(z)Az, where z 20 is the amount of labor the firm hires at a wage of w > 0 Note that a feasible production plan for this firm is a vector (z,q) such that 0S q S f(z) Az. The firm sells a unit of output at price of p > 0. Since the firm operates in a competitive environment, both price and wage are fixed. (a) Write down the firms profit maximization problem in terms of choosing the optimal [4 points] amount of labor z (b) Suppose 0 < α < 1. Find the optimal labor demand for the firm and the optimal quantity supplied by it. If you are doing things right, these two objects will be functions [4 points] Hint solve the firms profit maximization problem to obtain the labor demand, and then use the production function to obtain the optimal quantity supplied by the firm. Because 0 < a <1, the profit function is concave and thus FOC are sufficient and necessary for an interior solution. of w and p (c) Suppose a 1. Can you find the optimal labor demand for the firm using FOC? If not, [1 points] why not? Can you find the firms optimal quantity supplied? (d) Suppose finally that a-1. Can you replicate your findings for part (b)? Whats going [1 points] on here?](http://img.homeworklib.com/questions/a292d670-96c8-11eb-a99e-d3ad9da645b6.png?x-oss-process=image/resize,w_560)
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Problem 5. This problem asks you to find the supply function of a firm that only...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this form with both the two step and 1 step methods and provine that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K'(..) and labor L'(w. ), and the long run minimized cost C"(w.ne). (Hint: reduce...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,r,q) and labor L*(w,r,q), and the long run minimized cost C* (w,r,q). (Hint: reduce the cost function for the next part. (b) Setup and solve the profit maximization problem over quantity using the cost function you solved for in the previous part. Solve for the profit maximizing quantity q *(p,w,r), cost...
A firm operates in a perfectly competitive market with a price of P = 50 for...
A firm operates in a perfectly competitive market with a price of P = 50 for the product. TVC = 0.5Q3 − 18Q2 + 170Q Q (output) TFC = 300. Write an equation expressing the firm’s total revenue (TR) as function of Q. Write an equation expressing the firm’s total cost (TC), as a function of Q. Write an equation expressing the firm’s profit (π), as a function of Q.Find the first-order condition for the firm’s profit-maximization decision. Find the...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
6. Suppose you have a job analyzing a perfectly competitive market. The aggregate demand is o p) = 98 - P and the...
6. Suppose you have a job analyzing a perfectly competitive market. The aggregate demand is o p) = 98 - P and the cost function for the firms is C(q) = 79 +35. Suppose all firms use the same cost function. (a) Setup and solve the profit maximization problem over quantity. Write the quantity an individual firm will produce as a function of the sale price. (3 points) (b) Solve for the price, quantity, and profits for each individual shop...
2. Consider a market with one firm. The firm's cost function is c(g)-2, and the market...
2. Consider a market with one firm. The firm's cost function is c(g)-2, and the market demand is Q 1000-P (a) Suppose the monopolist does not exereise any market power and behaves like a competitive firm. Find the equilibrium price, the quantity produced and the firm's profit. (b) Suppose the monopolist exercises market power but does not price dis- criminate (that is, the firm uses MR MC pricing strategy). Find the price the firm charges, the quantity produced, and the...
Competitive Firms - Optimal Labor and Capital 1. A competitive firm has production technology q A...
Competitive Firms - Optimal Labor and Capital
1. A competitive firm has production technology q A K La. lt can sell output at price P and hire capital and labor at competitive factor prices r and w. Write down the firm's profit maximization problem. What are the firm's first- order necessary conditions for a maximum. a. w Suppose now that α-,P-1 and -1. b. What is the firm's optimum capital labor-intensity? Why can't the optimum scale of production q be...
1. Consider a firm in the short run, when capital is fixed and the only variable...
1. Consider a firm in the short run, when capital is fixed and the only variable input is labor. For simplicity, we will simply ignore capital. In this situation, suppose that the firm’s production function is given by Q = f(L) = αL – (1/2)L2 , where Q represents the quantity of output produced, L represents the amount of labor employed, and the parameter α is a positive constant. a. Derive this firm’s marginal product of labor function? Under what...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
5. Consider a market with a monopolist that can price discriminate between two groups. The inverse...
5. Consider a market with a monopolist that can price discriminate between two groups. The inverse demand equation for group 1 is R(Q.) = 156 - 50 where P is the price group 1 is charged and Q1 is the total quantity demanded by group 1. The inverse demand equation for group 2 is B(O2) = 48-22 where B, is the price group 2 is charged and Q2 is the total quantity demanded by group 2. The total amount the...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this form with both the two step and 1 step methods and provine that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K'(..) and labor L'(w. ), and the long run minimized cost C"(w.ne). (Hint: reduce...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
6. Suppose you have a job analyzing a perfectly competitive market. The aggregate demand is o p) = 98 - P and the cost function for the firms is C(q) = 79 +35. Suppose all firms use the same cost function. (a) Setup and solve the profit maximization problem over quantity. Write the quantity an individual firm will produce as a function of the sale price. (3 points) (b) Solve for the price, quantity, and profits for each individual shop...
2. Consider a market with one firm. The firm's cost function is c(g)-2, and the market demand is Q 1000-P (a) Suppose the monopolist does not exereise any market power and behaves like a competitive firm. Find the equilibrium price, the quantity produced and the firm's profit. (b) Suppose the monopolist exercises market power but does not price dis- criminate (that is, the firm uses MR MC pricing strategy). Find the price the firm charges, the quantity produced, and the...
Competitive Firms - Optimal Labor and Capital
1. A competitive firm has production technology q A K La. lt can sell output at price P and hire capital and labor at competitive factor prices r and w. Write down the firm's profit maximization problem. What are the firm's first- order necessary conditions for a maximum. a. w Suppose now that α-,P-1 and -1. b. What is the firm's optimum capital labor-intensity? Why can't the optimum scale of production q be...
5. Consider a market with a monopolist that can price discriminate between two groups. The inverse demand equation for group 1 is R(Q.) = 156 - 50 where P is the price group 1 is charged and Q1 is the total quantity demanded by group 1. The inverse demand equation for group 2 is B(O2) = 48-22 where B, is the price group 2 is charged and Q2 is the total quantity demanded by group 2. The total amount the...
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