Q7. The production function is y=L¹/aK¹/B The price of the output is $100, w = $15, and r= $12. a. Find the optimal input of labor and capital.
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- Q7. The production function is y=L¹/aK¹/B. The price of the output is $100, w = $15, and r= $12. a. Find the optimal input of labor and capital. b. Find the optimal output which maximizes the profit.1. A firm’s production function is Q = L1/2 K1/2 They have 16 units of capital (which is fixed in the short-run). The unit cost of labour is 2 and the unit cost of capital is 4. They receive an order of 4. a) Calculate the optimal choice of inputs used to fulfil the order in the short-run.With a production function like Y=zN, which of the following must be true at the optimum? A).The marginal product of labor is smaller than real wage. B).The marginal product of labor is bigger than real wage. C).The representative firm makes positive profits. D). Profits of the representative firm are zero.
- B. Suppose that your production process is characterized by the production function x = f(e) = 100 In ( + 1). For purposes of this problem, assume w > 1 and p > 0.01. a. Set up your profit-maximization problem. b. Derive the labor demand function. C. The labor demand curve is the inverse of the labor demand function with p held fixed. Can you demonstrate what happens to this labor demand curve when p changes? d. Derive the output supply function. e. The supply curve is the inverse of the supply function with w held fixed. What happens to this supply curve as w changes? (Hint: Recall that In x = y implies e' = x, where e ≈ 2.7183 is the base of the natural log.) f. Suppose p = 2 and w profit will you make? = 10. What is your profit-maximizing production plan, and how muchA firm produces output according to a production function: Q = F(K,L) = min {4K,4L). a. How much output is produced when K= 2 and L = 1? unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $40 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $40 per hour but the rental rate on capital remains at $40 per hour? O Capital decreases and labor increases. O It does not change. O Capital increases and labor decreases. O Capital and labor increase.A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3?unit(s)b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $10 per hour?multiple choice Capital and labor increase. Capital decreases and labor increases. Capital increases and labor decreases. It does not change.
- A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3? unit(s)b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $10 per hour? (Choose one that is the best answer) Capital decreases and labor increases. It does not change. Capital increases and labor decreases. Capital and labor increase.The production function of a firm is f(x, y) = x + y. The marginal product of input xdiminishes with an increase of x.• True• False Please explain!A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3?unit(s)b. If the wage rate is $45 per hour and the rental rate on capital is $25 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $25 per hour but the rental rate on capital remains at $25 per hour? Capital decreases and labor increases. Capital and labor increase. It does not change. Capital increases and labor decreases. Only typed answer
- Suppose that a production function of a firm is given by q = f(1) = 2√ī. It depends only on labor, whose price per unit is w. The firm is a price taker and the price for the good it produces is p. What is the quantity produced by the firm if the firm maximizes profits and what is the value of profit at that quantity?Calvin’s Furniture store also has a Production function of TP = 90K2 − K3 1. Optimize the Marginal Production Function. Also, check if the quantity maximizes or minimizes. 2. Check if the Total Production Function has an inflection point.Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?