5. Find the supply function and the input demand functions for the CES production function: f(#1, F2) = A(ax{ +(1 – a)a%)8/e, where A > 0, B > 0, 0 < a < 1, and 0 + p< 1. Lind tho funoticon for t he CEs ndu funotion
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- 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 =…what is the marginal rate of substitution when the price of coffee is $1.00 per ounce? the prof said the answer is -2.
- Explain the properties of production function? Given a production function of this nature AX1a X2b=Y, determine the Marginal Rate of Technical Substitution.3. Production of taxi rides (15%) GlobalTaxi runs taxi services around the globe. GlobalTaxi uses two inputs in production: capital K and labor L. Capital has a rental cost of r, while labor is paid a wage w. (a) Derive the expression for GlobalTaxi's isocost function with labor on the right-hand side, and explain what it means. (b) Explain what happens to the slope of the isocost function when the wage w increases. How will an increase in w typically affect the choice of inputs for a company that has a smoothly declining marginal rate of technical substitution? Why?4 Find the marginal rate of technical substitution of the following production function: q = L + L^aK^b + K
- Write out an example Cobb-Douglas production function. Derive the signsfor the relationship between labor and output and for marginal product oflabor and labor, holding other inputs fixed. Explain with economic intuition.Joe owns a small coffee shop. His production function is q = 2K0.5 L where q is the number of cups of coffee produces, K is the number of coffee machines, and L is the number of employees. a) If K=1 and L=2, the marginal rate of technical substitution is _________. b) If, starting from 1 machine and 2 employees, Joe hires one more employee, then he can produce the same quantity of cups of coffee with _________ less machines.Suppose a firm is planning to replace a labor intensive production process with an automated robot production line. Calculate the marginal rate of technical substitution (MRTS) using the following information. Labor Intensive Production: 27 workers / 2 machines Automated Robot Production: 70 workers / 14 machines Assume both production process can produce the same level of output.
- There are two factors of production, X and Y. They are being used to produce a fixed amount of output called A. If the amount of output, A is held constant, and the isoquants are convex, would the price of X going down always mean less of Y is used? Explain why or why not by explaining through the use of a graph.Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. Draw isoquants for q = 1, q = 2 and q = 3 on a diagram with labour on horizontal axisand wool on vertical axis.Gıven two inputs X1 and X2 with Prices W1 and W2, and a production function Y=F(X1X2) show that the marginal rate of substitution between the two inputs is equal to the ratio of their prices.