Given the production function y= f(x1,x2)=x11/3x21/3. The amount of x2 is equal to 216 in the short run. Calculate the factor demand function Given the product price (P) is 6 and the price of factor 1 (w1) is 12, calculate the optimum amount of factor 1. Show your results on a graph.
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Given the production function y= f(x1,x2)=x11/3x21/3. The amount of x2 is equal to 216 in the short run.
- Calculate the factor demand function
- Given the product price (P) is 6 and the price of factor 1 (w1) is 12, calculate the optimum amount of factor 1. Show your results on a graph.
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- What is the elasticity of substitution for the production function f(K, L) = K¹/4 [³/4? (a) o = 1 (b) o = -1 (c) o = 1 (d) σ = 3 2Juan 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?Find the elasticity of scale and the elasticity of substitution for the CES production function (x1; x2) = (x1rho + x2tho 1/P, where 0 * p > !!!
- If a firm has the production function f(k, I) = (2k1/4 + 14)" what is the firm's elasticity of substitution? O a. G = O b. o = O c. o = 1 O d. a = 2 O e. o = 4 114 -/2*Find the elasticity of scale and the elasticity of substitution for the CES production function f(x1,x2) = (x{ + x%)¯,where 0 #p<1.Question 2: For this problem you will analyze the elasticity of substitution and the isoquant graphs for two different production functions F₁(K, L) = 4K + 2L F₂(K, L) = K²/³ [1/3 (a) Graph the isoquant for F₁(K, L) = 4K+2L that represents an output of 8. Be sure to show your work and label the axes clearly (b) What is the marginal rate of technical substitution (MRTS) for F₁ ? (c) What is the elasticity of substitution for F₁ ? /
- Suppose the production function is Cobb-Douglas and f(x1;x2)=x11/2x23/2 Write an expression for the marginal product of x1. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain What is the the technical rate of substitution between x2 and x1? What is the type of returns to scale of this production function? (Increasing, decreasing, constant)Given the production function y= f(x1,x2)=x11/3x21/3. The amount of x2 is equal to 216 in the short run. Calculate the factor demand function Given the product price (P) is 6 and the price of factor 1 (w1) is 12, calculate the optimum amount of factor 1. Show your results on a graph.1. Juan Valdez owns a coffee farm in Colombia. His production function is: f (x1, x2) = (x1 – 1)0.25 x9-5. 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? 2. Show that the profit function is convex in (p, w). 3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x" with A > 0, a1, ¤2 > 0 and a1 + a2 0, B > 0, 0 < a < 1, and 0 + p< 1. 6. Find the profit function for the CES production function. 7. Verify Hotelling's Lemma for the CES production function with B < 1.
- Calculate the elasticity of substitution for the production functionSuppose the production function is Cobb-Douglas and f(x1,x2)) = x11/2x3/221. Write an expression for the marginal product of x1.2. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain3. Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain4. What is the the technical rate of substitution between x2 and x1?5. What is the type of returns to scale of this production function? (Increasing, decreasing,constant)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?
