A firm has a production function f(x) = f(x1,2) = (2122). 1. Does f exhibit increasing...

 

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A firm has a production function f(x) = f(x1,2) = (2122). 1. Does f exhibit increasing or decreasing returns to scale? 2. Denote the price of input-I as p and the price of input-2 as p2. Further, let Q denote a target quantity level for the firm. Suppose, p.p2. QE R. Solve the firm's cost minimization problem to compute the conditional input demand functions: ((P-P2.2).1(P1-P2.2)). 3. Using your solution to the previous part, find the firm's cost function TC(ps, pa. Q). Verify that Shep- hard's Lemma holds for this example. 4. Compute the average cost (AC) and the marginal cost (MC) functions for this firm. 5. Sketch the TC, AC and MC curves on the same graph. Question 2 Consider a firm with no setup costs. Suppose that the AC and MC functions for the firm are differentiable. Use L'Hpital's Rule to show that the slope of MC is twice the slope of AC at the origin, i.e. prove the following: MC(4) =2. AC (4) 10-0 Hint: Evaluate the slope of AC using the quotient rule. Due by Feb 29, 5 PM, via Gradescope A firm has a production function f(x) = f(x1,2) = (2122). 1. Does f exhibit increasing or decreasing returns to scale? 2. Denote the price of input-I as p and the price of input-2 as p2. Further, let Q denote a target quantity level for the firm. Suppose, p.p2. QE R. Solve the firm's cost minimization problem to compute the conditional input demand functions: ((P-P2.2).1(P1-P2.2)). 3. Using your solution to the previous part, find the firm's cost function TC(ps, pa. Q). Verify that Shep- hard's Lemma holds for this example. 4. Compute the average cost (AC) and the marginal cost (MC) functions for this firm. 5. Sketch the TC, AC and MC curves on the same graph. Question 2 Consider a firm with no setup costs. Suppose that the AC and MC functions for the firm are differentiable. Use L'Hpital's Rule to show that the slope of MC is twice the slope of AC at the origin, i.e. prove the following: MC(4) =2. AC (4) 10-0 Hint: Evaluate the slope of AC using the quotient rule. Due by Feb 29, 5 PM, via Gradescope