Assume a profit-maximizing firm produces its output according to this response function, Y = 35+ 120x...

  

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Assume a profit-maximizing firm produces its output according to this response function, Y = 35+ 120x₁ + 150x2 -1.5x1²-2.5x₂² Assume also that this firm receives $2.00 per unit for what it sells and it pays $64.00 per unit for the input X₁ and $48.00 per unit for input x2. Using this response function and price information: a. (10 points) Derive this firm's optimal input levels. (4 points) Verify these critical values satisfy the second order conditions for a profit maximum. points) Derive this firm's optimal output level. Doints) Verify that your solution satisfies the Total Condition. Dints) Derive this firm's maximum profit. (17 points) Using the production function and input and output price information from Question 5 above, suppose that the firm now faces a budget constraint that limits the amounts of the two variable inputs it can purchase. Specifically, assume the firm has only $3,000 available to purchase its variable inputs. How much of each input will the firm use to maximize its output, given the budget constraint? How much will it produce? What will its profit be at that point? Interpret the Lagrangean multiplier calculated. (8 points) Illustrate graphically, using ridgelines and psuedoscale lines, the solution to the budget-constrained output maximization problem from Question 6, as compared to the optimal solution derived in Question 5. Explain your graph. Assume a profit-maximizing firm produces its output according to this response function, Y = 35+ 120x₁ + 150x2 -1.5x1²-2.5x₂² Assume also that this firm receives $2.00 per unit for what it sells and it pays $64.00 per unit for the input X₁ and $48.00 per unit for input x2. Using this response function and price information: a. (10 points) Derive this firm's optimal input levels. (4 points) Verify these critical values satisfy the second order conditions for a profit maximum. points) Derive this firm's optimal output level. Doints) Verify that your solution satisfies the Total Condition. Dints) Derive this firm's maximum profit. (17 points) Using the production function and input and output price information from Question 5 above, suppose that the firm now faces a budget constraint that limits the amounts of the two variable inputs it can purchase. Specifically, assume the firm has only $3,000 available to purchase its variable inputs. How much of each input will the firm use to maximize its output, given the budget constraint? How much will it produce? What will its profit be at that point? Interpret the Lagrangean multiplier calculated. (8 points) Illustrate graphically, using ridgelines and psuedoscale lines, the solution to the budget-constrained output maximization problem from Question 6, as compared to the optimal solution derived in Question 5. Explain your graph.

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To derive the firms optimal input levels we need to maximize its profit by setting the first derivatives of the profit function equal to zero Lets sta... View the full answer