Problems on Math Concepts

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Econ340: Practice Questions on Review of Math concepts 1. Given the following demand function: Q = 50 – 0.5P a) Determine the level of output Q* and price level, P*, that maximizes total revenue. b) Show that Q* determined in (a) above maximizes, rather than minimizes revenues 2. The Bowden Corporation's average variable cost (AVC) function is given by the following equation (where Q is the number of units produced and sold): AVC = 25,000 – 180Q + 0.5Q2 a) Determine the output level (Q*) that minimizes AVC. b) How could you know that Q* in part (a) minimizes rather than maximizes AVC? 3. The Bound's Inc. has the following total cost (TC) function (where Q is the number of units produced and sold): TC = 50 + 100Q – 6Q2 + 0.5Q3 a) Determine the output level (Q*) that minimizes marginal cost (MC). b) How could you know that the value of Q* in part (a) minimizes rather than maximizes MC? 4. A firm's demand function is given as follows: Q = 180 – 2P and its total cost (TC) function as: TC = 50 + 100Q – 6Q2 + 0.5Q3 a) Determine the level of output Q* that maximizes profits. b) Determine the level of output Q* that minimizes profits. 5. Hameed Electronics Company operates in the highly competitive electronics industry. Prices for its control switches are stable at \$100 each. Engineering estimates indicate that relevant total and marginal cost relations for its switch model are: TC = \$500,000 - \$25Q + \$0.0025Q2 MC = ∂TC/∂Q = -\$25 + \$0.005Q (a) Calculate the output level that will minimize TC. (b) Calculate the output level that will maximize the company's profit. What is this maximum profit? 6. Eastern Aluminum is a manufacturer of aluminum kitchens. Its revenue and cost relations are: TR = \$3,000Q - \$0.5Q2 and TC = \$100,000 + \$1,500Q + \$0.1Q2 Calculate output,