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 ```QUESTION 1 Assume a production function: 0.5 0.25 Q= 10L K with a selling price for the product of 10, and factor prices of 5 for L and 10 for K , determine the firm?s profit maximizing levels of inputs. Ensure you have found a maximum by checking the second-order sufficient conditions. Determine the level of output that this will produce. Determine the corresponding values for total cost, total revenue and profit. L0000 QUESTION 2 Assume a production of the form: Q= F(k) where K is capital input and L is fixed. Confirm that average product (AP ) is equal to marginal product (MP ) when AP is at a maximum QUESTION 3 -0.6p. The demand function of a firm is given by Q= 20e If fixed costs are 100 and the variable costs are 2 per unit, find the price needed to maximize profit QUESTION 4 A monopolistic producer charges different prices at home and abroad. The demand functions of the domestic and foreign markets are given by, P + Q = 100 1 1 and P + 2Q = 80 , respectively. 2 2 1 2 2. The firm?s total cost function is, TC= ( Q + Q ) (a)Determine the profit maximizing level of demand for both markets. Calculate the second-order sufficient conditions to ensure you have found a maximum. (b)The foreign country believes that the firm is guilty of dumping because the good sells at a higher price in the home market, so decides to restrict the sales to a maximum of 2. Use calculus to find the value of Q1 and compare the corresponding profit with that of the free market in part (a).```